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Formulation and selection of timber management strategies : description of the problem context and development… Marshall, Peter Lawrence 1984

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FORMULATION AND SELECTION OF TIMBER MANAGEMENT STRATEGIES: DESCRIPTION OF THE PROBLEM CONTEXT AND DEVELOPMENT OF A METHODOLOGY by PETER LAWRENCE MARSHALL B .Sc .F , U n i v e r s i t y Of T o r o n t o , 1976 M.Sc .F , U n i v e r s i t y Of T o r o n t o , 1979. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES F o r e s t r y . . We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA August 1984 © Peter Lawrence M a r s h a l l , 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of F o r e s t r y  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main M a l l Vancouver, Canada V6T 1Y3 Date S e p t . 2 5 , 1984 )E-6 (3/81) i i A b s t r a c t Fo res t management i n v o l v e s i n t e r v e n i n g in f o r e s t system processes to c o n t r o l system dynamics in a manner thought to be b e n e f i c i a l to the f o r e s t owner. P e r f e c t c o n t r o l i s not p o s s i b l e because the system i s n e i t h e r c l o s e d nor d e t e r m i n i s t i c . The f o r e s t manager must make d e c i s i o n s r ega rd ing present and fu tu re l e v e l s of use fo r v a r i o u s f o r e s t r e sou rces as we l l as choose the type and magnitude of system i n t e r v e n t i o n s to impose which w i l l maximize the owner 's expec t a t i ons of p resent and f u tu r e r e tu rns from the f o r e s t . The d e c i s i o n p rocess i s comp l i c a t ed by u n c e r t a i n t y about the present and fu tu re s t a t e of the f o r e s t system, p resen t and fu tu re requ i rements from the system, measurement of r e tu rns and the i n f l u e n c e of management i n t e r v e n t i o n s on the system dynamics . T h i s d i s s e r t a t i o n s p e c i f i c a l l y addresses the p rocess of s e l e c t i n g a management s t r a t egy fo r the t imber resource on a s p e c i f i c un i t such as a t imber supply a r e a . As management of any one f o r e s t r esource shou ld not be imposed in t o t a l i s o l a t i o n from the other f o r e s t r e s o u r c e s , the contex t of t imber management s t r a t e g y d e c i s i o n s w i t h i n the management of the f o r e s t as a whole i s examined from a d e c i s i o n a n a l y t i c a l pe r spec t i v e . Management of the t imber resource i s d e s c r i b e d as c o n s i s t i n g of two i n t e r r e l a t e d d e c i s i o n s : (1) what l e v e l of t imber e x t r a c t i o n to a l low over time and (2) what management a c t i o n s to impose in order to secure the l e v e l of t imber e x t r a c t i o n d e s i r e d . These d e c i s i o n s are shown to be l i n k e d by p r o j e c t i o n s of t imber supp l y . Arguments are p resen ted suppo r t i ng the a n a l y t i c a l s epa r a t i on of these two d e c i s i o n p r o c e s s e s . D e c i s i o n s gove rn ing the l e v e l of t imber e x t r a c t i o n over time must address the present and p r o j e c t e d demands f o r , and r e tu rns f rom, d i f f e r e n t f o r e s t r e sou r ces as we l l as the supp ly of t imber a v a i l a b l e under d i f f e r e n t management s c e n a r i o s . S e l e c t i o n of a t imber management s t r a t e g y shou ld be made on the b a s i s of a c h i e v i n g a p a r t i c u l a r h a r v e s t i n g l e v e l over t ime fo r a minimum c o s t . T h i s d e c i s i o n i s comp l i c a t ed by the u n c e r t a i n t y of response to any management a c t i v i t y . A l i n e a r programming approach to f o r m u l a t i n g t imber management s t r a t e g i e s i s p r e s e n t e d . The approach s e l e c t s cand ida te management sequences fo r i n c l u s i o n in a management s t r a t e g y on the b a s i s of t h e i r c o n t r i b u t i o n to t o t a l c o s t sub jec t to the r e s t r i c t i o n s imposed by present f o r e s t s t r u c t u r e and fu tu re h a r v e s t i n g l e v e l s . T o t a l cos t i s d e f i n e d as the sum of the d i r e c t c o s t a s s o c i a t e d w i th implementing the management sequence and the i n d i r e c t cos t a s s o c i a t e d wi th the p r o b a b i l i t y of not a c h i e v i n g the d e s i r e d r esponse . I n d i r e c t cos t i s c a l c u l a t e d by a s s o c i a t i n g s u b j e c t i v e p r o b a b i l i t i e s w i th p o t e n t i a l outcomes under any management sequence and a s s i g n i n g b e n e f i t and c o s t va lues r e f l e c t i v e of the degree of r i s k a v e r s i o n to p o t e n t i a l p o s i t i v e and nega t i ve d e v i a t i o n s from the expected r e sponse . The i m p l i c a t i o n s and p o t e n t i a l a p p l i c a t i o n s of t h i s mode l l i ng approach are i l l u s t r a t e d through a s i m p l e , h y p o t h e t i c a l example. The g r ea t e r the importance p l a c e d on meet ing f u t u r e ha rves t r equ i r ements , the h ighe r the d i r e c t c o s t i v a s s o c i a t e d w i th implementing the s t r a t e g y . A l though cho i c e of an a p p r o p r i a t e degree of r i s k a v e r s i o n i s not an easy t a s k , examinat ion of s t r a t e g i e s fo rmu la ted assuming d i f f e r e n t l e v e l s of r i s k a v e r s i o n p rov i des i n s i g h t i n t o the s e n s i t i v i t y of the s t r a t e g i e s to changes in a t t i t u d e s towards r i s k . V TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS V LIST OF TABLES v i i i L IST OF FIGURES ix ACKNOWLEDGEMENTS X I INTRODUCTION 1 1.1 Purpose of the D i s s e r t a t i o n 1 1 .2 Rat i o n a l e 2 1.3 Scope and S t r u c t u r e of the D i s s e r t a t i o n 8 II TIMBER MANAGEMENT CONTEXT 13 2.1 Management of the Fo r e s t 13 2.2 Timber Management 18 2.3 Timber Management/Supply Models 22 2.4 De te rm ina t i on of A l l owab l e Cut in B r i t i s h Columbia 24 III DECISION-MAKING, UNCERTAINTY AND FOREST MANAGEMENT . . . 27 3.1 Termino logy 27 3.2 R i sk P ropens i t y 29 3.3 Timber Management S t r a t egy S e l e c t i o n as a D e c i s i o n Problem 33 IV TIMBER SUPPLY MODELLING 38 4.1 M o d e l l i n g of the F o r e s t System 38 4.2 Timber Supply M o d e l l i n g i n H i s t o r i c a l P e r s p e c t i v e 41 4.3 Computer-based Timber Supply Models 44 4.3.1 Mathemat ica l Programming Models 45 4 .3 .2 S imu l a t i on Models 47 4.4 Development of a Gene ra l D e t e r m i n i s t i c Timber Supply Model 49 4.5 Development of a Gene ra l S t o c h a s t i c Model of Timber Supply 57 V SOURCES OF UNCERTAINTY IN FORMULATING FOREST MANAGEMENT STRATEGIES 61 5.1 Sources of U n c e r t a i n t y E x t e r n a l to Timber Supply Models 63 5.1.1 Improper S p e c i f i c a t i o n of Returns from the Fo r e s t System 64 5.1.2 P o l i t i c a l C o n s t r a i n t s 66 5.1 .3 P o l i c y S p e c i f i c a t i o n s 67 5 .1 .4 S e l e c t i o n of the Timber Supply Mode l ( s ) 69 5 .1 .5 Fo rmu la t i on of Model O b j e c t i v e s 74 v i V SOURCES OF UNCERTAINTY IN FORMULATING FOREST MANAGEMENT STRATEGIES — (cont inued) 5.2 U n c e r t a i n t y A r i s i n g from Model I n fo rmat ion Requirements 76 5.2.1 U n c e r t a i n t y Regarding Present C o n d i t i o n s 76 5.2.2 U n c e r t a i n t y Regarding Future C o n d i t i o n s 78 VI GENERAL STRATEGIES FOR COPING WITH UNCERTAINTY AND POTENTIAL APPLICATIONS TO TIMBER MANAGEMENT DECISIONS 86 6.1 Pass i ve S t r a t e g i e s 86 6.1.1 Game Theory S t r a t e g i e s 87 6 .1 .2 S t r a t e g i e s fo r Reducing Pe r c ep t i ons of U n c e r t a i n t y 90 6 .1 .3 Gene ra t i on of A l t e r n a t i v e s 94 6 .1 .4 S t r a t e g i e s fo r Changing Adverse Consequences 95 6 .1 .5 N o n d e l i b e r a t e d D e c i s i o n s 96 6.2 A c t i v e S t r a t e g i e s 99 6.2.1 S t r a t e g i e s fo r M o d e l l i n g U n c e r t a i n t y . . . 99 6 .2 .2 S t r a t e g i e s I n vo l v i ng In fo rmat ion A q u i s i t i o n 101 VII ACTUAL TREATMENT OF UNCERTAINTY IN FOREST MANAGEMENT . 107 7.1 Use of Most L i k e l y Va lues 108 7.2 S e n s i t i v i t y Ana l yses 116 7.3 Other Methods A p p l i e d to Fo r e s t Management D e c i s i o n s 118 VII I DEVELOPMENT OF A DECISION METHODOLOGY 123 8.1 R a t i o n a l e fo r the M o d e l l i n g Context 124 8.2 R e l a t i o n s h i p Between the Mode l l ed and Non-model led Aspec ts of the Problem 130 8.3 Development of a Methodology fo r Fo rmu la t i on and S e l e c t i o n of a Timber Management S t r a t egy 133 8.3.1 Fo rmu la t i on of Timber Management S t r a t e g i e s 134 8 .3 .2 I n c o r p o r a t i o n of U n c e r t a i n t y 138 8 .3 .3 De te rmina t ion of Expected Y i e l d s 140 8 .3 .4 C a l c u l a t i o n of D i r e c t and I n d i r e c t Cos ts 141 8 .3 .5 S e l e c t i o n of a Timber Management S t r a t egy 144 IX AN EXAMPLE ILLUSTRATING THE FORMULATION OF TIMBER MANAGEMENT STRATEGIES 146 9.1 D e s c r i p t i o n of the Problem 146 9.1.1 D e s c r i p t i o n of the I n i t i a l F o r e s t 146 9 .1 .2 Management Opt ions Cons ide red 147 9 .1 .3 Timber H a r v e s t i n g Pa t t e rns 150 9 .1 .4 Cos ts 150 9 .1 .5 Model S t r u c t u r e 156 9.2 R e s u l t s and I n t e r p r e t a t i o n 159 9.2.1 Comparison of S o l u t i o n s to S cena r i o s 1 , 2 and 3 167 9 .2 .2 Comparison of S o l u t i o n s to S cena r i o s 4, 5, 6 and 7 169 9 .2 .3 Comparison of Cos t s 171 v i i X IMPLICATIONS 176 10.1 D i s c u s s i o n of Methodology 176 10.2 Implementat ion of the Methodology 181 10.2.1 De te rm ina t i on of the S u i t a b i l i t y of the I n d i r e c t Cost Approach Employed 182 10 .2 .2 Development of G u i d e l i n e s fo r De te rm ina t i on of A p p r o p r i a t e B e n e f i t / C o s t L e v e l s 183 10 .2 .3 Development of Computer Rout ines 184 XI CONCLUSIONS 190 11.1 Gene ra l Summary 190 11.2 E v a l u a t i o n of the Methodology 197 11.3 Fuuture D i r e c t i o n s 207 REFERENCES 210 APPENDICES 224 APPENDIX 1: A Summary of the A c t i v i t i e s A v a i l a b l e and Cor respond ing Y i e l d s 224 APPENDIX I I : Y i e l d s and S u b j e c t i v e P r o b a b i l i t i e s A s s o c i a t e d wi th the V a r i o u s Outcomes Cons ide r ed fo r Each Management Opt ion 231 APPENDIX I I I : I n d i r e c t Cos ts fo r the D i f f e r e n t Op t ions by P e r i o d of I n i t i a l Harvest . 234 APPENDIX IV: A L i s t i n g of the T o t a l Cos t s A s s o c i a t e d w i th the V a r i o u s Management Opt ions by P e r i o d of I n i t i a l Harvest f o r the D i f f e r e n t Cost S cena r i o s 236 v i i i LIST OF TABLES TABLE 1: An I l l u s t r a t i o n of the E f f e c t of Left-Skewness and D i s t r i b u t i o n Spread on the D i f f e r e n c e Between Expected Va lue and Most L i k e l y Va lue 110 TABLE 2: D e p i c t i o n of the I n i t i a l F o r e s t 148 TABLE 3: Expec ted Y i e l d s and MAI 's at Ro t a t i on Age fo r the D i f f e r e n t Management Opt ions 149 TABLE 4: D i s coun ted D i r e c t Cos ts of Management Opt ions by P e r i o d of I n i t i a l Harvest 152 TABLE 5: D e s c r i p t i o n of Cost S cena r i o s Ana l ysed 155 TABLE 6: Summary of S o l u t i o n fo r S cena r i o 1 160 TABLE 7: Summary of S o l u t i o n fo r S cena r i o 2 161 TABLE 8: Summary of S o l u t i o n fo r S c ena r i o 3 162 TABLE 9: Summary of S o l u t i o n fo r S cena r i o 4 163 TABLE 10: Summary of S o l u t i o n fo r S cena r i o 5 164 TABLE 11: Summary of S o l u t i o n fo r Scena r io . 6 165 TABLE 12: Summary of S o l u t i o n fo r S c ena r i o 7 166 TABLE 13: Cost Components A s s o c i a t e d w i th Va r i ous S cena r i o s Assuming a B e n e f i t / C o s t S t r u c t u r e of $5/210 . . . . 172 TABLE 14: Comparison of Cost Components f o r S cena r i o s 4 and 6 Assuming a $5/$20 B e n e f i t / C o s t S t r u c t u r e fo r I n d i r e c t Cos ts 173 ix LIST OF FIGURES FIGURE 1: A Schematic Rep resen t a t i on of the F o r e s t System 14 FIGURE 2: P a r t i t i o n i n g of the Fo r e s t Management Problem . 36 FIGURE 3: Schematic I l l u s t r a t i o n of the F o r e s t Management D e c i s i o n Environment 62 FIGURE 4: F a c t o r s A f f e c t i n g Future Y i e l d 82 FIGURE 5: Schematic I l l u s t r a t i o n of the Role of Timber Supply M o d e l l i n g in Harves t Pa t t e rn D e c i s i o n s . 131 FIGURE 6: Schematic I l l u s t r a t i o n of the Role of Timber Supply M o d e l l i n g in Fo rmu la t i on of Timber Management S t r a t e g i e s 132 FIGURE 7: D e p i c t i o n of the Two Timber H a r v e s t i n g Pa t t e rns 151 FIGURE 8: I l l u s t r t a t i o n of the Components of a Computer Rout ine fo r A i d i n g the S o l u t i o n and I n t e r p r e t a t i o n of a Timber Management S t r a t egy Fo rmu la t i on Problem , 187 X ACKNOWLEDGEMENTS The author wishes to thank the chairman of h i s s u p e r v i s o r y commit tee , D r . J . H . G . Smi th , and h i s r e sea r ch s u p e r v i s o r , D r . D.H. W i l l i a m s , fo r t h e i r gu idance and pa t i ence throughout the a u t h o r ' s p e r i o d of graduate s t u d i e s . The development of the ideas p resen ted in the f i n a l manuscr ip t e vo l ved through the p r e p a r a t i o n of many working papers which were always c h e e r f u l l y rev iewed . T h e i r h e l p f u l c r i t i c i s m s were a s i g n i f i c a n t f a c t o r in c r y s t a l i z i n g the ideas p r e s e n t e d . D r . A. Kozak and Dr . T . H a l l rev iewed the d r a f t manuscr ip t and commented on s e v e r a l of the working pape r s . T h e i r c o n t r i b u t i o n i s g r e t e f u l l y acknowledged. S p e c i a l thanks are extended to Mr. Steve Johnson who p r o o f r e a d much o f the m a t e r i a l and p r o v i d e d a w i l l i n g ear fo r many of the a u t h o r ' s i d e a s . 1 CHAPTER I INTRODUCTION 1.1 Purpose of the D i s s e r t a t i o n The goa l of t h i s d i s s e r t a t i o n i s to deve lop a gene ra l framework fo r the f o r m u l a t i o n and s e l e c t i o n of t imber management s t r a t e g i e s which i n c o r p o r a t e s r e l e v a n t sources of u n c e r t a i n t y and employs t imber supply mode l l i ng t e c h n i q u e s . As an a i d to a c h i e v i n g t h i s g o a l , the f o l l o w i n g s p e c i f i c o b j e c t i v e s were f o rmu l a t ed : (1) D e s c r i b e the f o r e s t management d e c i s i o n environment in a manner conduc ive to d e c i s i o n a n a l y s i s ; (2) Des c r i be sources of u n c e r t a i n t y in f o r e s t management p l a n n i n g ; ( 3 ) P rov ide a c r i t i c a l a n a l y s i s of the p o t e n t i a l use of s p e c i f i c t e chn iques f o r dec i s i on-mak ing under u n c e r t a i n t y in t imber management s t r a t e g y d e c i s i o n s ; (4) P rov ide an e x t e n s i v e survey of e x i s t i n g l i t e r a t u r e in the a reas of t imber supp ly m o d e l l i n g , dec i s i on-mak ing in gene ra l and dec i s i on-mak ing in f o r e s t management in pa r t i c u l a r ; (5) Deve lop a procedure fo r i n c o r p o r a t i n g p a r t i c u l a r sources of u n c e r t a i n t y i n t imber supply m o d e l l i n g procedures to improve t imber management s t r a t e g y d e c i s i o n s ; ( 6 ) Tes t the p r a c t i c a l i t y of the a n a l y t i c t echn ique on a s imple t imber management s t r a t e g y d e c i s i o n p rob lem; and (7) Document the apparent s t r e n g t h s and weaknesses of the techn ique and o u t l i n e a d d i t i o n a l work necessa ry i f the methodology i s to be implemented on an o p e r a t i o n a l b a s i s . 2 1.2 R a t i o n a l e The p r e p a r a t i o n of a management p l an fo r a f o r e s t e d area i s a m u l t i f a c e t e d p rob lem. It i n v o l v e s p o l i c y a n a l y s i s , f o r e c a s t i n g of f u tu re demands fo r v a r i o u s f o r e s t r e s o u r c e s , a l l o c a t i o n of l and to d i v e r s e resource use c a t e g o r i e s and d e c i s i o n s on what management s t r a t e g i e s to employ fo r each . A l l these a spec t s are i n t e r r e l a t e d and s imul taneous c o n s i d e r a t i o n i s necessary to ensure the p r e p a r a t i o n of a good p l an fo r the f o r e s t . The problem i s comp l i c a t ed by u n c e r t a i n t y r ega rd ing fu tu re requ i rements from the f o r e s t system and the f u t u r e s t a t e of the system under any g iven management s t r a t e g y . Any i n t e r v e n t i o n in the f o r e s t system p rocesses produces a change in the system. Management, in the broadest sense , i s an attempt to o r g a n i z e these i n t e r v e n t i o n s in such a f a sh i on that the system i s moved towards some d e s i r e d s t a t e . P o l i c y a n a l y s i s a t tempts to i d e n t i f y the e f f e c t s of p a r t i c u l a r p o l i c i e s on the movement towards the d e s i r e d s t a t e . P l ann ing i s a broader concept and e s s e n t i a l l y i n v o l v e s d e c i d i n g on the s t a t e towards which the system shou ld be moved and the r a t e at which t h i s movement shou ld o c c u r . P l ann ing o b v i o u s l y encompasses some e lements of both management and p o l i c y a n a l y s i s . The r a t i o n a l e fo r f o r e s t p l a n n i n g i s tha t o r g a n i z a t i o n of f u t u r e l e v e l s of resource use and management a c t i o n s to be a p p l i e d i s neccessa ry i f some degree of c o n t r o l i s to be ma in ta ined over the system. Complete c o n t r o l i s not p o s s i b l e because the system i s n e i t h e r c l o s e d nor d e t e r m i n i s t i c (see Chapter I I ) . T h i s does not negate the b e n e f i t of the p l ann ing p rocess or of deve l op ing a management s t r a t e g y thought to be 3 compat ib l e w i th some fu tu r e d e s i r e d s t a t e fo r the sys tem; i t i n c r e a s e s the impor tance . The g r ea t e r the u n c e r t a i n t y i n v o l v e d in f u t u r e p r o j e c t i o n s , the l a r g e r the need fo r some d i r e c t i o n fo r p resen t a c t i o n s . The f u t u r e i s c o n s t r u c t e d from a c t i o n s and events which have o c c u r r e d in the p a s t . A d e s i r e d fu tu re can be c r e a t e d to the extent tha t these a c t i o n s and events can be c o n t r o l l e d and t h e i r outcome p r e d i c t e d . Even i f complete c o n t r o l over the system were p o s s i b l e , however, the fu tu re thought to be d e s i r a b l e today i s not l i k e l y to be the same f u t u r e c o n s i d e r e d d e s i r a b l e some time from now. T h i s shou ld be r e cogn i zed in the p l a n n i n g p r o c e s s . Returns from t imber h a r v e s t i n g o f t en r ep resen t the l a r g e s t p o r t i o n of the o v e r a l l d o l l a r r e tu rn from the f o r e s t system. T h i s can r ep resen t a c o n s i d e r a b l e p o r t i o n of the economy of a count r y w i th a l a rge p r o d u c t i v e f o r e s t l and base l i k e Canada. F o r e s t i n d u s t r i e s a l o n e , d i r e c t l y or i n d i r e c t l y , accounted fo r over one m i l l i o n jobs in 1979. The revenue genera ted by t h i s a c t i v i t y f o r the f e d e r a l and p r o v i n c i a l governments in tha t year by c o r p o r a t e t a x e s , charges and taxes on d i r e c t employees amounted to th ree b i l l i o n d o l l a r s (Canadian F o r e s t r y A s s o c i a t i o n 1982). The m a j o r i t y of p r o d u c t i v e f o r e s t l and (about 85 per cent ) e x i s t s as p r o v i n c i a l Crown l and ( S t a t i s t i c s Canada 1981). B r i t i s h Columbia a lone c o n t a i n s about 20 per cent of the n a t i o n a l f o r e s t l and base c o n s i d e r e d s u i t a b l e fo r h a r v e s t i n g (Bonner 1982) and approx ima te l y 95 per cent of t h i s i s p r o v i n c i a l Crown land (Apsey 1980). The c o n t r i b u t i o n of t imber 4 e x t r a c t i o n from these lands to the economy of B r i t i s h Columbia i s ex t ens i v e ( M i n i s t r y of F o r e s t s 1980a; 1980b; 1980c) . Much concern has been expressed in the l a s t few decades r ega rd ing the s t a t e of t imber management in t h i s p r o v i n c e and a c ross the coun t r y as a whole. (See, f o r example, Reed and A s s o c i a t e s 1978 and Pearse 1976.) Concern has c e n t r e d around whether c u r r e n t t imber management s t r a t e g i e s and a s s o c i a t e d p o l i c i e s w i l l produce s u f f i c i e n t s u p p l i e s of a c cep t ab l e t imber in the f u t u r e . Returns from t imber management are i n t r i c a t e l y l i n k e d to the ra te of h a r v e s t i n g (the a l l o w a b l e cu t ) and the q u a l i t y of m a t e r i a l h a r v e s t e d . Dav i s (1966) i d e n t i f i e d h a r v e s t i n g r a te as the s i n g l e most important v a r i a b l e in f o r e s t management. Changes in the r a te can produce s i g n i f i c a n t economic r e p e r c u s s i o n s as we l l as change the f u tu r e resource base (Fowler 1978). Moore (1980) and Young (1981) d i s c u s s e d p o t e n t i a l economic impacts of d i f f e r e n t h a r v e s t i n g l e v e l s in B r i t i s h Co lumb ia . F i g h t and B e l l (1977) l i s t e d r e g i o n a l and economic consequences of the h a r v e s t i n g l e v e l in the Un i t ed S t a t e s , many of which p e r t a i n to B r i t i s h Co lumb ia . The Timber H a r v e s t i n g S chedu l i ng I ssues Study (USDA 1976) a l s o c o n t a i n s some r e f e r ence to the e f f e c t s of h a r v e s t i n g l e v e l on the American economy. Numerous o ther s t u d i e s e x i s t . T h e i r common theme i s tha t economic impacts of d r a s t i c changes in the h a r v e s t i n g l e v e l would be enormous. Timber management in Canada i s in a s t a t e of t r a n s i t i o n from e s s e n t i a l l y a min ing o p e r a t i o n to p r o d u c t i o n of a p lanned f o r e s t . The c h a l l e n g e i s to make t h i s t r a n s i t i o n wi thout p roduc ing a d i s c o n t i n u i t y in wood supp ly ( B a s k e r v i l l e 1982). The 5 problem i s augmented by e x t e r n a l p r e s s u r e s e rod ing the p r o d u c t i v e f o r e s t l and base . The f o r e s t manager in the f u tu r e must produce good q u a l i t y t imber on a sma l l e r l and base in a s h o r t e r t ime to ma in ta in cu r r en t h a r v e s t i n g l e v e l s in many a r e a s . In order to ach ieve t h i s g o a l , management must be i n t e n s i f i e d and combined w i th an e f f i c i e n t p l ann ing system which w i l l f o r e c a s t the i m p l i c a t i o n s of p a r t i c u l a r management s t r a t e g i e s . Such a system would i n d i c a t e p o t e n t i a l f u tu re s h o r t f a l l s in t imber supp ly and p rov ide l e ad time to deve lop a l t e r n a t i v e s fo r m i n i m i z i n g t h e i r impact . P l ann ing systems fo r t imber management on p u b l i c l and tend to be h i e r a r c h i a l in n a t u r e . D e c i s i o n s made at h ighe r l e v e l s ac t as p o l i c y fo r d e c i s i o n s which need to be made at lower l e v e l s (Duerr 1974b). Flow of i n f o r m a t i o n between the d i f f e r e n t l e v e l s i s e s s e n t i a l i f the p l a n n i n g system i s to respond to p e r c e i v e d changes in the o w n e r ' s . p r e f e r e n c e s and the s t a t e of the f o r e s t sys tem. Two important d e c i s i o n s embodied in a t imber management p l a n a r e : (1) how much to ha r ves t now and through t ime (the t imber ha r ves t pa t t e rn ) and (2) how to manage the f o r e s t l and and a l l o c a t e the cut among the d i f f e r e n t age and t imber c l a s s e s p resen t to ' a l l o w ' the h a r v e s t i n g p a t t e r n d e s i r e d in an e f f i c i e n t manner (the t imber management s t r a t e g y ) . These d e c i s i o n s can occur at d i f f e r e n t h i e r a r c h i a l l e v e l s in a p l a n n i n g system but are l i n k e d c o n c e p t u a l l y by the b i o l o g i c a l and p h y s i c a l p rocesses of the f o r e s t system and the p o l i c y s t r u c t u r e i n e f f e c t . A n a l y t i c a l l y , some e x p l i c i t or i m p l i c i t p r o j e c t i o n of t imber supp ly o f t e n p r o v i d e s an important 6 i n f o r m a t i o n source fo r f i n a l d e c i s i o n s . Models of t imber supp ly have t r a d i t i o n a l l y been fo rmu la ted wi thout e x p l i c i t l y c o n s i d e r i n g the u n c e r t a i n t y p resen t in the d e c i s i o n env i ronment . The approach has g e n e r a l l y been to make assumpt ions conce rn ing the most l i k e l y occu r rence (or the expec ted occur rence ) of f u tu r e events and ac t as though these assumpt ions w i l l prove c o r r e c t . T h i s e s s e n t i a l l y reduces the mode l l ed environment to one of c e r t a i n t y . D e c i s i o n s made under c o n d i t i o n s of c e r t a i n t y (assumed or o therw ise ) shou ld t h e o r e t i c a l l y be a s t r a i g h t f o r w a r d procedure of r ank ing outcomes and s e l e c t i n g the a l t e r n a t i v e which produces the best outcome. In a c t u a l p r a c t i c e , the comp lex i t y of the f o r e s t system and the d i f f i c u l t y i n v o l v e d in rank ing p o t e n t i a l r e t u r n s have made s e l e c t i o n of an a p p r o p r i a t e t imber management s t r a t e g y d i f f i c u l t . R e c o g n i t i o n of the i m p l i c a t i o n s of u n c e r t a i n t y in t imber management d e c i s i o n s has encouraged s e v e r a l au thors in recent years to recommend r e sea r ch i n t o t h i s p rob lem. (See, f o r example, Ben t l ey 1980, Ha r tg raves 1980 and Pearse 1976.) Whi le the re has been c o n s i d e r a b l e t h e o r e t i c a l development of methods fo r dec i s i on-mak ing under u n c e r t a i n t y , there are many p r a c t i c a l d i f f i c u l t i e s in t r a n s l a t i n g t h i s theory i n t o p r a c t i c e ( R a i f f a 1968). To d a t e , few e x p l i c i t t e chn iques fo r i n c o r p o r a t i n g u n c e r t a i n t y i n t o the dec i s i on-mak ing p rocess have been a p p l i e d to t imber management d e c i s i o n s . The degree of r i s k a s s o c i a t e d w i th a p a r t i c u l a r management s t r a t e g y i s r e f l e c t e d by the p r o b a b i l i t y of the s t r a t e g y not p roduc ing the expected r e sponse , and the magnitudes and impacts 7 of p o s s i b l e d e v i a t i o n s from the expected response p e r c e i v e d by the d e c i s i o n maker. It i s apparent tha t an expens i ve but l e s s r i s k y s t r a t e g y might be p r e f e r a b l e to a s t r a t e g y w i th lower cos t but g r ea t e r r i s k . In order to f a c i l i t a t e e v a l u a t i o n of the t r a d e o f f between r i s k and c o s t , i t i s necessary tha t u n c e r t a i n t y be e x p l i c i t l y c o n s i d e r e d in the t imber supp ly m o d e l l i n g p rocedu re . D e t e r m i n i s t i c t imber supply models e x p l i c i t l y ignore the u n c e r t a i n t y p resen t and y i e l d a s i n g l e es t imate of t imber supp ly at a g iven t ime . It i s p o s s i b l e to use such models to produce v a r i o u s p r o j e c t i o n s depending upon the assumpt ions made w i th r espec t to response under a p a r t i c u l a r set of c o n d i t i o n s . Some models ( fo r example, WOSFOP, Wood Supply F o r e c a s t i n g P rocedure , ( B a s k e r v i l l e 1978, C l i f f o r d 1981, H a l l 1978)) were s p e c i f i c a l l y des igned f o r t h i s purpose . However, such models have no mechanism fo r a s s i g n i n g p r o b a b i l i t y va lues to p a r t i c u l a r s c e n a r i o s . A l s o , no b a s i s i s p r o v i d e d fo r choos ing between a l t e r n a t i v e s when t h e i r ranges of responses o v e r l a p g r e a t l y . D e s c r i p t i o n of the f o r e s t management d e c i s i o n environment in a manner conduc ive to d e c i s i o n a n a l y s i s i s necessa ry to p rov ide a con tex t fo r the framework subsequent l y d e v e l o p e d . Such a d e s c r i p t i o n i s a l s o of va lue in i t s e l f . I t i s on l y through r e c o g n i t i o n of u n c e r t a i n t y in the d e c i s i o n environment and the r o l e of t imber management w i t h i n the broader framework of f o r e s t management tha t the necessa ry i n s i g h t s to improve t imber management can be a c h i e v e d . The a n a l y t i c a l procedure deve loped and the framework upon 8 which i t i s based i s not the on l y way of approach ing t imber management s t r a t e g y d e c i s i o n s . Much l i t e r a t u r e on techn iques fo r dec i s i on-mak ing under u n c e r t a i n t y e x i s t s . My review of the l i t e r a t u r e and the c r i t i c a l a n a l y s i s of the p o t e n t i a l a p p l i c a t i o n of these t echn iques to t imber management s t r a t egy d e c i s i o n s shou ld h e l p p rov ide p o t e n t i a l use rs w i th a more complete unders tand ing of dec i s ion-mak ing in an u n c e r t a i n env i ronment. It i s important that any prob lem, and the methodology a v a i l a b l e f o r a i d i n g d e c i s i o n s concerned wi th tha t prob lem, be adequa te l y unders tood by the d e c i s i o n maker i f the methodology i s to be p r o p e r l y a p p l i e d . Edelman (1972) s t a t e d : "No manager wi th r e a l r e s p o n s i b i l i t i e s fo r a r e a l bus iness [ shou ld ] base important d e c i s i o n s on the outcome of a p rocess which he h imse l f does not adequa te l y u n d e r s t a n d " . The t h rus t of t h i s d i s s e r t a t i o n w i l l be to deve lop the framework fo r f o rmu l a t i on and s e l e c t i o n of t imber management s t r a t e g i e s w i t h i n a con tex t which can be r e a d i l y unders tood by p o t e n t i a l u s e r s . 1.3 Scope and S t r u c t u r e of the D i s s e r t a t i o n Timber management s t r a t e g y d e c i s i o n s shou ld not be made in i s o l a t i o n from other a spec t s of the t imber p l a n n i n g p rocess and other f o r e s t use d e c i s i o n s . G e n e r a l l y , l i n k a g e s are ma in ta ined i m p l i c i t l y by the p o l i c y s t r u c t u r e in e f f e c t and the p l ann ing p rocess employed. It i s not the i n t e n t i o n of t h i s d i s s e r t a t i o n to d e s c r i b e an e x i s t i n g p l a n n i n g p rocess or to deve lop a s p e c i f i c p l a n n i n g methodology. Whi le i t i s r e c o g n i z e d that the framework deve loped must be u l t i m a t e l y embedded w i t h i n some 9 p l a n n i n g system i f i t i s to be employed o p e r a t i o n a l l y , f o r the sake of g e n e r a l i t y , assumpt ions r ega rd ing the p l a n n i n g p rocess are kept to a minimum. The on l y major assumpt ion r e q u i r e d i s that the management agency employs a t imber supply m o d e l l i n g p roces s as one source of i n f o rma t i on fo r t imber management d e c i s i o n s . There can be fundamental d i f f e r e n c e s in the type and b read th of o b j e c t i v e s and in the f o r m u l a t i o n of the o r g a n i z a t i o n a l h i e r a r c h y r e s p o n s i b l e fo r making and implement ing t imber management d e c i s i o n s between p u b l i c and p r i v a t e l a n d . P u b l i c l and ownership i s i m p l i c i t l y assumed throughout the d i s s e r t a t i o n because most f o r e s t e d l and in Canada i s owned by the v a r i o u s P r o v i n c i a l or the F e d e r a l Governments. T h i s does not mean that the a n a l y t i c a l t echn ique deve loped c o u l d not be adapted fo r use on p r i v a t e l y owned f o r e s t l a n d , but on l y that subsequent d i s c u s s i o n s are o r i e n t e d s p e c i f i c a l l y towards p u b l i c a l l y owned l a n d . In o rder to s i m p l i f y development and ma in t a i n g e n e r a l i t y , a s i n g l e d e c i s i o n maker, a l s o r e f e r r e d to as the f o r e s t manager, i s assumed th roughou t . However, i t i s i m p l i c i t in some of the d i s c u s s i o n tha t t h i s d e c i s i o n maker i s in tu rn r e s p o n s i b l e to an i n d i v i d u a l or i n d i v i d u a l s h ighe r in the d e c i s i o n h i e r a r c h y . Expans ion of the methodology to i n c o r p o r a t e more than one d e c i s i o n maker w i th i d e n t i c a l or d i f f e r i n g b e l i e f s and the p o s s i b i l i t y of d i f f e r e n t p r e f e r e n c e s t r u c t u r e s i s t h e o r e t i c a l l y p o s s i b l e . I n fo rmat ion s t r u c t u r e s and d e c i s i o n r u l e s fo r o r g a n i z a t i o n s such as Team Theory (Marschalk and Radner 1972, MacCrimmon 1970,1974a) , S ynd i ca te Theory (Ros ing 1970, W i l son 10 1968) and Agency Theory (Holmstrom 1979, Ross 1973, S h a v e l l 1979) c o u l d be i n c o r p o r a t e d i n t o the methodology subsequent l y i f so d e s i r e d . Re ference i s made to B r i t i s h Columbia M i n i s t r y of F o r e s t s (MOF) p rocedures fo r s e t t i n g h a r v e s t i n g r a t e s in v a r i o u s s e c t i o n s . There i s no i n t e n t to s i n g l e out the MOF system fo r undue c r i t i c i s m or p r a i s e , o r . t o s t a t e that i t i s n e c e s s a r i l y any b e t t e r or worse than any o ther system c u r r e n t l y in use . No attempt i s made to d e s c r i b e t h i s system in d e t a i l because i t i s complex and s t i l l e v o l v i n g . It i s used on ly as a gene r i c example of a d e c i s i o n p rocess used by a p u b l i c agency to implement t imber management and r e g u l a t e the h a r v e s t i n g of t imber w i t h i n the framework of managing the f o r e s t as a whole. The r e l a t i o n s h i p between t imber management s t r a t e g i e s and ha rves t p a t t e r n s i s e x p l o r e d in the next chapte r and the contex t of t imber management s t r a t e g y d e c i s i o n s i s d e s c r i b e d . Chapter III i n t r o d u c e s the d e c i s i o n a n a l y t i c t e rmino logy employed and d i s c u s s e s the r o l e of u n c e r t a i n t y in f o r e s t management d e c i s i o n s in a gene ra l f a s h i o n . Chapter IV i s devoted to a d e s c r i p t i o n of t imber supp ly m o d e l l i n g . Sources of u n c e r t a i n t y p resen t i n the t imber management d e c i s i o n environment are examined in Chapter V. Chapters VI and VII p resen t some gene ra l and s p e c i f i c s t r a t e g i e s , r e s p e c t i v e l y , f o r cop ing w i th u n c e r t a i n t y in d e c i s i o n s . The methodology fo r s e l e c t i n g a t imber management s t r a t e g y under u n c e r t a i n t y i s p r e sen ted in Chapter V I I I . Chapter IX c o n t a i n s an example of the methodology and a d i s c u s s i o n of s p e c i f i c i m p l i c a t i o n s of the app roach . Chapter X e x p l o r e s the 11 more gene ra l i m p l i c a t i o n s of c o n s i d e r i n g u n c e r t a i n t y in f o r e s t management. Recommendations are made r ega rd ing implementat ion of the proposed approach and sugges t i ons are made wi th respec t to a d d i t i o n a l r e s e a r c h r e q u i r e d in t h i s a r e a . C r i t e r i a must be e s t a b l i s h e d fo r j udg ing whether the methodology deve loped f o r any d e c i s i o n problem i s a p p r o p r i a t e . T h i s i s e s s e n t i a l even in. d e c i s i o n s about t imber management s t r a t e g i e s where o b j e c t i v e c r i t e r i a are d i f f i c u l t to e s t a b l i s h . The f i n a l chap te r of the d i s s e r t a t i o n w i l l d i s c u s s the a p p l i c a b i l i t y of the framework deve loped by a d d r e s s i n g the f o l l o w i n g q u e s t i o n s : (1) Is the framework fo r t imber management s t r a t egy d e c i s i o n s based on a p l a u s i b l e d e s c r i p t i o n of the d e c i s i o n environment? (2) Is the i n f o r m a t i o n r e q u i r e d r e a d i l y a v a i l a b l e ? (3) Do the c r i t e r i a employed by the mode l l i ng procedure in f o r m u l a t i n g the t imber management s t r a t e g y r e f l e c t c o n s i d e r a t i o n s important to the model user when making the a c t u a l d e c i s i o n ? (4) Can the framework be implemented o p e r a t i o n a l l y ? (5) Does the framework demonstrate an improvement over e x i s t i n g procedures? An important c o n s i d e r a t i o n when d e a l i n g w i th an u n c e r t a i n f u tu r e i s tha t d e c i s i o n s made in the present w i th respec t to f u tu r e c o n d i t i o n s are l i k e l y to be non-op t ima l . C o n d i t i o n s w i l l seldom deve lop as expected and p e r c e p t i o n s of a d e s i r e d fu tu re s t a t e w i l l change. Desp i t e these c o m p l i c a t i o n s , the f o r e s t manager must s t i l l choose a management s t r a t e g y f o r the f o r e s t . The methodology deve loped i s s t r i c t l y no rmat i ve . There i s no attempt to d e s c r i b e how t imber management d e c i s i o n s are a c t u a l l y made, but on l y how they c o u l d be made in a r a t i o n a l 1 2 f a s h i o n . Under such a scheme the re are no ' r i g h t ' or 'wrong ' answers, on l y d e c i s i o n s which are ' c o n s i s t e n t ' or ' no t c o n s i s t e n t ' w i th the p r i o r b e l i e f s and p r e f e r ence s t r u c t u r e of the d e c i s i o n maker. No attempt i s made to address what the p r i o r b e l i e f s or the p r e f e r ence s t r u c t u r e shou ld be. Such i s s u e s are impor t an t , but imposs ib l e to c o n s i d e r m a t h e m a t i c a l l y . The f u tu r e depends upon the a t t i t u d e s of the d e c i s i o n maker in the p r e s e n t , in t h a t ' a t t i t u d e s towards u n c e r t a i n t y and the r e s u l t a n t r i s k , present r e t u r n s , and the d e s i r e d s t a t e of the f o r e s t system a l l a f f e c t u l t i m a t e d e c i s i o n s and hence shape the f u t u r e . A d i s c u s s i o n of these and other a s s o c i a t e d a spec t s conc ludes the d i s s e r t a t i o n and r e l a t e s p h i l o s o p h i c a l c o n s i d e r a t i o n s which p rov ide d i r e c t i o n to the s t r u c t u r a l c o n s i d e r a t i o n s which p rov ide a framework fo r t imber management d e c i s i o n s . 1 3 CHAPTER II  THE TIMBER MANAGEMENT CONTEXT 2.1 Management of the F o r e s t The f o r e s t can be v i s u a l i z e d as a system employ ing v a r i o u s l e v e l s of c o m p l e x i t y . (See C h r i s t i a n s e n 1968, Duerr 1966, 1974a and Sea le 1965 fo r examples . ) The f o l l o w i n g d e s c r i p t i o n i s s i m p l i s t i c , but i t i s s u f f i c i e n t to p rov ide con tex t fo r the d i s c u s s i o n which f o l l o w s . The b i o p h y s i c a l p o r t i o n of the f o r e s t system i s compr ised of a number of b i o t i c and a b i o t i c components which are i n t e r r e l a t e d through i n t r i c a t e b i o l o g i c a l and p h y s i c a l mechanisms. (See F i g u r e 1.) The number of components r e cogn i zed i s a r b i t r a r y and depends on the l e v e l of d e t a i l d e s i r e d in the d e s c r i p t i o n . The system i s dynamic s i n ce i t i s sub j ec t to e x t e r n a l s t i m u l i which a f f e c t component l e v e l s and change the f o r e s t s t r u c t u r e . Returns can on ly be i n c o r p o r a t e d in the f o r e s t system by i n t r o d u c i n g a s o c i a l component s i n ce r e t u r n s can on l y be q u a n t i f i e d through a va lue system s p e c i f i c to the p e r c e i v e r . Returns from the f o r e s t a r i s e in two d i f f e r e n t ways. Some r e t u r n s , such as a e s t h e t i c s , may e x i s t s imply as a r e s u l t of our p r e f e r e n c e f o r n a t u r a l f o r e s t s t r u c t u r e and r e q u i r e no a c t i v e input from man. Other r e t u r n s are consumpt ive in nature and r e s u l t in changes to the b i o p h y s i c a l s t r u c t u r e of the sys tem. Examples of t h i s i n c l u d e t imber e x t r a c t i o n and w i l d l i f e h a r v e s t i n g . 14 F i g u r e 1: A Schematic R e p r e s e n t a t i o n of the F o r e s t System. FOREST MANAGEMENT. ACTIONS NATURAL EXTERNAL STIMULI BIOTIC COMPONENTS (INTER-RELATED BY BIOLOGICAL PROCESSES) -i * - H ABIOTIC COMPONENTS (INTER-RELATED BY PHYSICAL PROCESSES) FOREST SYSTEM -OWNERS PERCEPTIONS RETURNS Management of the f o r e s t system i n v o l v e s d e l i b e r a t e i n t e r v e n t i o n i n the system p r o c e s s e s . S t i m u l i (management a c t i o n s ) a re i n t r o d u c e d to the sys tem, at some input c o s t , which a f f e c t the dynamics of the system and a l t e r f u t u r e r e t u r n s . A sequence of management a c t i o n s i n t r o d u c e d at d i f f e r e n t p o i n t s i n t ime and space c o n s t i t u t e s a management s t r a t e g y . The purpose of such i n t e r v e n t i o n s i s to a l t e r expec ted r e tu rns i n some manner b e n e f i c i a l to the owner. Assume, f o r a moment, tha t the system i s c l o s e d to e x t e r n a l i n f l u e n c e s o the r than d e l i b e r a t e l y i n t r o d u c e d management a c t i o n s . F u r t h e r , assume that the p resen t s t a t e of the system i s known e x a c t l y a long w i th the p roces ses which govern the 15 t r a n s i t i o n of the system from one s t a t e to another over t ime . Under such c o n d i t i o n s i t would be p o s s i b l e to p r e d i c t f u tu r e s t a t e s of the system without e r r o r fo r every management s t r a t e g y c o n s i d e r e d . If an a c cep tab l e p rocedure e x i s t e d fo r combin ing the v a r i o u s r e tu rn c r i t e r i a i n t o one measure of r e t u r n , then the s e l e c t i o n of the best management s t r a t e g y from among a cand ida te set of s t r a t e g i e s would be a r e l a t i v e l y s t r a i g h t f o r w a r d p rocedu re . The f o r e s t system c l e a r l y v i o l a t e s such assumpt ions . The present s t a t e of the f o r e s t system i s not known e x a c t l y , but i s based on i n ven to r y i n f o r m a t i o n . The b i o l o g i c a l and p h y s i c a l p rocesses which govern the dynamics of the system are not p e r f e c t l y unde r s tood . E x t e r n a l f a c t o r s beyond the manager 's c o n t r o l a f f e c t the dynamics of the system as w e l l , and make the t r a n s i t i o n from one s t a t e to another a s t o c h a s t i c p r o c e s s . F i n a l l y , there u s u a l l y i s no agreed procedure fo r combin ing d i f f e r e n t r e t u r n c r i t e r i a i n t o one q u a n t i f i a b l e v a l u e , e s p e c i a l l y in s i t u a t i o n s i n v o l v i n g group ownersh ip . These f a c t o r s c o n t r i b u t e to the u n c e r t a i n t y which sur rounds f u t u r e p r e d i c t i o n s of system s t a t e s and c l o u d the i s sue of how to best manage the f o r e s t . I t would be p o s s i b l e , a l b e i t d i f f i c u l t , f o r the owner of a f o r e s t r esource on a p a r t i c u l a r a rea to d e f i n e an i d e a l s t r u c t u r e ( d e s i r e d s t a t e ) , based on p resen t p e r c e p t i o n s , f o r the f o r e s t sys tem. It i s u n l i k e l y tha t the p resen t s t r u c t u r e (the a c t u a l s t a t e ) i s i d e n t i c a l to the i d e a l s t r u c t u r e . A d i f f e r e n c e (gap) between the a c t u a l s t a t e and the d e s i r e d s t a t e can be d e f i n e d as a problem (MacCrimmon 1980). For the sake of 16 conven ience , the gap between the a c t u a l s t a t e of the f o r e s t system and the d e s i r e d s t a t e w i l l be i d e n t i f i e d as the f o r e s t management p rob lem. Management of the f o r e s t system i n v o l v e s t r y i n g to so l ve t h i s problem ( i . e . c l o s e the gap ) . S o l u t i o n of the f o r e s t management problem r e q u i r e s i d e n t i f y i n g the p resen t and the d e s i r e d s t a t e s of the system and movement of the system from i t s p resent s t a t e to the d e s i r e d s t a t e . T r a d i t i o n a l l y on ly the t imber component of the f o r e s t system has been addressed in t h i s f a s h i o n . The d e s i r e d s t a t e of the f o r e s t was the s o - c a l l e d ' f u l l y r e g u l a t e d f o r e s t ' and f o r e s t r e g u l a t i o n was a p p l i e d to govern the t r a n s i t i o n of the f o r e s t from an un regu l a t ed s t a t e to a f u l l y r e g u l a t e d s t a t e . A l though there i s no th ing i n h e r e n t l y wrong wi th t h i s concep t , i t does represen t a s i m p l i s t i c view of the f o r e s t management problem in the way i t has been a p p l i e d . Fo res t r e sou r ces other than t imber are not e x p l i c i t l y c o n s i d e r e d . The d e s i r e d s t a t e i s assumed to be a f u l l y r e g u l a t e d f o r e s t , both at the p resen t t ime and f o r p e r p e t u i t y . Most important of a l l , i t t r e a t s the problem a s ' d e t e r m i n i s t i c by not r e c o g n i z i n g the s t o c h a s t i c na ture of demands fo r v a r i o u s r esources and responses of the system to d i f f e r e n t management a c t i o n s . The s t o c h a s t i c na ture of the problem i s r e f l e c t i v e of the u n c e r t a i n t y which e x i s t s about f u tu r e impacts of f a c t o r s ou t s i de the sphere of the f o r e s t system and u n c e r t a i n t y about the b i o l o g i c a l and p h y s i o l o g i c a l p rocesses which govern the movement of the f o r e s t system from one s t a t e to another through t ime . It i s not a s imple matter to cha r t a course which w i l l 1 7 c l o s e the gap i d e n t i f i e d as the f o r e s t management p rob lem. The d e s i r e d s t a t e of the f o r e s t system as a whole i s seldom e x p l i c i t l y s t a t e d , nor would i t be easy to do s o . I t i s , in p a r t , dependent upon the goa l s of the agency r e s p o n s i b l e f o r the management of the f o r e s t . Such goa l s are u s u a l l y q u a l i t a t i v e and serve p r i m a r i l y to p rov ide a sense of d i r e c t i o n . N e v e r t h e l e s s , they are important (A l s ton 1972). As an example, the goa l of the MOF i s : " t o r e a l i z e the maximum c o n t r i b u t i o n of a v a i l a b l e f o r e s t and range r e s o u r c e s , now and in the f u t u r e , towards the s o c i a l and economic we l l -be ing of B r i t i s h Co lumbia " ( M i n i s t r y of F o r e s t s 1980b). The end r e s u l t i s that the gap between the a c t u a l and the d e s i r e d s t a t e of the f o r e s t i s q u i t e d i f f i c u l t to c l o s e , and once c l o s e d , d i f f i c u l t to keep c l o s e d . U n c e r t a i n t i e s a r i s i n g from w i t h i n and ou t s i de the system hand icap the movement of the f o r e s t towards some d e s i r e d s t a t e . F a c t o r s a c t i n g e x t e r n a l to the f o r e s t system c o n t r i b u t e to chang ing p e r c e p t i o n s of the d e s i r e d s t a t e . Even i f s u f f i c i e n t r e s e a r c h were to be conducted on the p h y s i c a l and b i o l o g i c a l mechanisms of the system and u n l i m i t e d i n f o r m a t i o n was a v a i l a b l e about the p resen t s t a t e , u n c e r t a i n t y about the f u t u r e would p r e c l ude the development of a management s t r a t e g y which i s sure to be o p t i m a l . T h i s shou ld not be taken as an i n d i c a t i o n tha t r e sea r ch i n t o the b i o l o g i c a l and p h y s i c a l mechanisms of the f o r e s t system i s of l i t t l e v a l u e . C l e a r l y , the b e t t e r the system i s unde rs tood , the more the r e d u c t i o n i n u n c e r t a i n t y r e g a r d i n g the fu tu re system s t a t e g i ven a p a r t i c u l a r sequence of management a c t i o n s . A s i m i l a r argument can be made w i th r e spec t to 18 c o l l e c t i o n of i n f o rma t i on on the p resen t s t a t e of the f o r e s t system. Returns from the f o r e s t can be r e c o g n i z e d as be l ong ing to p a r t i c u l a r . r e source use c a t e g o r i e s . Examples of such c a t e g o r i e s i n c l u d e t imbe r , r e c r e a t i o n , w i l d l i f e , et c e t e r a . S o l u t i o n of the f o r e s t management problem i n vo l v e s answer ing two i n t r i c a t e l y l i n k e d q u e s t i o n s : (1) What mixture of r esource uses i s d e s i r e d ? (2) How shou ld each resource be managed to maximize r e tu rn ? The comp lex i t y of a t tempt ing to answer these two q u e s t i o n s s imu l t aneous l y comp l i c a t e s h o l i s t i c a t tempts at p r o v i d i n g answers on p u b l i c f o r e s t l a n d . O f ten the s o l u t i o n procedure i n v o l v e s s u b d i v i d i n g the f o r e s t management problem c o n c e p t u a l l y and j u r i s d i c t i o n a l l y i n t o subproblems each p e r t a i n i n g to a r esource use c a t e g o r y . The subproblems c o n s i s t of d e v e l o p i n g a s t r a t e g i c p l an fo r a p a r t i c u l a r r e sou rce use ca tegory on a w e l l - d e f i n e d f o r e s t area which i s compa t ib l e w i th some o v e r a l l s t r a t e g y fo r the f o r e s t as a whole. Whi le the subproblems are g e n e r a l l y so l v ed in p a r t i a l i s o l a t i o n from one ano the r , l i n k a g e s are ma in ta ined by e x i s t i n g p o l i c y . 2.2 Timber Management Management of the t imber r esource i s one of the subproblems compr i s i ng the f o r e s t management p rob lem. In many a reas of Canada i t i s the dominant subproblem to such a degree tha t many people do not d i f f e r e n t i a t e between management of the f o r e s t and management of the t imber r e s o u r c e . A d i s t i n c t i o n i s ne ces sa r y , 1 9 p a r t i c u l a r l y on p u b l i c l a n d s , s i n ce the terms of r e f e r e n c e fo r t imber management are c o n s i d e r a b l y narrower than those fo r f o r e s t management. Most of the o ther f o r e s t r e sou r ces are s p a t i a l l y and/or t empora l l y i n compa t ib l e w i th t imber h a r v e s t i n g . R e s o l u t i o n of c o n f l i c t s , t h e r e f o r e , u s u a l l y n e c e s s i t a t e s compromise between resource uses to i n c r ea se t o t a l r e t u r n from the f o r e s t a l though r e tu rn from the i n d i v i d u a l r e sou r ces may be l e s s than i f each resource were c o n s i d e r e d in i s o l a t i o n . S ince the purpose of t h i s d i s s e r t a t i o n i s to deve lop a framework fo r f o r m u l a t i o n and s e l e c t i o n of t imber management s t r a t e g i e s , t imber w i l l be c o n s i d e r e d the predominant use on the l and area c o n s i d e r e d . Increments t o , or e r o s i o n s f rom, t h i s l and base in the f u tu r e remain a d i s t i n c t p o s s i b i l i t y . T h i s c o n t r i b u t e s to the u n c e r t a i n t y a s s o c i a t e d w i th the f u t u r e d e s i r e d s t a t e of the f o r e s t . D i s c u s s i o n of t h i s fundamental i s sue i s resumed in subsequent c h a p t e r s , but f o r the p r e s e n t , d i s c u s s i o n i s l i m i t e d to the t imber r esource in i s o l a t i o n of o ther p o t e n t i a l r esource u s e s . S ince t imber e x t r a c t i o n i s a consumpt ive use of the f o r e s t sys tem, the r a te of e x t r a c t i o n has a p ro found i n f l u e n c e on the f u t u r e s t a t e of the f o r e s t sys tem. Some p o l i c y s t r u c t u r e ( e . g . s u s t a i n e d y i e l d ) u s u a l l y e x i s t s to govern the r a te of t imber e x t r a c t i o n and c o n t r o l changes in the s t a t e of the t imber r esource through t ime . The extent to which the f o r e s t manager i n t e r venes in the n a t u r a l system p rocesses f o l l o w i n g e x t r a c t i o n ( i . e . s i l v i c u l t u r e , p r o t e c t i o n , et c e t e r a ) i n f l u e n c e s the dynamics of the system response and a l s o i n f l u e n c e s f u tu r e s t r u c t u r e of the t imber r e s o u r c e . 20 As o u t l i n e d in the f i r s t c h a p t e r , the f o r e s t manager must address two i n t r i c a t e l y l i n k e d d e c i s i o n s when p r e p a r i n g a t imber management p l an fo r the f o r e s t : c h o i c e of a t imber management s t r a t e g y and s e l e c t i o n of a h a r v e s t i n g p a t t e r n . S ince these two d e c i s i o n s r ep resen t the on ly c o n t r o l the f o r e s t manager can exe r t over the fu tu re s t a t e of the t imber r e s o u r c e , the c l o s e r e l a t i o n s h i p between them i s not s u r p r i s i n g . A major c o n s i d e r a t i o n in the cho i c e of a t imber management s t r a t e g y i s the ra te of h a r v e s t i n g ' a l l o w e d ' by e x i s t i n g p o l i c y under that p a r t i c u l a r s t r a t e g y . In a s i m i l a r sense , the cho i ce of a p a r t i c u l a r h a r v e s t i n g p a t t e r n i m p l i e s the c h o i c e of a sequence of management a c t i o n s which w i l l attempt to ma in ta in a f o r e s t s t r u c t u r e which i s compat ib l e w i th such a ha r ves t ra te under the g u i d e l i n e s s p e c i f i e d by p o l i c y . In s h o r t , s e t t i n g a h a r v e s t i n g p a t t e r n i m p l i e s , or at l e a s t c o n s t r a i n s , the s e l e c t i o n of a t imber management s t r a t e g y . Cho i ce of a h a r v e s t i n g p a t t e r n and s e l e c t i o n of an a p p r o p r i a t e t imber management s t r a t e g y are e s s e n t i a l l y two s i de s of the same c o i n . D e c i s i o n s can not be made about a p p r o p r i a t e l e v e l s f o r one wi thout c o n s i d e r i n g the o t h e r . T h i s i s not to say tha t there i s a d i r e c t one-to-one r e l a t i o n s h i p between the two nor tha t t h i s r e l a t i o n s h i p i s as we l l unders tood as would be l i k e d . The r e l a t i o n s h i p i s f i r s t shaped by p o l i c y and then m o d i f i e d by the p h y s i c a l and b i o l o g i c a l mechanisms of the f o r e s t system and f a c t o r s e x t e r n a l to the system beyond the manager 's c o n t r o l . Thus a p a r t i c u l a r s t r a t e g y may a l l ow a c e r t a i n l e v e l of c u t , but the e f f e c t on the system may not be as p r e d i c t e d or w i t h i n the range of responses 21 a l lowed by e x i s t i n g p o l i c y . The i m p l i c a t i o n s of p o l i c y v i o l a t i o n s , and more fundamenta l l y , the e x p l o r a t i o n of e x i s t i n g and p o t e n t i a l p o l i c i e s in terms of t h e i r c o n t r i b u t i o n towards the s o l u t i o n of the f o r e s t management problem can on l y be ana l yzed at a l e v e l of agg rega t i on above that at which they are a p p l i e d . T h i s means tha t the i m p l i c a t i o n s of e x i s t i n g and p r o s p e c t i v e p o l i c i e s which set the con tex t fo r s e l e c t i o n of a t imber management s t r a t e g y must be examined" in terms of t h e i r i n f l u e n c e on the o v e r a l l r e t u rn from the f o r e s t , not s imply in terms of t h e i r i n f l u e n c e on r e tu rns from managing the t imber component. Any o ther e v a l u a t i o n would be l a c k i n g in p e r s p e c t i v e . Fo rmu la t i on of a p p r o p r i a t e p o l i c y remains the fundamental mechanism fo r s o l v i n g the forest .management p rob lem. In a ve ry r e a l sense , c o n s t r u c t i o n of a s t r a t e g i c p l an fo r the t imber resource i s more a matter of p o l i c y a n a l y s i s than a r e s u l t of any p a r t i c u l a r method or methods of p r o j e c t i n g t imber s u p p l y . The development of a means fo r t e s t i n g p o l i c y i m p l i c a t i o n s i s comp l i c a t ed by the need to c o n s i d e r d i f f e r e n t l e v e l s of government, the g e o g r a p h i c a l d i s t r i b u t i o n of the r e s o u r c e , f u t u r e p r o j e c t i o n s of supp ly and demand fo r the v a r i o u s r e sou r ce c a t e g o r i e s and i n t e r a c t i o n s among the f o r e s t s e c t o r and o ther s e c t o r s of the economy. The i n i t i a l s teps i n a n a l y z i n g p o l i c y a l t e r n a t i v e s at l e a s t in terms of the t imber component of the f o r e s t system are we l l under way in the U n i t e d S t a t es and Canada. (See, f o r example, Adams and Haynes 1980, A l s t o n 1972, Berck 1979, Hyde 1979, Pearse et a L 1983 and USDA 1976.) The end r e s u l t of such p o l i c y ana l y ses c o u l d be a s i g n i f i c a n t change 22 in f o r e s t p o l i c y fo r both c o u n t r i e s . Major changes are not l i k e l y to occur in the near f u t u r e , however, because of the long-term nature and inheren t c o m p l e x i t i e s of such a n a l y s e s . As long as the re i s a demand fo r t imber from p u b l i c f o r e s t l and the re w i l l be a need fo r s e l e c t i n g t imber management s t r a t e g i e s . The s e l e c t i o n of a t imber management s t r a t e g y i s a complex procedure governed by e x i s t i n g p o l i c y as we l l as p resen t and f u t u r e demands fo r t imber and o ther r e s o u r c e s . Presumably , the t imber management s t r a t e g y s e l e c t e d i s the one c o n s i d e r e d to be the most compat ib l e wi th an o v e r a l l f o r e s t management s t r a t e g y thought to produce the ' b e s t ' r e t u rn from the f o r e s t system. The impacts of v a r i o u s ha rves t p a t t e r n s under d i f f e r e n t l e v e l s of management can on ly be a s c e r t a i n e d through an unders tand ing of the dynamics of the sys tem. 2.3 Timber Management/Supply Models Models of c e r t a i n components of the f o r e s t system p rov i de an a i d to the f o r e s t manager. They serve as a guide fo r c h o i c e between d e c i s i o n a l t e r n a t i v e s . The consequences of d e p a r t i n g from c e r t a i n c o n s t r a i n t s can be t e s t e d us ing m o d e l l i n g . Models a l s o f u r n i s h a means fo r employee o r i e n t a t i o n and t r a i n i n g as we l l as p rov i de a framework fo r r e sea r ch program a n a l y s i s (Duerr 1967) . Models of some so r t are employed to a i d in the f o rmu l a t i on of t imber management s t r a t e g i e s and/or to p r o j e c t the impact on t imber supp ly of a p a r t i c u l a r h a r v e s t i n g p a t t e r n under an assumed management s t r a t e g y . The use of such models c o n t r i b u t e to the s e l e c t i o n of a t imber h a r v e s t i n g p a t t e r n and the c h o i c e 23 of a t imber management s t r a t e g y . There are two b a s i c m o d e l l i n g approaches which w i l l be i d e n t i f i e d as t imber management models and t imber supp ly mode ls . Timber management models c o n s t r u c t a management s t r a t e g y which o p t i m i z e s , a c c o r d i n g to the r u l e s and s t r u c t u r e of the model , r e t u rn from h a r v e s t i n g under the c o n s t r a i n t s imposed by e x i s t i n g p o l i c y based on some f i n i t e set of management a c t i o n s . Examples of e x i s t i n g mathemat ica l programming models of f o r e s t management which can be used to r e a d i l y c o n s t r u c t a f e a s i b l e management s t r a t e g y i n c l u d e Timber RAM (Timber Resource A l l o c a t i o n Method; Navon 1971) or MUSYC ( M u l t i p l e Use-Sus ta ined Y i e l d Resource S chedu l i ng C a l c u l a t i o n ; Johnson and Jones 1979). Timber supp ly models p r o j e c t supp ly assuming a p a r t i c u l a r set of management a c t i o n s and a p rede te rmined ha r ves t p a t t e r n . Such models can be used in c o n j u n c t i o n wi th other models which suggest a p p r o p r i a t e l e v e l s of ha r ves t based on shor t- te rm commitments and proposed a l l o c a t i o n of the cut (Rustag i 1978). Timber supp ly models may take the same s t r u c t u r e as t imber management models or they may be based on l e s s r i g i d s t r u c t u r e s and s o l v e d by s i m u l a t i o n t e c h n i q u e s . Examples of t imber supp ly models s o l v e d u s i n g s i m u l a t i o n i n c l u d e ECHO (Economic Harves t O p t i m i z a t i o n Mode l ; Walker 1978) and TREES (Timber Resource Economic E s t i m a t i o n System; Tedder e_t a l . 1980). The d i s t i n c t i o n between t imber management models and t imber supply models i s somewhat b l u r r e d in a c t u a l p r a c t i c e . Models c o n s t r u c t e d p r i m a r i l y f o r the purpose of t imber management can be used to model t imber supp ly and v i c e v e r s a . T h i s i s a r e s u l t of the i n t r i c a t e r e l a t i o n s h i p between t imber management s t r a t e g y 24 and t imber s u p p l y . Timber supp ly models must i n vo l v e some i m p l i c i t or e x p l i c i t cho i ce of management s t r a t e g y e i t h e r i n t e r n a l or e x t e r n a l to the model (s ) employed. Timber management models must i n v o l v e some c o n s i d e r a t i o n of t imber supp ly in the c o n s t r u c t i o n of t imber management s t r a t e g i e s and/or in the cho i c e of d i f f e r e n t s t r a t e g i e s . In the f i n a l a n a l y s i s , the i d e n t i f i c a t i o n of a g iven model as e i t h e r a t imber supp ly model or a t imber management model depends more on i t s use than on any necessary s t r u c t u r a l d i f f e r e n c e s between the mode ls . In order to a vo id c o n f u s i o n , the gene ra l term ' t imbe r supp ly model ' w i l l be used to r e f e r to both these m o d e l l i n g approaches throughout t h i s d i s s e r t a t i o n . The contex t of the d i s c u s s i o n shou ld i n d i c a t e which model use i s i m p l i e d i f any d i s t i n c t i o n i s ne ces sa r y . 2.4 De te rm ina t i on of the A l l owab l e Cut in B r i t i s h Columbia F o r e s t e d P r o v i n c i a l Crown l and in B r i t i s h Columbia i s d i v i d e d i n t o two major . t y p e s of management u n i t s f o r which a l l owab l e cut l e v e l s are s e t : Timber Supply Areas (TSA 's ) and Tree Farm L i c e n s e s ( T F L ' s ) . T F L ' s a re g e n e r a l l y h e l d by l a r g e , u s u a l l y i n t e g r a t e d , f o r e s t product companies and may i n c l u d e some p r i v a t e l and h o l d i n g s . The l i c e n s e i s g ran ted fo r a 25 year p e r i o d , but i s r e n e g o t i a t e d every 10 yea rs (Apsey 1980). Management and Working P lans are r e q u i r e d and are deve loped by the l i c e n s e e in c o n s u l t a t i o n w i th the MOF. P e r i o d i c a l l o w a b l e cu t s must be suppor ted by an approved t imber supp ly p r o j e c t i o n p rocedu re . (For more i n f o rma t i on see M i n s t r y of F o r e s t s 1983a and 1983b.) Management of the TSA ' s i s the d i r e c t r e s p o n s i b i l i t y of the 25 MOF. The p l a n n i n g p rocess i n v o l v e d i s d e s c r i b e d in d e t a i l in M i n i s t r y of F o r e s t s (1984) and w i l l on ly be b r i e f l y summarized he re . A TSA p l an i s norma l l y deve loped over a one year p e r i o d every f i v e y e a r s . F a c i l i t y i s p rov i ded fo r more f requent r e v i s i o n shou ld c i r cums tances warrant i t . The p lan e s t a b l i s h e s the f o l l o w i n g fo r each TSA : . 1) TSA supp ly o b j e c t i v e s fo r t imbe r , range and r e c r e a t i o n , expressed as q u a n t i t a t i v e long-range f o r e c a s t s ; 2) management s t r a t e g i e s fo r t imbe r , range and r e c r e a t i o n , used in the p r e p a r a t i o n of D i s t r i c t annual F i v e Year Program p r o p o s a l s and the c o o r d i n a t i o n of L o c a l and Development p l a n s ; 3) resource use assumpt ions u n d e r l y i n g s t a t ed TSA o b j e c t i v e s , documented on p l ann ing maps; and 4) l i c e n s e e supp ly a reas fo r t imber h a r v e s t i n g over the next 20 y e a r s . P e r i o d i c a l l o w a b l e cut i s r ep resen ted by the f i r s t f i v e years of the long range t imber supp ly o b j e c t i v e s fo r the TSA. Timber supp ly ana l y ses p l a y an important r o l e in both TSA and TFL p l a n n i n g p r o c e s s e s . The t imber supp ly model o r i g i n a l l y employed by the MOF was Timber RAM. Seve ra l a l t e r n a t i v e model forms have been employed in recent y e a r s . For example, in the F r a s e r TSA y i e l d a n a l y s i s , MUSYC was used in c o n j u n c t i o n w i th IPS ( I n t e r a c t i v e P l ann ing System) , a s i m u l a t i o n model deve loped by the MOF, to exp lo r e the r a m i f i c a t i o n s of s e v e r a l management s c e n a r i o s ( M i n i s t r y of F o r e s t s 1982a). Rega rd l ess of the type of model used to p r o j e c t t imber supp l y , i t remains on ly one source of i n f o rma t i on upon which the a l l owab l e cut i s based . The u l t i m a t e h a r v e s t i n g l e v e l i s set by the Ch i e f F o r e s t e r on the b a s i s of the t imber supp ly a n a l y s e s , 26 p u b l i c i n p u t , o ther r e sou rce requ i rements and economic and s o c i a l f a c t o r s . (See M i n s i t r y of F o r e s t s 1978, 1979, I980e and Young 1981 fo r more d e t a i l s . ) 27 CHAPTER III DECISION-MAKING, UNCERTAINTY AND FOREST MANAGEMENT 3.1 Termino logy D e c i s i o n s i n v o l v e s e l e c t i n g one a l t e r n a t i v e from a set of a l t e r n a t i v e s . Each a l t e r n a t i v e i s compr ised of a sequence of a c t i o n s which w i l l e v e n t u a l l y l e ad to some consequence (outcome) . D e c i s i o n s are made in an environment d e f i n e d by p o t e n t i a l s t a t e s of nature beyond the d e c i s i o n maker ' s c o n t r o l . These s t a t e s must be mutua l l y e x c l u s i v e and c o l l e c t i v e l y exhaus t i v e ( R a i f f a and S c h l a i f e r 1961; S c h l a i f e r 1959). The a l t e r n a t i v e s e l e c t e d and the s t a t e which occu rs toge ther determine the outcome. S e l e c t i o n of an a l t e r n a t i v e i s made on the b a s i s of some c r i t e r i o n or c r i t e r i a a p p l i e d to p o t e n t i a l outcomes. S ince the outcome i s a f u n c t i o n of the s t a t e of na ture which w i l l o c c u r , i n f o r m a t i o n c o n c e r n i n g the p o t e n t i a l s t a t e s of nature determines the con tex t under which the d e c i s i o n s are made. T r a d i t i o n a l l y , most au thors c i t e the th ree c o n d i t i o n s f i r s t r e cogn i zed by Kn igh t (1921) : c e r t a i n t y , r i s k and u n c e r t a i n t y . C e r t a i n t y a p p l i e s to s i t u a t i o n s in which there i s on l y one p o t e n t i a l outcome fo r each a l t e r n a t i v e . Such a c o n d i t i o n i m p l i e s tha t the s t a t e of na ture i s known as we l l as the consequences a s s o c i a t e d w i th each a l t e r n a t i v e . D e c i s i o n s are made under c o n d i t i o n s of r i s k when there i s more than one p o t e n t i a l outcome f o r each a l t e r n a t i v e and the p r o b a b i l i t y of each outcome i s known. T h i s i m p l i e s a known p r o b a b i l i t y d i s t r i b u t i o n f o r the 28 s t a t e s of n a t u r e . C o n d i t i o n s of u n c e r t a i n t y are s a i d to occur when more than one outcome i s p o s s i b l e fo r any a l t e r n a t i v e and the p r o b a b i l i t y of any one outcome i s not known wi th c e r t a i n t y . The i n c r e a s e d use of s u b j e c t i v e p r o b a b i l i t y in recent years has b l u r r e d the d i s t i n c t i o n between r i s k and u n c e r t a i n t y . Some au thors ( f o r example, C h r i s t i a n s e n 1974) no longer make a d i s t i n c t i o n . I f the d e c i s i o n maker b e l i e v e s in u s i ng s u b j e c t i v e p r o b a b i l i t i e s f o r a n a l y z i n g d e c i s i o n s i t u a t i o n s , the approach-used to s e l e c t the a p p r o p r i a t e a l t e r n a t i v e w i l l not vary whether the d i s t r i b u t i o n a s s o c i a t e d w i th the p o t e n t i a l outcomes fo r a g i ven a l t e r n a t i v e i s s u b j e c t i v e or e n t i r e l y o b j e c t i v e . The important d i s t i n c t i o n i s between s i t u a t i o n s i n which there i s on ly one outcome a s s o c i a t e d w i th each a l t e r n a t i v e and s i t u a t i o n s in which there i s more than one. The d i s t i n c t i o n between K n i g h t ' s c o n d i t i o n s of u n c e r t a i n t y and r i s k in terms p r a c t i c a l to f o r e s t management i s r e a l l y on ly a matter of s eman t i c s . Seldom, i f e ve r , i s the p r o b a b i l i t y d i s t r i b u t i o n of p o t e n t i a l s t a t e s ever ' e x a c t l y ' known. S ince the methodology subsequent l y deve loped w i l l advocate the use of s u b j e c t i v e p r o b a b i l i t y , no formal d i s t i n c t i o n w i l l be made between r i s k and u n c e r t a i n t y . The term ' u n c e r t a i n ' w i l l be used to r e f e r to s i t u a t i o n s in which there i s more than one p o t e n t i a l outcome f o r some or a l l of the a l t e r n a t i v e s . T h i s c o u l d be due to l a ck of i n f o r m a t i o n , or to p o t e n t i a l o ccu r rences p a r t i a l l y or whole ly beyond the d e c i s i o n maker ' s c o n t r o l or a combina t ion of t he se . ' U n c e r t a i n t y ' w i l l be used to r e f e r to the spread of p o t e n t i a l outcomes f o r s p e c i f i c management a c t i o n s . I t w i l l c o n t r i b u t e to 29 the r i s k a s s o c i a t e d w i th a p a r t i c u l a r management s t r a t e g y . Hence, a s t r a t e g y which c o n t a i n s more u n c e r t a i n t y than another w i l l be c o n s i d e r e d r i s k i e r . S t r i c t l y d e f i n e d , u n c e r t a i n t y i s a c h a r a c t e r i s t i c of p e o p l e , not of even ts , s i n c e on l y one outcome w i l l e v e n t u a l l y o c c u r . It i s c l o s e l y r e l a t e d to knowledge. The more i n f o r m a t i o n a v a i l a b l e conce rn ing the d e c i s i o n env i ronment , the sma l l e r the u n c e r t a i n t y (Duerr 1974c) . The f a c t o r s which i n f l u e n c e the s t a t e s of nature a r e , by d e f i n i t i o n , beyond the d e c i s i o n maker ' s c o n t r o l and no amount of i n f o r m a t i o n can a l t e r the d i s t r i b u t i o n . Some r i s k w i l l con t inue to be p resen t as long as there i s more than one p o t e n t i a l outcome. 3.2 R isk P ropens i t y The d e c i s i o n maker 's a t t i t u d e towards r i s k i s an i n t e g r a l par t of any d e c i s i o n . Reac t i on v a r i e s from i n d i v i d u a l to i n d i v i d u a l . I f a u t i l i t y f u n c t i o n c o u l d be d e r i v e d f o r the d e c i s i o n maker, i t s shape would i n d i c a t e h i s r i s k p r o p e n s i t y . In gene ra l terms, an i n d i v i d u a l w i th a s t r i c t l y convex u t i l i t y f u n c t i o n i s c o n s i d e r e d a r i s k taker wh i le someone w i th a s t r i c t l y concave u t i l i t y f u n c t i o n i s c o n s i d e r e d a r i s k a v e r t e r . If the u t i l i t y f u n c t i o n i s l i n e a r , the d e c i s i o n maker i s r i s k n e u t r a l (DeGroot 1970, R a i f f a 1968). In many i n s t ances p a r t i c u l a r u t i l i t y f u n c t i o n s can assume a l l these shapes at d i f f e r e n t p o i n t s throughout t h e i r range . T h i s makes i t d i f f i c u l t to c l a s s i f y the d e c i s i o n maker ' s a t t i t u d e towards r i s k in a s imple manner. The d e c i s i o n maker may reduce the r i s k which he a s s o c i a t e s 30 wi th any d e c i s i o n s i t u a t i o n by changing e i t h e r the p r o b a b i l i t i e s or the r e tu rns a s s o c i a t e d wi th p a r t i c u l a r outcomes. There are many t echn iques fo r cop ing wi th u n c e r t a i n t y (see Chapter V I ) , but these make no e x p l i c i t sugges t i on as to what the d e c i s i o n maker ' s r i s k p r o p e n s i t y shou ld be a l though some approaches do imply a p a r t i c u l a r a t t i t u d e . The a p p r o p r i a t e a t t i t u d e of a p u b l i c agency towards r i s k i s d i f f i c u l t to a s c e r t a i n . Three s choo l s of thought e x i s t w i th regards to the p o s i t i o n p u b l i c agenc ies shou ld take towards r i s k ( B e l l and F i gh t 1976, F i g h t and B e l l 1977). The p o s i t i o n advocated by H i r s h l e i f e r (1965,1966) i s that government agenc i es shou ld ac t l i k e the p r i v a t e s e c t o r . Investments shou ld be made which maximize the net p resen t worth a f t e r a d j u s t i n g fo r u n c e r t a i n t y . The argument p resen ted i s that i g n o r i n g the ad justments fo r u n c e r t a i n t y may l e ad to poor a l l o c a t i o n of funds and that the market i s the best mechanism fo r de te rm in ing a l l o c a t i o n of r e s o u r c e s . The second s choo l of thought , r ep resen ted by Samuelson and V i c k e r y (1964) and Arrow and Lund (1970) , i s tha t government agenc i es shou ld ignore u n c e r t a i n t y and ac t as though i t were i n d i f f e r e n t to r i s k . The reason ing beh ind t h i s p o s i t i o n i s tha t the l a r g e s i z e of the government a l l ows i t to absorb or o the rw ise d i s p e r s e r i s k and to c o n t r o l the u n c e r t a i n t y to some e x t e n t . Proponents of the t h i r d p o s i t i o n s t a t e tha t the market and the p r i v a t e s e c t o r shou ld be i gnored by the government in respond ing to r i s k because of i m p e r f e c t i o n s in the system. They b e l i e v e tha t proper p u b l i c a t t i t u d e shou ld be set through p o l i t i c a l r a the r than economic p r o c e s s e s . No i n d i c a t i o n i s g i ven 31 as to how t h i s shou ld be done, however. F i g h t and B e l l (1977) argued tha t the t h i r d p o s i t i o n h e l d the most mer i t g i ven the c u r r e n t c o n d i t i o n of the resource management a r e a . The d i f f i c u l t y i s tha t governments are u s u a l l y r e l u c t a n t to e s t a b l i s h e x p l i c i t p o l i c i e s towards r i s k . The a t t i t u d e adopted i s seldom e x p l i c i t l y s t a t e d and appears to vary w i th the d e c i s i o n . Of ten the s tance taken i s a r e f l e c t i o n of the views of the p a r t i c u l a r agency or i n d i v i d u a l i n v o l v e d r a the r than government p o l i c y . A s t rong i n t u i t i v e argument can be p resen ted suppo r t i ng the adop t i on of a r i s k averse a t t i t u d e fo r t imber management s t r a t e g y s e l e c t i o n . F i g h t and B e l l (1977) noted that i t i s g e n e r a l l y e a s i e r to i n c r ease c u t t i n g l e v e l s in f u tu r e years than to decrease l e v e l s . A decrease in f u tu r e c u t t i n g l e v e l s can occur as a r e s u l t of o v e r c u t t i n g at the p resen t t ime . O v e r c u t t i n g i s not d i r e c t l y an e f f e c t of the h a r v e s t i n g r a t e , but r a the r a r e s u l t of the f a i l u r e of the t imber management s t r a t e g y employed to ma in ta in a l e v e l and d i s t r i b u t i o n of growing s tock which can support the cut under e x i s t i n g p o l i c y . If F i g h t and B e l l ' s premise i s a c c e p t e d , i t i s a s imple ex t ens i on to s t a t e tha t the r e p e r c u s s i o n s of o v e r e s t i m a t i n g response to a management s t r a t e g y would be more severe than u n d e r e s t i m a t i n g response by a comparable amount. T h i s would suggest a c o n s e r v a t i v e s tance by the management agency w i th r espec t to performance assumpt ions fo r any management a c t i v i t y . The approach taken in B r i t i s h Columbia r e g a r d i n g i n c r e a s e s i n c u t t i n g r a t e s to r e f l e c t i n c r e a s e s in f u tu r e y i e l d s , a t t r i b u t e d to s tand management p r a c t i c e s , suppor t s t h i s premise 32 ( M i n i s t r y of F o r e s t s I 980 f ) : " . . . t h e ga in in p r o d u c t i v i t y f o r t imber p r o d u c t i o n w i l l be c a l c u l a t e d us i ng c o n s e r v a t i v e es t ima tes and e s t a b l i s h e d as a c r e d i t to the a l l owab l e cut a u t h o r i z e d under the l i c e n s e . Any i nc rementa l p r o d u c t i v i t y ga in over that es t imated fo r c r e d i t under S e c t i o n 52 p o l i c y s h a l l be i n c o r p o r a t e d i n t o the t o t a l annual a l l o w a b l e cut fo r the Timber Supply Area and used at the d i s c r e t i o n of the M i n i s t r y of F o r e s t s " It i s not the i n t e n t i o n of t h i s d i s s e r t a t i o n to specu l a t e as to what the r i s k p r o p e n s i t y of a t imber management agency shou ld be beyond the assumption tha t the agency i s r i s k averse to some deg ree . C l e a r l y i t i s dependent upon l o c a l and r e g i o n a l c o n d i t i o n s . R i sk p r o p e n s i t y i s u s u a l l y not e x p l i c i t l y s t a t e d in t imber management d e c i s i o n s . T h i s mat te rs l i t t l e i f no e x p l i c i t statement of u n c e r t a i n t y i s made r ega rd ing p r o s p e c t i v e t imber management s t r a t e g i e s . If p a r t i c u l a r sources of u n c e r t a i n t y are i n c o r p o r a t e d i n t o the t imber supp ly m o d e l l i n g p rocedu re , r i s k then becomes an important c r i t e r i o n fo r choos ing among s t r a t e g i e s . In such s i t u a t i o n s an e x p l i c i t p o l i c y towards r i s k would be u s e f u l in a c h i e v i n g c o n s i s t e n c y between d e c i s i o n s fo r the same management agency. The r i s k p r o p e n s i t y of the d e c i s i o n maker i s un important in the a b s t r a c t . I t i s on ly important tha t the d e c i s i o n model employed i n c o r p o r a t e h i s a t t i t u d e so tha t the model i s r e f l e c t i v e of the d e c i s i o n maker ' s p o s i t i o n . The methodology subsequent l y deve loped remains a p p l i c a b l e fo r any a t t i t u d e towards r i s k . 33 3.3 Timber Management S t r a t egy S e l e c t i o n as a D e c i s i o n Problem The idea of cho i ce i s c r i t i c a l to any d e c i s i o n s i t u a t i o n (MacCrimmon 1974b). T h e o r e t i c a l l y , in order to choose an a p p r o p r i a t e a l t e r n a t i v e one has to i m p l i c i t l y or e x p l i c i t l y rank the p o t e n t i a l consequences and s e l e c t the a c t i o n which w i l l maximize the p o t e n t i a l r e t u r n or min imize p o t e n t i a l l o s s . Cho i ces must be made at the present time based on p e r c e i v e d f u tu r e r e t u r n s which w i l l be shaped by f u t u r e e ven t s . The f u r t h e r i n t o the fu tu re one i s a t tempt ing to p r o j e c t , the g r ea t e r the u n c e r t a i n t y i n v o l v e d . F o r e s t r y has been d e f i n e d as " the study and p r a c t i c e of managing f o r e s t l and and a s s o c i a t e d r e s o u r c e s " (Duerr 1974a). The term 'management' i s o f t e n used synonymously w i th p l ann ing and i n v o l v e s making d e c i s i o n s wi th regard to f u t u r e a c t i o n s (Duerr e_t a l . 1968). A p p l y i n g some of these i d e a s , the d e f i n i t i o n p rov ided above may be paraphrased to d e f i n e f o r e s t r y as ' t he study and p r a c t i c e of making c h o i c e s r e g a r d i n g f o r e s t l and and a s s o c i a t e d r e sou r ces under c o n d i t i o n s of u n c e r t a i n t y ' . Whether t h i s i s a s u i t a b l e d e f i n i t i o n of f o r e s t r y i s sub jec t to deba te , but i t i s apparent that the concepts of dec i s i on-mak ing and u n c e r t a i n t y are inheren t in f o r e s t management. In a gene ra l sense , the e f f e c t of u n c e r t a i n t y in the d e c i s i o n environment i s the c r e a t i o n of some p o s s i b i l i t y of a 'wrong ' d e c i s i o n . The d e c i s i o n s are 'wrong ' in the sense that the outcome i s not c o n s i s t e n t wi th the p r e f e r e n c e s of the d e c i s i o n maker. In o ther words, u n c e r t a i n t y can produce outcomes other than the most p r e f e r r e d . The d i f f e r e n c e between the a c t u a l outcome and the outcome which would have been s e l e c t e d under 34 c e r t a i n t y r e p r e s e n t s a l o s s to the d e c i s i o n maker. O f ten t h i s l o s s can not be r e a d i l y expressed in monetary te rms . The d e c i s i o n s made by the f o r e s t manager are termed management a c t i o n s in the d e s c r i p t i o n of the f o r e s t system p rov ided in Chapter I I . The manager s e l e c t s a set of a c t i o n s , termed a management s t r a t e g y , on the b a s i s of what he p e r c e i v e s as t h e i r impact on the r e tu rn from the f o r e s t sys tem. Once an a c t i o n i s a p p l i e d , the system responds in a manner d i c t a t e d by the u n d e r l y i n g b i o l o g i c a l ' and p h y s i o l o g i c a l p rocesses of the system and the l e v e l of the v a r i o u s e x t e r n a l f a c t o r s ( s t a t e s of nature ) to produce a r e t u r n . The management s t r a t e g y s e l e c t e d shou ld maximize the expected r e tu rn from the f o r e s t sys tem, however tha t may be d e f i n e d . The 'opt imum' management s t r a t e g y fo r a f o r e s t w i l l be d e f i n e d as tha t set of management a c t i o n s which ' b e s t ' meets the o b j e c t i v e s of the f o r e s t management agency. ' B e s t ' can be d e f i n e d a c c o r d i n g to whatever c r i t e r i a the management agency may wish to use . The management d e c i s i o n p rocess can be v i s u a l i z e d as c o n s i s t i n g of two components: (1) s e t t i n g the d e s i r e d l e v e l of r e sou rce usage both now and in the f u tu r e ( r esource use pa t t e rn ) and (2) choos ing the sequence of management a c t i o n s which w i l l ' a l l o w ' such usage under e x i s t i n g p o l i c y . The s e l e c t i o n of an a p p r o p r i a t e t imber ha r ves t p a t t e r n to f o l l ow over t ime i s one such r esou rce use d e c i s i o n . Together with the l o c a t i o n and a l l o c a t i o n of the t imber ha r ves t ed i t determines one component of the r e t u r n from the f o r e s t sys tem. The t imber management s t r a t e g y s e l e c t e d to ' a l l o w ' t h i s h a r v e s t i n g p a t t e r n compr ises a c e r t a i n p r o p o r t i o n of the 35 management a c t i o n s which w i l l form the management s t r a t e g y fo r the f o r e s t as a whole. Chapter II r a t i o n a l i z e d the s e p a r a t i o n of the f o r e s t management problem i n t o a s e r i e s of subproblems p e r t a i n i n g to d i f f e r e n t r esource use c a t e g o r i e s . These subproblems are l i n k e d toge the r through the p o l i c y system in e f f e c t . To t h i s e x t e n t , each subproblem can be c o n s i d e r e d as a separa te d e c i s i o n problem i n v o l v i n g the cho i ce of a p a r t i c u l a r p a t t e r n of r esource usage and a management s t r a t e g y which w i l l ' a l l o w ' such usage w i t h i n the bounds of e x i s t i n g p o l i c y . ' Such a d e s c r i p t i o n i s q u i t e compat ib l e w i th the MOF p l a n n i n g p rocess fo r T F L ' s and TSA ' s c u r r e n t l y under development in t h i s p r o v i n c e ( M i n i s t r y of F o r e s t s 1983b). The t imber management subproblem can be f u r t h e r s u b d i v i d e d i n t o i t s component p a r t s . (See F i g u r e 2 ) . Such a s e p a r a t i o n i s made p u r e l y f o r a n a l y t i c pu rposes . The s t rong i n t e r r e l a t i o n s h i p between h a r v e s t i n g r a te and management s t r a t e g y was s t r e s s e d in S e c t i o n 2 .2 . I t would be q u i t e i m p r a c t i c a l to c o n s i d e r e i t h e r the d e s i r e d ha rves t p a t t e r n or the management s t r a t e g y in i s o l a t i o n from one ano the r . There a r e , however, d e f i n i t e d e c i s i o n a n a l y t i c advantages to such a s e p a r a t i o n . These r e l a t e to the i s o l a t i o n of the sources of u n c e r t a i n t y which p e r t a i n to the cho i c e of a t imber management s t r a t e g y . I t shou ld be r e a d i l y apparent from p r e v i o u s d i s c u s s i o n that o ther sources of u n c e r t a i n t y p e r t a i n to the f o r e s t management problem as a whole. P a r t i t i o n i n g the f o r e s t management problem in the manner suggested does not remove these s o u r c e s . Rather i t i d e n t i f i e s t h e i r coverage by e x i s t i n g p o l i c y . 36 F i g u r e 2: P a r t i t i o n i n g of the F o r e s t Management P rob lem. FOREST MANAGEMENT PROBLEM How to best manage the f o r e s t to meet the o b j e c t i v e s of the owner OTHER RESOURCE I TIMBER MANAGEMENT ! OTHER RESOURCE CATEGORY j I SUB-PROBLEM < I > CATEGORY SUB-PROBLEMS . ( SUB-PROBLEMS What l e v e l of r esource use and / \ what management s t r a t e g y to s e l e c t WHAT HARVESTING LEVEL WHAT TIMBER MANAGEMENT STRATEGY ? C o n s i d e r a t i o n of such u n c e r t a i n t y i s an important t a s k . I t i s on l y through such c o n s i d e r a t i o n s tha t the fundamental unde rs tand ing necessa ry f o r the development of sound f o r e s t p o l i c y can be a c h i e v e d . Such concerns p r o p e r l y f a l l w i t h i n the realm of p o l i c y a n a l y s i s which norma l l y occurs at a l e v e l of agg rega t i on g r e a t e r than tha t f aced by the f o r e s t manager. In a sense , p resen t p o l i c y s t r u c t u r e can be c o n s i d e r e d as p a r t of the f o r e s t manager 's terms of r e f e r e n c e . (He may d i s a g r e e w i th them, however. ) He w i l l make h i s d e c i s i o n s 37 r ega rd ing h a r v e s t i n g p a t t e r n and a p p r o p r i a t e t imber management s t r a t e g y w i t h i n the the con tex t of e x i s t i n g p o l i c y . T h i s w i l l ho ld t rue i r r e s p e c t i v e of the p o l i c y s t r u c t u r e in e f f e c t . D i s c u s s i o n of the r a t i o n a l i z a t i o n f o r , and the i m p l i c a t i o n s o f , a n a l y t i c s e p a r a t i o n of the t imber management s t r a t e g y d e c i s i o n from the h a r v e s t i n g p a t t e r n d e c i s i o n w i l l be resumed in Chapter V I I I . T h i s d i s c u s s i o n w i l l l e a d to the development of a methodology fo r the r a t i o n a l c h o i c e of a t imber management s t r a t e g y based on the s e p a r a t i o n of the two d e c i s i o n p r o c e s s e s . In order to set the contex t f o r such a d i s c u s s i o n , i t i s necessary to f i r s t examine in some d e t a i l t imber supp ly models in g e n e r a l , sources of u n c e r t a i n t y in the f o r e s t management prob lem, gene r a l s t r a t e g i e s f o r dec i s ion-mak ing under u n c e r t a i n t y and some s p e c i f i c dec i s i on-mak ing approaches which have been a p p l i e d to the t imber management prob lem. These t o p i c s form the b a s i s of the next four c h a p t e r s . 38 CHAPTER IV TIMBER SUPPLY MODELLING 4.1 M o d e l l i n g of the Fo r e s t System Models are symbol i c a b s t r a c t i o n s of r e a l i t y . One of the purposes of m o d e l l i n g i s to p rov ide added i n s i g h t i n t o a system by r educ ing i t s c o m p l e x i t y . Models a l s o can a i d dec i s ion-mak ing by h e l p i n g the d e c i s i o n maker c o n s t r u c t and t e s t p r o s p e c t i v e s t r a t e g i e s . One way of m o d e l l i n g the f o r e s t system i s to take an h o l i s t i c or i n t e g r a t e d resource use approach and i n c o r p o r a t e some means fo r e v a l u a t i n g r e t u r n s from some or a l l of the r esource use c a t e g o r i e s d i r e c t l y i n t o the model . Such an approach i s a t t r a c t i v e because i t approx imates the f o r e s t management p rob lem. U n f o r t u n a t e l y , the i n t e r a c t i o n s among d i f f e r e n t r e sou rce uses are complex and i n comp le t e l y unde r s tood . I t i s d i f f i c u l t to s p e c i f y a p p r o p r i a t e t r a d e o f f s among non-compat ib le r esource use c a t e g o r i e s . T h i s comp l i c a t e s the development of an adequate o b j e c t i v e f u n c t i o n , or set of f u n c t i o n s , which p rov i de c r i t e r i a f o r choos ing a p p r o p r i a t e management s t r a t e g i e s . At tempts at h o l i s t i c m o d e l l i n g of the f o r e s t system have been made. The use of goa l programming f o r l and and f o r e s t management p l a n n i n g in p a r t i c u l a r i s q u i t e p r e v a l e n t in the f o r e s t r y l i t e r a t u r e . Examples i n c l u d e B e l l (1975) , Bottoms and B a r t l e t t (1975) , Dane et a l ^ (1977) , Dyer et a l . (1979) , F i e l d (1973) , Hotvedt et aJU (1982) , Hrubes and Rens i (1981) , Kao and B rod ie (1979) and Rus tag i (1976) . 39 I n t e g r a t i o n of a goa l programming model w i th a more s p e c i f i c l i n e a r programming model of t imber management has been r epo r t ed by F i e l d (1978) and F i e l d et a l ^ (1980a) . H o l i s t i c models have g e n e r a l l y been a p p l i e d to N a t i o n a l F o r e s t l ands in the Un i t ed S t a t e s where s t r i n g e n t m u l t i p l e - u s e p o l i c i e s e x i s t . The c u r r e n t U n i t e d S t a t es Fo r e s t S e r v i c e p l a n n i n g model , FORPLAN ( Fores t P l ann ing Language and S i m u l a t o r ) , a l i n e a r programming model , ma in ta ins many e x p l i c i t l i n k a g e s between d i f f e r e n t f o r e s t r e s o u r c e s . (See, f o r example, C a t t e l i n o et a l . 1979; Johnson et a l . 1980; K e s s e l l et al± 1979; Po t t e r et a l . 1979a and 1979b.) To d a t e , h o l i s t i c m o d e l l i n g of f o r e s t systems has not been used o p e r a t i o n a l l y in Canada. T h i s i s because resource agenc i es in Canada have not pursued i n t e g r a t e d resource use p o l i c i e s and p r a c t i c e s to an extent which has made the development or use of such p l a n n i n g t o o l s a top p r i o r i t y . T h i s , in t u r n , i s p r i m a r i l y due to the l a r g e r p u b l i c f o r e s t base and c o n s i d e r a b l y sma l l e r p o p u l a t i o n l e a d i n g to fewer r e sou rce use c o n f l i c t s . As p o p u l a t i o n l e v e l s con t i nue to r i s e a long wi th demands fo r non-t imber f o r e s t u se s , the p o t e n t i a l b e n e f i t s of an h o l i s t i c m o d e l l i n g approach w i l l make i t s implementat ion more a t t r a c t i v e . An a l t e r n a t i v e to h o l i s t i c m o d e l l i n g i s to model some or a l l of the v a r i o u s resource components i n d i v i d u a l l y . Management s t r a t e g i e s based s o l e l y on models of any s i n g l e resource component in i s o l a t i o n from the o ther components are u n l i k e l y to be a c c e p t a b l e f o r the f o r e s t as a whole, un l e s s one i s the agreed upon dominant use . T h i s i s because r e t u r n s f rom, and i n t e r a c t i o n s w i t h , o ther f o r e s t r e sou r ces are not e x p l i c i t l y 40 accounted f o r . In order to make s i n g l e resource models more a p p l i c a b l e , l i n k a g e s must be ma in ta ined to the o ther r e s o u r c e s . T h i s i s u s u a l l y done in two b a s i c ways: 1) through i m p o s i t i o n of v a r i o u s p o l i c y and resource-use c o n s t r a i n t s ; and 2) by removing l and f o r o ther uses from the f o r e s t base p r i o r to a n a l y s i s of a p a r t i c u l a r use . Models of the t imber r esource des igned to a i d in t imber management d e c i s i o n s were des i gna t ed as t imber management/supply models in Chapter I I . Such models i n vo l v e f u r t h e r a b s t r a c t i o n from the f o r e s t system than h o l i s t i c approaches , but the comp lex i t y of the mode l led environment i s g r e a t l y r educed . T h i s in tu rn reduces the i n fo rma t i on requ i rements of the model f o r any g iven l e v e l of d e t a i l . The r e s u l t a n t t imber management s t r a t e g y shou ld be compat ib le w i th the more gene ra l f o r e s t management s t r a t e g y to the extent tha t l i n k a g e s are m a i n t a i n e d . M o d e l l i n g of t imber supp ly can occur at v a r i o u s l e v e l s of agg rega t i on r ang ing from n a t i o n a l to a s p e c i f i c management u n i t . Timber supp ly m o d e l l i n g fo r a broad area i s known as ' aggrega te t imber supply a n a l y s i s ' (Marty 1969). Such a procedure i n v o l v e s i n c o r p o r a t i o n of the f o l l o w i n g p rocesses ( A l i g et a l . 1984): 1) P r o j e c t i n g changes in the f o r e s t l and base ; 2) Sampl ing and measur ing the f o r e s t i n ven to r y a c c o r d i n g to v a r i o u s c r i t e r i a and assembl ing i n ven to r y i n f o rma t i on to f a c i l i t a t e m o n i t o r i n g of changes in v a r i o u s i nven to ry s t r a t a ; 3) P r o j e c t i n g the growth and y i e l d of the t imber r e sou rce i n c l u d i n g response to v a r y i n g degrees of management; 4) P r o j e c t i n g t imber remova ls ; and 5) P r o j e c t i n g t imber investment p o t e n t i a l s and s t r a t e g i e s over t i m e . 41 An e x c e l l e n t review was p rov ided by A l i g et a l . (1984) fo r the Un i t ed S ta tes Fo r e s t S e r v i c e . Cur ren t work (Pearse et a l . 1983) i s des igned to l ead to a n a t i o n a l a n a l y s i s f o r Canada. Aggregate t imber supp ly ana l y se s w i l l not be t r e a t e d e x p l i c i t l y in t h i s c h a p t e r . The gene ra l t imber supp ly models fo rmula ted w i l l p e r t a i n on ly to l o c a l i z e d problems s p e c i f i c to a s i n g l e management u n i t . Some of the ideas p resen ted here might be i n c o r p o r a t e d in an aggregate a n a l y s i s . However, focus would s h i f t from u n c e r t a i n t y p e r t a i n i n g to s e l e c t i o n of s p e c i f i c t imber management s t r a t e g i e s to u n c e r t a i n t y r e l a t e d to o ther a spec t s of an aggregate a n a l y s i s such as p r o j e c t i n g changes in the f o r e s t l and base or p r o j e c t i n g t imber investment p o t e n t i a l s and s t r a t e g i e s over t ime . 4.2 Timber Supply M o d e l l i n g in H i s t o r i c a l P e r s p e c t i v e E lementary models have been used to a i d the d e c i s i o n maker in f o r e s t management d e c i s i o n s fo r many y e a r s . Most of the e a r l y methods were deve loped in Europe and were c l o s e l y l i n k e d to the concepts of a r e g u l a t e d f o r e s t and s u s t a i n e d y i e l d . F o r e s t growth was e s s e n t i a l l y t r e a t e d a s . a d e t e r m i n i s t i c parameter and a r a te of ha r ves t was deve loped which would u l t i m a t e l y produce a f o r e s t which would have cons tan t annua l or p e r i o d i c p r o d u c t i o n . Management of a p a r t i c u l a r i n t e n s i t y was i m p l i c i t in the growth r a te assumed and no economic c r i t e r i a were employed. These so c a l l e d ' a l l o w a b l e c u t ' or ' y i e l d r e g u l a t i o n ' models f o l l owed three b a s i c approaches : a rea c o n t r o l , volume c o n t r o l and v a r i o u s combinat ions such as the area/volume a l l o t m e n t check method. Area c o n t r o l approaches s p e c i f i e d the volume to be 42 ha rves ted as the t imber to be removed on the a rea a l l o c a t e d fo r c u t t i n g . Area was a s s i gned to be cut a c c o r d i n g to the premise of o l d e s t t imber f i r s t and e q u a l l y p r o d u c t i v e areas to be ha r ves ted in each age c l a s s in each p e r i o d . S t r i c t l y a p p l i e d to a reas of equa l p r o d u c t i v i t y , a rea c o n t r o l would t h e o r e t i c a l l y r e s u l t in a r e g u l a t e d f o r e s t by the end of a r o t a t i o n p e r i o d . The drawback to a rea c o n t r o l i s that p e r i o d i c c u t s can vary c o n s i d e r a b l y in volume i f the f o r e s t i s i r r e g u l a r in na tu re . Fu r the rmore , the volume a s s i gned to be ha r ves t ed i s comp le te l y i n s e n s i t i v e to e x i s t i n g age c l a s s d i s t r i b u t i o n s . Volume c o n t r o l approaches determine the volume to be ha r ves t ed a c c o r d i n g to the volume and d i s t r i b u t i o n of growing s tock p resen t and/or i t s i nc rement . T h i s appears to be an improvement over s imple area c o n t r o l . Dav is (1966) c l a s s i f i e d and d i s c u s s e d s e v e r a l volume c o n t r o l methods a c c o r d i n g to the type of i n f o rma t i on they r e q u i r e d fo r de t e rm in ing the c u t . Volume c o n t r o l methods have proven to be u s e f u l as an i n i t i a l s t ep i n b r i n g i n g p r e v i o u s l y unmanaged f o r e s t s under some degree of r e g u l a t i o n and tend to generate a more un i fo rm l e v e l of c u t t i n g from i r r e g u l a r f o r e s t s . They do not n e c e s s a r i l y l e ad towards a r e g u l a t e d f o r e s t . In a c t u a l p r a c t i c e , a rea and volume c o n t r o l p rocedures are o f t en used together in an area/volume a l l o tmen t system wi th a check on minimum age. T h i s p r o v i d e s the d e c i s i o n maker wi th a more complete overview of what the a c t u a l c u t t i n g l e v e l shou ld be (Roberts 1984). The major l i m i t a t i o n of these s imple methods i s t h e i r f a i l u r e to e x p l i c i t l y c o n s i d e r the p o t e n t i a l impacts of 43 d i f f e r e n t management a c t i o n s on the growth of the f o r e s t . T h i s was a necessa ry omiss ion in o rde r to keep the models s imple enough to a l l ow manual s o l u t i o n . The advent of computer t echno logy a l lowed a p p l i c a t i o n of mechan i c a l l y complex s o l u t i o n t echn iques to f o r e s t r y p rob lems. T h i s f a c i l i t a t e d more complex f o r m u l a t i o n s which b e t t e r r e f l e c t the nature of the prob lem. Problems of t imber supply and r e g u l a t i o n were among the f i r s t f o r e s t r y problems to be r e fo rmu l a t ed fo r s o l u t i o n by these t echn iques because t h e i r s t r u c t u r e appeared q u i t e amenable ( F i e l d 1977). Some of the e a r l i e s t examples of the use of these more complex f o r m u l a t i o n s were l i n e a r programming models deve loped to produce s u s t a i n e d y i e l d c u t t i n g schedu les by Jones (1960), K idd et a l . (1966) and Loucks (1964). Other e a r l y approaches i n c l u d e d the c o m p u t e r i z a t i o n of t r a d i t i o n a l area and volume c o n t r o l methods (Chappe l l e 1966, Chappe l l e and Sassaman 1968, Sassaman and Chappe l l e 1967). The l a t e s i x t i e s and e a r l y s e v e n t i e s saw the development of many computer-based t imber supply models i n c o r p o r a t i n g management a c t i o n s i n t o the development of a h a r v e s t i n g schedu le fo r the f o r e s t . The f i r s t such models to ga in widespread acceptance and a p p l i c a t i o n were MAX-MILLION ( C l u t t e r 1968, Ware and C l u t t e r 1971) and Timber RAM (Navon 1971). The l a s t decade has seen s i g n i f i c a n t improvements in computer t echno logy and so f twa re . A n a l y t i c a l p rocedures are becoming s t i l l more complex and b e t t e r r e f l e c t i v e of the t rue nature of the p rob lem. N e v e r t h e l e s s , growth i s s t i l l c o n s i d e r e d a d e t e r m i n i s t i c v a r i a b l e in many mode ls . A p a r t i c u l a r s e r i e s of 44 management a c t i o n s i s assumed to produce a p a r t i c u l a r r e sponse . The next l o g i c a l improvement to .the m o d e l l i n g procedure would be to i n c o r p o r a t e the s t o c h a s t i c nature of the p r e d i c t e d responses in an o p e r a t i o n a l l y a c cep t ab l e model . Whi le t h i s would add f u r t h e r c o m p l i c a t i o n s , i t shou ld p rov ide the d e c i s i o n maker wi th a b e t t e r i n d i c a t i o n of the p o t e n t i a l e f f e c t s of d i f f e r e n t management s t r a t e g i e s . At the p resen t t ime , the o p e r a t i o n a l development of t imber supp ly models i s at a c r o s s r o a d s . On one hand, d e t e r m i n i s t i c models are be ing made more c o m p l i c a t e d and s o l u t i o n techn iques more e f f i c i e n t , but they s t i l l ignore the u n c e r t a i n t y in the d e c i s i o n env i ronment . On the o ther hand, mathemat ica l d e c i s i o n theory has been deve loped which can r e a d i l y i n c o r p o r a t e u n c e r t a i n t y , but such t h e o r e t i c a l developments have not yet i proven e f f e c t i v e on an o p e r a t i o n a l b a s i s fo r t imber management. Beyond t h i s c r o s s r o a d s i s the t ime when s t o c h a s t i c models of t imber supp ly become common p l a c e . When t h i s w i l l happen i s con t i ngen t on improved unders tand ing of the dynamics of the f o r e s t system coup l ed wi th fundamental r e c o g n i t i o n of the sources and amount of u n c e r t a i n t y p r e s e n t . 4.3 Computer-based Timber Supply Models Timber supp ly models examine the a v a i l a b i l i t y of t imber at v a r i o u s p o i n t s i n time and space in the f u t u r e . I f the model i s an adequate r e p r e s e n t a t i o n of r e a l i t y , compar ison of d i f f e r e n t management s t r a t e g i e s may l e a d to e i t h e r a l o c a l l y optimum s t r a t e g y or at l e a s t to a p a r t i a l o r d e r i n g of s t r a t e g i e s depending on the s t r u c t u r e the model t a k e s . In a l l problems of a 45 p r a c t i c a l n a t u r e , proof tha t any p a r t i c u l a r optimum i s a g l o b a l optimum i s d i f f i c u l t because there i s always an i n f i n i t e number of management s t r a t e g i e s p o t e n t i a l l y a v a i l a b l e . I f the model conforms to p a r t i c u l a r s t r u c t u r e s i t may prove to be a n a l y t i c a l l y t r a c t a b l e , but such s t r u c t u r e s are seldom r e p r e s e n t a t i v e of the t rue nature of the p rob lem. N e v e r t h e l e s s , mathemat ica l models have proven to be of great va lue to the d e c i s i o n maker in p r o v i d i n g i n s i g h t s i n t o the complex i n t e r a c t i o n between t imber supp ly and t imber management. There are two bas i c s o l u t i o n approaches to models of t imber s u p p l y , mathemat ica l programming and s i m u l a t i o n . Each approach has seen s u f f i c i e n t use to warrant some gene ra l d e s c r i p t i o n . 4.3.1 Mathemat i ca l Programming Models Most e x i s t i n g mathemat ica l programming models of t imber supp ly are l i n e a r or q u a s i - l i n e a r in nature and employ some form of l i n e a r programming to p rov ide a s o l u t i o n . Goa l programming approaches have been used in c o n j u n c t i o n wi th l i n e a r programming to model t imber management at the same time as o ther r esource uses (see S e c t i on 4 . 1 ) , but these are not c o n s i d e r e d as s p e c i f i c t imber supply models fo r the purpose of t h i s d i s c u s s i o n . L i n e a r mode ls , a l though o f t e n not as r e p r e s e n t a t i v e of the r e a l problem as non- l i nea r mode ls , are much e a s i e r to s o l v e . L i n e a r programming models can be f u r t h e r s u b d i v i d e d i n t o Type I and Type II models on the b a s i s of t h e i r approach to m o d e l l i n g t imber supply (Johnson and Scheurman 1977). Type I models assume the f o r e s t to be d i v i d e d i n t o t reatment u n i t s , each c o n s i s t i n g of a g roup ing of s tands 46 c o n s i d e r e d to be s u f f i c i e n t l y s i m i l a r to be t r e a t e d i d e n t i c a l l y . Each management un i t may be managed a c c o r d i n g to one or more management sequences . A management sequence i s a schedu led s e r i e s of a c t i v i t i e s (management a c t i o n s ) which cove r s management of the f o r e s t e d l and over the p l a n n i n g h o r i z o n . Each management sequence i s comp le te l y d e f i n e d by p e r i o d i c inputs of l a n d , l abour and c a p i t a l and outputs of t imber volumes and revenues . The d e c i s i o n problem to be so l v ed c o n s i s t s of de te rm in ing the amount of l and in each t reatment un i t which shou ld be managed under a p a r t i c u l a r management sequence. The c o n s t r a i n t s r e q u i r e d in Type I models tend to f a l l i n t o four d i f f e r e n t c l a s s e s . Area c o n s t r a i n t s p l a c e an upper bound on the area in each treatment u n i t a v a i l a b l e to be managed. The sum of a l l the a reas managed a c c o r d i n g to d i f f e r e n t management sequences fo r any one un i t must be l e s s than or equa l to the t o t a l a rea of tha t u n i t which i s a v a i l a b l e f o r management. P e r i o d i c c o n s t r a i n t s p l a ce bounds on any p e r i o d i c requ i rements where bounds are a p p l i c a b l e . For example, the a rea which might be p l a n t e d in any one p e r i o d o f t e n r e q u i r e s bounds. Harvest f low c o n s t r a i n t s c o n t r o l the ha rves t l e v e l s du r i ng the c o n v e r s i o n of the f o r e s t to a t a rge t s t a t e . D i f f e r e n t types of c o n t r o l s are p o s s i b l e and the form of the c o n s t r a i n t v a r i e s wi th the type employed. F i n a l l y , r e g u l a t i o n c o n s t r a i n t s are r e q u i r e d to s t a b i l i z e ha r ves t l e v e l s f o l l o w i n g the c o n v e r s i o n p e r i o d . U s u a l l y these c o n s t r a i n t s r e s t r i c t the p o s t - c o n v e r s i o n ha rves t l e v e l s to a range around the a ve rage . The o b j e c t i v e f u n c t i o n , the c r i t e r i o n fo r s e l e c t i n g the l e v e l s of the d i f f e r e n t d e c i s i o n v a r i a b l e s , can take on one of a 47 number of d i f f e r e n t forms depending on the f o r m u l a t i o n of the problem by the d e c i s i o n maker. The op t ima l s o l u t i o n i s tha t combina t ion of a c t i v i t y l e v e l s which p r o v i d e s the op t ima l o b j e c t i v e va lue sub jec t to the c o n s t r a i n t s inheren t in the problem s t r u c t u r e . Type II models c o n s i d e r t reatment u n i t s to be ephemeral e n t i t i e s . Treatment u n i t s c o n s i s t of each t imber type and age c l a s s tha t i s p resen t at the beg inn ing of the p l a n n i n g h o r i z o n and e x i s t u n t i l h a r v e s t e d . New u n i t s are formed from the areas ha r ves t ed and regenera ted to a s i m i l a r s p e c i e s d u r i n g the same ha rves t p e r i o d . Any l and wi th a s i m i l a r t imber type and age c l a s s s t r u c t u r e l e f t s t and ing at the end of the p l a n n i n g h o r i z o n i s a l s o c o n s i d e r e d a t reatment u n i t . The d e c i s i o n problem c o n s i s t s of de te rm in ing the op t ima l amount of l and to cut in p e r i o d i and subsequent l y cu t in p e r i o d j f o r each spec i e s t ype . G e n e r a l l y Type II models r e q u i r e fewer d e c i s i o n v a r i a b l e s than Type I mode ls , but need more c o n s t r a i n t s . C o n s t r a i n t s are r e q u i r e d fo r each s t a r t i n g t reatment u n i t and fo r each u n i t c r e a t e d d u r i n g the p l a n n i n g h o r i z o n gove rn ing the input and output of l and from each t reatment u n i t . 4 .3 .2 S i m u l a t i o n Models U n l i k e mathemat ica l programming models of t imber s u p p l y , s i m u l a t i o n mode ls , by t h e i r very na tu re , p r e c l u d e c l a s s i f i c a t i o n by s t r u c t u r e . S i m u l a t i o n models do not seek an optimum s o l u t i o n , but r a the r p r o v i d e r e p l i e s to any number of 'what i f q u e s t i o n s . I f the model c ap tu res the essence of the r e a l wor ld p rob lem, then the r e p l i e s p rov ided shou ld be b e n e f i c i a l to the d e c i s i o n 48 maker. Many s i m u l a t i o n models have been deve loped to p r o v i d e d e c i s i o n makers wi th added i n s i g h t s i n t o the p o t e n t i a l e f f e c t s of v a r i o u s management a c t i o n s on f u tu r e t imber s u p p l y . Some have ga ined acceptance and a p p l i c a t i o n , but many have no t . The l a ck of a d e f i n i t e model s t r u c t u r e has l e d to a m u l t i t u d e of approaches . F o r e s t management games and s i m u l a t o r s deve loped in the m i d - s i x t i e s r ep resen ted the e a r l i e s t at tempts at t imber supp ly s i m u l a t i o n . (See, fo r example, C l u t t e r and Bamping 1966, Gould and O'Regan 1965, O'Regan et a l . 1966 among o t h e r s . ) These e a r l y models were q u i t e crude in compar ison wi th those of more recent v i n t age and were g e n e r a l l y used fo r t each ing purposes r a the r than as d e c i s i o n a i d s fo r a c t u a l p rob lems . L a t e r a t tempts at f o r e s t management gaming were more s o p h i s t i c a t e d and were, in g e n e r a l , more a p p l i c a b l e as a c t u a l a i d s in f o r e s t management d e c i s i o n making. (See Bare 1970; 1972 and Gould 1977 fo r examples . ) Two of the most w ide ly a p p l i e d t imber supp ly s i m u l a t i o n models are ECHO (Walker 1974,1975,1978) and TREES (Schmidt et a l . 1980, Tedder 1980, Tedder et a l . 1980). ECHO and the p resen t net worth o p t i o n of TREES f o l l ow s i m u l a t i o n a l g o r i t h m s based on supp ly and demand and employ a b ina r y i n t e r a c t i v e sea r ch techn ique to deve lop a f e a s i b l e s o l u t i o n . Whi le n e i t h e r method guarantees r e g u l a t i o n or s t a b l e ha rves t r a t e s , expe r i ence has i n d i c a t e d tha t e i t h e r model a ch i eves these (at l e a s t in terms of p r e d i c t i o n s ) w i th reasonab le s u c c e s s . The models d i f f e r from each o the r i n the manner in which growth on the marg ina l u n i t a rea i s c a l c u l a t e d and i n the way in which the a l g o r i t h m 49 i t e r a t e s u n t i l a f e a s i b l e s o l u t i o n i s ach ieved (Schmidt and Tedder 1981). 4.4 Development of a Genera l D e t e r m i n i s t i c Fo r e s t Model T h i s s e c t i o n w i l l o u t l i n e the development of a gene ra l d e t e r m i n i s t i c f o r e s t model of management s t r a t e g y and the c o r r e s p o n d i n g t imber supp l y . It i s in tended to i l l u s t r a t e the r e l a t i o n s h i p between the optimum management sequences fo r i n d i v i d u a l t reatment u n i t s (groups of i n d i v i d u a l s tands) and the t imber management s t r a t e g y fo rmu la ted fo r the f o r e s t as a whole. The development w i l l f o l l ow the approach p resen ted by W i l l i ams (1976) in tha t i t i s sepa rab le i n t o an inner and oute r model . The inner model w i l l generate p o t e n t i a l management sequences fo r each t reatment un i t wh i le the oute r model w i l l c o o r d i n a t e the a c t i o n s taken in each s tand to meet the c o n s t r a i n t s p l a ced on the f o r e s t as a whole. Any attempt at m o d e l l i n g the e f f e c t of p r o s p e c t i v e management s t r a t e g i e s fo r a f o r e s t on t imber supp ly must d e a l w i th c o n s t r a i n t s which ' r e g u l a t e ' c e r t a i n a spec t s of the f low of p a r t i c u l a r ' commod i t i e s ' to and from the f o r e s t . Timber RAM (Navon 1971), MUSYC (Johnson and Jones 1979) and o ther Type I and Type II l i n e a r programming models do t h i s d i r e c t l y , but they f o r c e the model i n t o r i g i d s t r u c t u r e s to a l l ow s o l u t i o n . Fo r e s t s i m u l a t i o n models l i k e TREES (Tedder et a l . 1979) and ECHO (Walker 1974) i n c o r p o r a t e these c o n s t r a i n t s i n t o the mathemat ica l framework of the mode l , but do not p r o v i d e an ' o p t i m a l ' s o l u t i o n wi thout e x t e n s i v e e x p l o r a t i o n . W i l l i a m ' s (1976) f o r m u l a t i o n i n i t i a l l y r e q u i r e s no s t r u c t u r a l assumpt ions 50 and i s q u i t e i l l u s t r a t i v e of the i n t e g r a l l i n k between t imber management s t r a t e g y and t imber s u p p l y . Fu r the rmore , a model s t r u c t u r e of t h i s k ind i s amenable to the e x p l i c i t i n c o r p o r a t i o n of u n c e r t a i n t y . I t w i l l serve as the b a s i s f o r the s t o c h a s t i c f o r e s t model deve loped in the next s e c t i o n . Assume the f o r e s t i s compr i sed of U t reatment u n i t s and tha t the p l a n n i n g h o r i z o n i s p a r t i t i o n e d i n t o T p e r i o d s . A management a c t i v i t y a p p l i e d to t reatment u n i t u d u r i n g time p e r i o d t i s d e f i n e d as a wh i l e the set of f e a s i b l e a c t i v i t i e s ut on u at t i s A u t « Hence, a ^ z A u t « A management sequence fo r t reatment u n i t u i s d e f i n e d as a sequence of management a c t i v i t i e s on tha t un i t ex tend ing over the whole of the p l a n n i n g h o r i z o n and i s denoted as a , a e A . u u u A t reatment u n i t at any p o i n t in time i s c h a r a c t e r i z e d by i t s management and commodity s t a t e s . The management s t a t e i s compr i sed of a set of d e s c r i p t i v e v a r i a b l e s which c o n t a i n s a l l the p e r t i n e n t i n f o rma t i on f o r p resen t and f u t u r e management d e c i s i o n s . The commodity s t a t e i s r ep resen ted by a set of v a r i a b l e s which r ep re sen t s the s t a t u s of c e r t a i n commodit ies whose d i s t r i b u t i o n a c ross the f o r e s t or over t ime i s c o n s t r a i n e d in some f a s h i o n . V w i l l be a v e c to r which r e p r e s e n t s the ut management s t a t e of t reatment u n i t u at the end of t ime p e r i o d t and C w i l l be a v e c t o r r e p r e s e n t i n g the c o r r e s p o n d i n g ut commodity s t a t e . The s t a t e s change from one p e r i o d to the next a c c o r d i n g to a s t a t e t r a n s i t i o n f u n c t i o n which i s dependent upon the i n i t i a l s t a t e v e c t o r s and the a c t i o n t aken . {V ;C } = F({V ;C J , a ) u t u t u , t - l u , t - l u t 51 A r e t u r n i s a s s o c i a t e d wi th each management a c t i o n t aken . The r e t u r n i s a f u n c t i o n of the a c t i o n and the management s t a t e of the u n i t at the t ime the a c t i o n was t aken . R = F(V , , a J ut u , t - l ' ut The r e t u r n f o r a management sequence i s found by summing the r e t u r n s a s s o c i a t e d w i th each i n d i v i d u a l a c t i o n t a k e n . T R = F(V ,a ) = x R u u u t = 1 ut The r e tu rn f o r the whole f o r e s t over the p l a n n i n g h o r i z o n i s s imp ly the sum of the management sequence r e t u r n s a s s o c i a t e d w i th each u n i t . U R = F (V ,a ) =E R u u=l C o n s t r a i n t s on the s o l u t i o n may be grouped i n t o th ree c a t e g o r i e s . 1) R e s t r i c t i o n s on the a l l o c a t i o n of c e r t a i n commodit ies a c ross the management u n i t . 2) S t r u c t u r a l r e l a t i o n s h i p s between the management s t a t e s of v a r i o u s t reatment u n i t s over t ime . 3) R e s t r i c t i o n s on the c h o i c e or the i n t e n s i t y of a management a c t i o n . The f i r s t c a t ego ry can be c o n s i d e r e d as c o n s t r a i n t s between t reatment u n i t s and the other two as c o n s t r a i n t s w i t h i n a t reatment u n i t . Commodity a l l o c a t i o n c o n s t r a i n t s w i l l be r ep resen ted in gene r a l form a s : g j ( C j u t ) = 0 f o r j = l ,...,J The second ca t ego ry of c o n s t r a i n t s i s u s u a l l y embodied in the 52 s t r u c t u r e of the model , but fo r g e n e r a l i t y they w i l l be r ep resen ted in equa t ion form a s : h (V ,a ) = 0 f o r q = 1 , . . . , Q qu u u u=1 U where Q i s the number of management s t a t e d imens ions . The t h i r d ca t ego ry determines the e lements of A and aga in i s o f t e n i m p l i c i t in the model s t r u c t u r e . They w i l l be r ep resen ted e x p l i c i t l y a s : a e A f o r u = 1 , . . . , U ut ut r = i T The gene ra l d e t e r m i n i s t i c f o r e s t model can now be expressed in mathemat ica l terms a s : ** ** F i n d a = { a u } f o r u = 1 , . . . , U ** such tha t R = F (V , a ) i s o p t i m i z e d . Sub jec t t o : 1) Commodity s t a t e t r a n s i t i o n f u n c t i o n c o n s t r a i n t s g j ( C j u t ) = 0 f o r j = 1 , . . . ,J 2) Management s t a t e t r a n s i t i o n f u n c t i o n c o n s t r a i n t s h u ( V u , a u ) = 0 f o r q = 1 , . . . , Q u=1 , . . . ,U 3) Management a c t i o n f e a s i b i l i t y c o n s t r a i n t s ** l u t e A u t a „ t e , 1 + f o r u = 1 , . . . ,U t= 1 T The problem upon which the above model i s based may be sepa ra ted i n t o two s imp le r p rob lems . The ' o u t e r ' p rob lem, termed MP1 by W i l l i a m s , c o n s i s t s of a l l o c a t i n g the commodit ies of i n t e r e s t by s e l e c t i n g management sequences from a subset of management sequences . The ' i n n e r ' p rob lem, termed MP2, c o n s i s t s of c r e a t i n g f e a s i b l e management sequences . 53 Assume a i s a set of management sequences c o n s t r u c t e d so that i t c o n t a i n s at l e a s t one f e a s i b l e s o l u t i o n . MP1 may be expressed a s : F i n d a e a such that Z = (V,a ) i s o p t i m i z e d . Sub jec t t o : g . ( C . ) = 0 fo r j=1 , , J MP2 may be exp ressed a s : * F i n d a u * such that Y =F(V , a ) i s o p t i m i z e d . u u Sub jec t t o : h (V ,a *) = 0 f o r q = 1 , . . . , Q ^ u u u u=1 U a e A f o r u = 1 , . . . , Q u t u t t = 1 , . . . , T S ince commodity a l l o c a t i o n c o n s t r a i n t s are not c o n s i d e r e d in MP2, the se t of management sequences which i s ob ta ined by s o l v i n g t h i s problem fo r each t reatment un i t w i l l o f t e n not r epresen t a f e a s i b l e s o l u t i o n f o r MP1. The necessa r y l i n k a g e s between the two problem components may be most e a s i l y unders tood i f the problem as a whole i s expressed as a s e r i a l m u l t i s t a g e sys tem. A s e r i a l m u l t i s t a g e system i n v o l v e s a sequence of d e c i s i o n s such tha t each d e c i s i o n a f f e c t s the c i r cums tances under which the next d e c i s i o n in the system w i l l be made. The input to any stage i s the output of the p r e v i ous s tage and the d e c i s i o n made at any s tage a f f e c t s a l l those f o l l o w i n g . MP1, exp res sed as a component of a s e r i a l m u l t i s t a g e sys tem, i n v o l v e s s e l e c t i n g a set of management sequences 54 (a , . . . , a y ) such that c e r t a i n c o n s t r a i n e d commodit ies are a l l o c a t e d a c r o s s the f o r e s t in an op t ima l manner. The a l l o c a t i o n must s t a r t w i th commodity l e v e l s a t known va lues ^ j ^ a n < ^ f i n i s h w i th them in a f e a s i b l e r eg i on (LB. < C . T T < UB . ) . The J - JU - 3 s tages of t h i s component w i l l be the U t reatment u n i t s . The d e c i s i o n v a r i a b l e at any stage w i l l be the management sequence a s e l e c t e d fo r tha t p a r t i c u l a r s t a g e , u The commodity s t a t e v e c to r C = (C „ , . . . , C T ) c o n t a i n s the u l u Ju s t a t e v a r i a b l e s of immediate importance to t h i s component. Each element of C c o n t a i n s the t o t a l l e v e l of a p a r t i c u l a r commodity u a f t e r s c h e d u l i n g u. u 0 C = Z c + C f o r ] = 1 , .. . , J j u i = l i j j where c . i s the amount of commodity j produced i j or consumed du r i ng stage i . The s t a t e t r a n s i t i o n f u n c t i o n computes the t o t a l commodity s t a t e r e s u l t i n g when management sequence a i s a p p l i e d . u C j u = w j u ( c j , u - l ' a u > = C j , u - 1 + c j u F O R J = 1 . . . . , J The stage r e tu rn of managing u w i th a i s s imp ly the u management sequence r e tu rn d e f i n e d p r e v i o u s l y and the t o t a l r e t u rn i s the sum of a l l the management sequence r e t u r n s . . U U T R = F (V ,a ) = Z R, = Z Z R l l t u-1 U u = l t = 1 u t The M P 1 component of the s e r i a l m u l t i s t a g e problem can now be expressed a s : * F i n d a = {a ^ , . . . ,a }^ such tha t R = i R i s o p t i m i z e d . u=l 55 Sub jec t t o : 1 ) Boundary c o n s t r a i n t s LBj < C jy < UBj f o r j = 1 , . . . , J 2) I n i t i a l l y d e f i n e d commodity s t a t e C.Q = C.° f o r j = 1 , . . . ,J 3) Commodity s t a t e t r a n s i t i o n f u n c t i o n c o n s t r a i n t s C . - W. (C. - , a ) = 0 f o r j = 1 , . . . , J J u ^ u ^ , u " u u=1 U 4) Management sequence f e a s i b i l i t y c o n s t r a i n t s a e A f o r u = 1 , . . . , U u u At each s tage of MP1, a management sequence must be s e l e c t e d so that the f i n a l r e t u r n i s maximized. T h i s r e q u i r e s the s o l u t i o n of MP2 fo r each output s t a t e of each stage of MP1. Expressed as a component of a s e r i a l m u l t i s t a g e prob lem, MP2 i n v o l v e s f i n d i n g a sequence of management a c t i o n s a = (a , . . . , a ) to app ly to each treatment un i t that w i l l u u l uT o p t i m i z e some management o b j e c t i v e d e f i n e d over the whole management u n i t . Fo rmu l a t i on and s o l u t i o n from MP2 in i s o l a t i o n of MP1 w i l l produce a management sequence f o r each t reatment un i t which i s o p t i m a l w i th r e spec t to some o p t i m a l c r i t e r i o n d e f i n e d on l y f o r tha t u n i t . O b v i o u s l y , i f t h i s combina t ion of sequences i s f e a s i b l e f o r MP1, i t w i l l a l s o be op t ima l f o r MP1. For any r e a l i s t i c problem t h i s s i t u a t i o n would be ex t reme ly u n l i k e l y to o c c u r . F e a s i b i l i t y can on l y be guaranteed by i n c o r p o r a t i n g the commodity a l l o c a t i o n c o n s t r a i n t s d i r e c t l y i n t o MP2. Each s tage of MP2 i s a d i s c r e t e t ime i n t e r v a l w i t h i n the t ime h o r i z o n of the problem ( t = 1 , . . . , T ) . Both the management 56 s t a t e and the commodity s t a t e v e c t o r s are necessa ry f o r s o l u t i o n of t h i s p rob lem. The t r a n s i t i o n of these s t a t e v e c t o r s from p e r i o d t - 1 t o p e r i o d t i s dependent upon the a c t i o n taken du r i ng t . V = F (V , ,a ) ut ut u , t - l u t C = W (C. .a ) f o r j = 1 , , J j u t j u j u , t - l ut where V i s the output management s t a t e of u t t reatment un i t u at t ime t . C_ i s the t o t a l amount of commodity j 3 u t produced or consumed a f t e r t reatment u n i t s 1 ,2 , . . . , u-1 have been schedu led and t reatment un i t u has been schedu led up to p e r i o d t . The stage r e t u r n from s c h e d u l i n g a management a c t i o n a i s ut s imply the a c t i o n r e t u r n R u t = F (V U t_^_ , a u t ) . The t o t a l r e t u rn fo r a management sequence i s the sum of a l l a c t i o n r e t u r n s in the sequence. MP2 can thus be summarized in a s e r i a l m u l t i s t a g e f a s h i o n a s : F i n d a * = (a , . . . , a ) u u l uT T such tha t R = I R. t i s o p t i m i z e d . t= l Sub jec t t o : 1) The i n i t i a l l y d e f i n e d management s t a t e of the t reatment u n i t V = v 0 uO u 2) The management s t a t e t r a n s i t i o n f u n c t i o n c o n s t r a i n t s V - F (V ,a ) = 0 f o r t = 1 , . . . , T u t u t u , t - l u t 57 3 ) The i n i t i a l l y d e f i n e d commodity s t a t e of the t reatment u n i t 0 C = C juO j u Q where C . i s the MP1 s tage u input J u s t a t e . 4) The commodity s t a t e t r a n s i t i o n f u n c t i o n c o n s t r a i n t s . C . - W. (C . -a ) = 0 f o r j = 1 , . . . , J j u t j u t j u , t - l ut t = 1 , . . . , T 5) F i n a l boundary c o n d i t i o n s ( a p p l i c a b l e on ly to t reatment u n i t U) LB < C < UB f o r j = 1 , . . . , J j " JUT- j 6) Management a c t i o n f e a s i b i l i t y c o n s t r a i n t s a e A f o r t=1 , . . . ,T ut ut 4.5 Fo rmu la t i on of a Genera l S t o c h a s t i c Model of Timber Supply In the i n t e r e s t of comp le teness , a gene ra l s t o c h a s t i c model of t imber supp ly w i l l be fo rmu la ted in the same manner as the gene ra l d e t e r m i n i s t i c model p r e sen t ed in the p r e v i o u s s e c t i o n . The i n t e n t of i l l u s t r a t i n g the development of the s t o c h a s t i c model i s not to p resen t the model i n a form which may be r e a d i l y s o l v e d , but r a the r to show the r e l a t i o n s h i p between the d e t e r m i n i s t i c and s t o c h a s t i c v e r s i o n s of the g e n e r a l , model of t imber s u p p l y . As w i l l be seen , changes to the d e t e r m i n i s t i c model w i l l be most l y c o n c e p t u a l . One major change to the complete model w i l l occur i n the i n t e r p r e t a t i o n of the s t a t e t r a n s i t i o n f u n c t i o n . Rather than the change in s t a t e from one p e r i o d to the next be ing e x a c t l y determined by the i n i t i a l s t a t e v e c t o r s and the a c t i o n t aken , a random component ( a ^) i s added to the f u n c t i o n . T h i s component 58 i s assumed to i n c o r p o r a t e the impact of a l l o the r f a c t o r s which may i n f l u e n c e the s t a t e t r a n s i t i o n f u n c t i o n . Hence the s t a t e t r a n s i t i o n f u n c t i o n becomes: {V ;C } = F({V ;C } ,a ) + a ut u t u , t - l u , t - l u t ut The outward form of the commodity a l l o c a t i o n c o n s t r a i n t s and the management s t a t e s t r u c t u r a l c o n s t r a i n t s in the model remain the same, but the a c t u a l f u n c t i o n s r ep resen ted w i l l no longer n e c e s s a r i l y be d e t e r m i n i s t i c . A s i m i l a r change i s r e q u i r e d in the r e tu rn f u n c t i o n . Rather than the r e tu rn be ing a d i r e c t r e s u l t of the input management s t a t e and the a c t i o n t aken , a random component (3 ) i s added to u t i n c o r p o r a t e a l l o ther f a c t o r s which may i n f l u e n c e the r e t u r n . The r e t u r n f u n c t i o n becomes: R . = F (V . -, ,a . ) + B . ut u , t-1 ut ut S ince R i s now a s t o c h a s t i c v a r i a b l e , the re can be many u t p o s s i b l e va lues and i t i s proper to t h i nk of the expected va lue of R r a the r than some s i n g l e v a l u e , ut I f R i s c o n s i d e r e d a d i s c r e t e v a r i a b l e w i th M p o s s i b l e u t v a l u e s , each w i th a p r o b a b i l i t y P , the expected va lue of R m ut can be expressed a s : M M E(R ) = E P (R ) where Z P = 1 ut m = l m utm m=l m I f R i s a con t inuous v a r i a b l e w i th a d e n s i t y f u n c t i o n f (R ) d e f i n e d over the i n t e r v a l - ° ° t o + 0 0 , then the expected va lue can be expressed a s : E(R ) = JR f (R ) cl where " f ( R ) cL = 1 ut -°° ut ut R U T - 0 0 ut Kut The management sequence r e t u r n (R^) and the r e t u r n f o r the whole 59 f o r e s t (R) can in tu rn be c o n s i d e r e d as expected v a l u e s , E(R ) u and E(R) r e s p e c t i v e l y . The gene r a l s t o c h a s t i c model of t imber supp ly can be expressed s y m b o l i c a l l y a s : F i n d a** = (a u ** ) f o r u = 1 , . . . , U such that E(R) i s o p t i m i z e d . Sub jec t t o : g (C ) = 0 fo r j = 1 , . . . ,J h (V ,a ) = 0 fo r q=1, . . . ,Q 3 U u u u = 1 , . . . , U a e . A f o r u = 1 , . . . , U u t u t t = 1 , . . . , T T h i s model may be separa ted i n t o an inner and oute r model i n e x a c t l y the same way as the gene ra l d e t e r m i n i s t i c t imber supp ly model . I f ijj i s d e f i n e d as the s t o c h a s t i c component in u the commodity s t a t e t r a n s i t i o n f u n c t i o n , then the MP1 component of the s t o c h a s t i c s e r i a l m u l t i s t a g e model can be expressed a s : F i n d a* = {a^ , . . . ,ajj} such tha t E(R) i s o p t i m i z e d . Sub jec t t o : LB. < C . I T < UB. f o r j = 1, . . . , J j - • j U — j C j Q = C-° f o r j = 1 , . . . , J C - W. (C. , ,a ) + . = 0 fo r j = 1 , . . . , J j u ju ] , u - l u j u u = 1 , . . . , U a e A fo r u = 1 , . . . , U u u The MP2 component of the s t o c h a s t i c s e r i a l m u l t i s t a g e model s t i l l needs to be so l v ed fo r each output s t a t e of every s tage of MP1 , I f <J> i s d e f i n e d as the random component i n the management u t s t a t e t r a n s i t i o n f u n c t i o n , then the MP2 component can be expressed a s : 60 F i n d a * = (a , . . . ,a ) u : 1 U such that E(R ) i s o p t i m i z e d , u Sub jec t t o : V = V 0 uO u V = F (V , , a ) + cb = 0 f o r t = 1 , . . . , T ut ut u , t - l u t / u t C . . = C . 0 f o r j = 1 ,...,J juO ju C - W ( C ,a ) + \p = 0 f o r j = 1 , . . . , J j u t j u t j u , t - l u t j u t t = 1 , . . . , T LB < C < UB f o r j = 1 , . . . , J j - JUT - j ( a p p l i c a b l e on l y to the Uth t reatment u n i t ) a e A fo r t=1 , ,T u t ut S o l u t i o n of t h i s model form would be d i f f i c u l t c o m p u t a t i o n a l l y . The s o l u t i o n procedure f o l l o w e d by W i l l i a m s (1976) , Wo l fe-Dantz ig d e c o m p o s i t i o n , a l t hough t h e o r e t i c a l l y a p p l i c a b l e to a s t o c h a s t i c p rob lem, would q u i c k l y run i n t o d i m e n s i o n a l i t y p rob lems . The same d i f f i c u l t y would occur i f the problem was r e s t r u c t u r e d fo r c o m p a t i b i l i t y w i th s t o c h a s t i c mathemat ica l programming p r o c e d u r e s . Some a t tempts have been made to app l y approximate p rocedures to reduce the comp lex i t y of the problem (see S e c t i o n 7 .3 ) , but none of the p rocedures yet deve loped which e x p l i c i t l y address u n c e r t a i n t y has ach i eved o p e r a t i o n a l a c cep t ance . The d i s c u s s i o n of sources of u n c e r t a i n t y in t imber management, and the a n a l y s i s of gene r a l and s p e c i f i c s o l u t i o n approaches found i n the next th ree chap t e r s shou ld p rov i de f u r t h e r i n s i g h t i n t o why t h i s might be s o . 61 CHAPTER V SOURCES OF UNCERTAINTY IN FORMULATING FOREST MANAGEMENT STRATEGIES S t r i c t l y speak ing , on l y the sources of u n c e r t a i n t y which bear d i r e c t l y on the problem of s e l e c t i n g a t imber management s t r a t e g y are d i r e c t l y a p p l i c a b l e to t h i s d i s s e r t a t i o n . To ana l yze on ly these sources i s to take a r e s t r i c t e d view of the p rob lem. It has been s t r e s s e d p r e v i o u s l y tha t the t imber management problem can on ly be p r o p e r l y unders tood w i t h i n the con tex t of managing the whole f o r e s t . In a s i m i l a r manner, d i s c u s s i o n of sources of u n c e r t a i n t y p e r t a i n i n g to the cho i c e of a t imber management s t r a t e g y can on ly be p l a c e d in contex t w i t h i n the sources of u n c e r t a i n t y a f f e c t i n g f o r e s t management as a whole . U n c e r t a i n t y en t e r s i n t o the f o r m u l a t i o n of f o r e s t management s t r a t e g i e s at many d i f f e r e n t l e v e l s . A schemat ic d iagram of the f o r e s t management d e c i s i o n env i ronment , assuming the use of a t imber supp ly model , i s p r esen ted in F i gu re 3. An attempt i s made to i l l u s t r a t e p a r t i c u l a r sources of u n c e r t a i n t y in the d e c i s i o n p r o c e s s . A major source of u n c e r t a i n t y , the ephemeral nature of the f o r e s t management problem i t s e l f , i s not r e a d i l y apparent from the f i g u r e . The f o r e s t management p rob lem, as d e s c r i b e d on page 15, i s v iewed as a gap between the a c t u a l s t a t e and the d e s i r e d s t a t e of the f o r e s t sys tem. The a c t u a l s t a t e i s in cons tan t f l u x as a r e s u l t of the implementat ion of p a r t i c u l a r management 62 F i g u r e 3 : Schematic I l l u s t r a t i o n of the Fo r e s t Management D e c i s i o n Env i ronment . ACTUAL STATE OF THE FOREST SYSTEM FOREST MANAGEMENT PROBLEM DESIRED STATE OF THE FOREST SYSTEM DIFFICULTY IN ASSESSING APPROPRIATE MEASURES OF CONTRIBUTION TO PUBLIC WELL-BEING PERCEIVED PROBLEM POLITICAL LIMITATIONS -POLICY SPECIFICATIONS OTHER RESOURCE TIMBER HARVESTING PROBLEMS * * PROBLEM I SELECTION OF "MODEL FORM OBJECTIVE "FORMULATION TIMBER SUPPLY MODEL FORMULATION AND IMPLEMENTATION OF MANAGEMENT STRATEGY -BIOLOGICAL PROCESSES . EXTERNAL FACTORS 63 a c t i o n s in concu r rence wi th the a c t i o n s of b i o l o g i c a l and p h y s i c a l p r o c e s s e s w i t h i n the system and c l i m a t i c f a c t o r s from w i thou t . The d e s i r e d s t a t e changes as p u b l i c demands fo r f o r e s t r esources change in accordance w i th t e c h n o l o g i c a l i n n o v a t i o n s , the s t a t e of the economy, and o ther f a c t o r s q u i t e e x t e r n a l to the f o r e s t system i t s e l f . S ince many changes to the f o r e s t system take a long time to man i f e s t themselves f o l l o w i n g some i n i t i a l a c t i o n , there i s no guarantee tha t the r e s u l t a n t ( a c tua l ) s t a t e of the system w i l l be on a t r a j e c t o r y toward the f u tu r e d e s i r e d s t a t e . T h i s i s t rue even i f a l l proposed changes to the p resen t s t a t e occur as p r e d i c t e d . P u t t i n g t h i s fundamental source of u n c e r t a i n t y a s i d e fo r the time b e i n g , a t t e n t i o n w i l l be d i r e c t e d fo r the remainder of t h i s chapte r to the other sources of u n c e r t a i n t y i n d i c a t e d in the f i g u r e . T h i s d i s c u s s i o n w i l l be d i v i d e d i n t o two p a r t s , sources of u n c e r t a i n t y e x t e r n a l to t imber supp ly models and sources of u n c e r t a i n t y r e s u l t i n g from the i n fo rma t i on requ i rements of t imber supply models themse l ves . 5.1 Sources of U n c e r t a i n t y E x t e r n a l to Timber Supply Models Timber supp l y models g e n e r a l l y on l y e x p l i c i t l y model the t imber r e s o u r c e . The u s e f u l n e s s of the t imber supp ly model in a i d i n g the f o r m u l a t i o n of a management s t r a t e g y r e l e v a n t to the f o r e s t management problem i s d i r e c t l y r e l a t e d to the adequacy of the l i n k a g e s ma in t a i ned wi th the o the r r esource use ca tegory subproblems. These , in t u r n , a re d i r e c t l y or i n d i r e c t l y r e l a t e d to the p e r c e p t i o n of the f o r e s t management p rob lem, the unders tand ing of the b i o l o g i c a l and p h y s i c a l b a s i s of the system 64 and the impact of f a c t o r s e x t e r n a l to the sys tem. 5.1.1 Improper S p e c i f i c a t i o n of Returns from the Fo res t  System The i n t e r p r e t a t i o n and we igh t ing of v a r i o u s r e tu rns from the f o r e s t p rov ide the s tandards by which a l t e r n a t i v e f o r e s t management s t r a t e g i e s are e v a l u a t e d . Imprec ise s p e c i f i c a t i o n of the i n d i v i d u a l c o n t r i b u t i o n of d i f f e r e n t r esource uses to some measure of the o v e r a l l r e t u rn from the f o r e s t system can l ead to s e l e c t i o n of a management s t r a t e g y o ther than the op t ima l even i f the r e t u r n s from d i f f e r e n t s t r a t e g i e s were known wi th c e r t a i n t y . E s s e n t i a l l y t h i s i s a q u e s t i o n of p e r c e p t i o n in that the problem p e r c e i v e d can be c o n s i d e r a b l y d i f f e r e n t than the a c t u a l p rob lem. Even under i d e a l c o n d i t i o n s in which a s o l u t i o n to the problem c o u l d be o b t a i n e d , the ' b e s t ' s o l u t i o n to the p e r c e i v e d problem would not l i k e l y be the ' b e s t ' s o l u t i o n to the a c t u a l p rob lem. It i s the r e s p o n s i b i l i t y of the f o r e s t management agency, and u l t i m a t e l y the p o l i t i c a l h i e r a r c h y to which the management agency i s r e s p o n s i b l e , to dec ide how r e t u r n s from d i f f e r e n t components of the f o r e s t system w i l l be weighted on p u b l i c l a n d s . C e r t a i n of the r e t u r n s , a e s t h e t i c s and r e c r e a t i o n a l va lues f o r example, are d i f f i c u l t to q u a n t i f y in monetary terms. T h i s makes t r a d e o f f s between d i f f e r e n t m ix tu res of f o r e s t r esource uses d i f f i c u l t to j u s t i f y in p u r e l y o b j e c t i v e te rms . No rma l l y , p l ann ing p rocesses fo r p u b l i c l and p rov ide o p p o r t u n i t y f o r p u b l i c i n p u t . Qu i t e o f t e n the e f f e c t s of a p l an are mon i to red du r i ng and a f t e r implementat ion and o p p o r t u n i t y i s p r o v i d e d f o r p u b l i c feedback . U n f o r t u n a t e l y , p u b l i c input tends 65 to come ma in ly from s p e c i a l i n t e r e s t groups wi th q u i t e p o l a r i z e d v i ewpo in ts and an onerous task of t r y i n g to f i n d some a c c e p t a b l e area of compromise s t i l l remains . In many s i t u a t i o n s the p u b l i c i s not we l l informed and l a c k s the necessary t r a i n i n g to unders tand the b i o l o g i c a l and economic p rocesses of the f o r e s t sys tem. There w i l l always be d i f f i c u l t y in d e f i n i n g some measure of we l l -be ing and in a s s e s s i n g how the v a r i o u s resource use components of the f o r e s t system c o n t r i b u t e to t h i s measure. T h i s i s comp l i c a t ed by the f a c t tha t s o c i a l a t t i t u d e s and p r i o r i t i e s change over t ime so that the c o n t r i b u t i o n of d i f f e r e n t r esource uses w i l l change as w e l l . I t i s f u r t h e r comp l i c a t ed by g e o g r a p h i c a l v a r i a t i o n s in both p e r c e p t i o n s o f , and requ i rements f rom, the f o r e s t . E x i s t i n g p o l i t i c a l and p l a n n i n g s t r u c t u r e s u s u a l l y p r o v i d e a mechanism fo r de te rm in ing the c o n t r i b u t i o n of v a r i o u s f o r e s t management s t r a t e g i e s to p u b l i c w e l l - b e i n g . Only in t h i s manner can a broad enough p e r s p e c t i v e be ach i eved to p l a ce l o c a l r esource use c o n f l i c t s w i t h i n the con tex t of the f o r e s t r esource as a whole. T h i s p rocess can be g r e a t l y a i ded by p u b l i c p a r t i c i p a t i o n in the p l ann ing p r o c e s s . Educa t i on of both the p u b l i c and the p o l i t i c i a n s i n v o l v e d i s e s s e n t i a l to a c h i e v i n g a p e r c e p t i o n of the f o r e s t management problem which i s c l o s e to the a c t u a l p rob lem. 66 5.1.2 P o l i t i c a l C o n s t r a i n t s The f a c t tha t management d e c i s i o n s fo r p u b l i c f o r e s t l and are u l t i m a t e l y made in a p o l i t i c a l forum imposes c e r t a i n r e s t r i c t i o n s on the s e l e c t i o n of management a c t i o n s which compr ise the f o r e s t management s t r a t e g y s e l e c t e d . There i s some p r o b a b i l i t y tha t the management a c t i o n s p r e c l uded cou ld compr ise pa r t of the optimum management s t r a t e g y . Co r tne r and Schwe i tzer (1980) cap tu red the essence of p o l i t i c a l l i m i t a t i o n s on s e l e c t i o n of p o t e n t i a l management a l t e r n a t i v e s fo r p u b l i c r esource p l a n n i n g in the Un i t ed S t a t e s . A l though t h e i r d i s c u s s i o n i s s p e c i f i c to the American s i t u a t i o n , they s t a t e d tha t much of i t c o u l d be g e n e r a l i z e d to o ther l o c a l i t i e s where p a r t i c u l a r c o n d i t i o n s h o l d . It i s apparent tha t these c o n d i t i o n s h o l d , at. l e a s t to some degree , in B r i t i s h Columbia and a c r o s s Canada as a whole . T h e i r c o n t e n t i o n i s that the b u r e a u c r a t i c nature of the p l ann ing agency p r e c l u d e s the s e l e c t i o n of c e r t a i n a c t i o n s . The s u r v i v a l of a b u r e a u c r a t i c agency i s dependent upon i t s a b i l i t y to a t t r a c t and ma in t a i n o u t s i d e p o l i t i c a l support (Rourke 1969). P l ann ing i s caught up in the very environment in which i t must o p e r a t e . Fu r the rmore , s i n ce p l a n n i n g by a p u b l i c agency i s taken as a s tance of the bureaucracy as a whole, most assumpt ions about f u tu r e c o n d i t i o n s are p o s i t i v e and growth o r i e n t e d s i n c e o ther assumpt ions c o u l d l ead to immediate p o l i t i c a l c o n f r o n t a t i o n s (Niskanen 1971). A l t e r n a t i v e s which w i l l l e a d to s i g n i f i c a n t changes in r esource a l l o c a t i o n , even in the d i s t a n t f u t u r e , c o u l d be avo ided fo r s i m i l a r reasons (Kaufman 1971, S toddard 1968). 67 P l ann ing d e c i s i o n s tend to be i s o l a t i o n i s t to the extent tha t j u r i s d i c t i o n a l o v e r l a p s o c c u r . S ince d i f f e r e n t agenc i es compete f o r budgetary d o l l a r s , c o m p e t i t i o n can occur which i s not in the best i n t e r e s t of s o c i e t y . A long-term p e r s p e c t i v e i s necessa ry to p r o p e r l y manage f o r e s t r e s o u r c e s . The p o l i t i c a l p rocess encourages d e c i s i o n makers to focus on the shor t- te rm and favor immediate p a y o f f s and de l ayed e x p e n d i t u r e s . T h i s a t t i t u d e c o u l d be d e t r i m e n t a l in the long run (Cor tner and Schwe i tzer 1980). 5 .1.3 P o l i c y S p e c i f i c a t i o n s D e c i s i o n s which are made at d i f f e r e n t h i e r a r c h i a l l e v e l s w i t h i n a f o r e s t management agency are made w i t h i n a p a r t i c u l a r con tex t s p e c i f i e d by p o l i c y e s t a b l i s h e d at h igher l e v e l s w i t h i n the h i e r a r c h y . P o l i c y s tatements attempt to u n i f y the d e c i s i o n o b j e c t i v e s of v a r i o u s d e c i s i o n makers in l i n e wi th the agency ' s o b j e c t i v e s or g o a l s . Such p o l i c i e s o f t e n have t h e i r r oo t s in l e g i s l a t i o n . P o l i c y i m p l i c i t l y or . e x p l i c i t l y d i c t a t e s the connec t i on of the t imber management d e c i s i o n to the o ther r esource l e v e l d e c i s i o n s and to the model of t imber s u p p l y . I t e s s e n t i a l l y determines the f o r e s t l and base c o n s i d e r e d a v a i l a b l e fo r t imber h a r v e s t i n g purposes and , in so d o i n g , segrega tes t imber management d e c i s i o n s from other resource-use l e v e l c o n s i d e r a t i o n s to a l a r g e e x t e n t . T h i s g r e a t l y reduces the comp lex i t y of the t imber management d e c i s i o n , but i n c r e a s e s the r i s k of p roduc ing a t imber management s t r a t e g y which i s i n compa t ib l e w i th a d e s i r a b l e s t r a t e g y fo r the f o r e s t as a 68 whole. E x i s t i n g p o l i c y a l s o d i c t a t e s the s t r u c t u r e of the t imber supply model or models employed in a i d i n g t imber management d e c i s i o n s through the s p e c i f i c a t i o n of a management p h i l o s o p h y . A commonly a ccep ted p o l i c y gove rn ing t imber management p l ann ing i s s u s t a i n e d y i e l d of some form or o t h e r . The l a s t few decades have seen c o n s i d e r a b l e d i s c u s s i o n conce rn ing the b e n e f i t s of such a p o l i c y . (See, f o r example, Beuter 1982, G i l b e r t 1982, Haley 1966, Lee 1982, Moore 1980, Waggener 1982). S t r i c t l y r e g u l a t e d even-f low seldom has been employed i n recent t imes , but such a r e g u l a t i o n concept s t i l l p r o v i d e s the r a t i o n a l e fo r the s t r u c t u r i n g of the t imber supp ly model in many c a s e s . If a s u s t a i n e d y i e l d approach i s not a p p r o p r i a t e , any t imber supply model i n c o r p o r a t i n g s u s t a i n e d y i e l d r e s t r i c t i o n s w i l l p rov ide l i t t l e u s e f u l i n f o r m a t i o n wi th regards to the management a c t i o n s which shou ld compr ise the op t ima l management s t r a t e g y . Whi le i t i s beyond the mandate of t h i s d i s s e r t a t i o n to examine in d e t a i l arguments fo r and a g a i n s t s u s t a i n e d y i e l d , i t i s worthwhi le to examine i t s i m p l i c a t i o n s w i th regard to the a p p l i c a b i l i t y of the t imber supp ly model to the op t ima l management s t r a t e g y fo r the f o r e s t . An i m p l i c i t assumpt ion of s u s t a i n e d y i e l d management i s tha t a con t inuous market w i l l e x i s t f o r a l l the t imber p roduced . I f f u t u r e demands fo r t imber p roduc ts d e c l i n e , then a more b e n e f i c i a l p o l i c y would i n vo l v e supp l y i ng more t imber when demand i s h i g h . In f a c t , when approached from a p u r e l y economic p o i n t of view i t i s d i f f i c u l t to j u s t i f y the t r a d i t i o n a l s u s t a i n e d y i e l d c o n c e p t . However, o ther f a c t o r s do e x i s t which suppor t such a p o l i c y , at l e a s t on 6 9 p u b l i c l a n d , not the l e a s t of which i s the u n c e r t a i n t y i n v o l v e d in p r e d i c t i n g f u tu r e economic c o n d i t i o n s . I f i t i s known wi th c e r t a i n t y tha t demand fo r t imber p roduc t s w i l l e s s e n t i a l l y d i sappea r in the f o r e seeab l e f u tu r e i t would be imposs ib le , to j u s t i f y managing a f o r e s t on a s u s t a i n e d y i e l d b a s i s . In the same sense , i f the r e a l va lue of t imber p roduc t s i s expected to i n c r ease s i g n i f i c a n t l y in the f u t u r e , i t would l i k e l y make sense to postpone h a r v e s t i n g some t imber and to i n ves t in more i n t e n s i v e f o r e s t management now so as to reap h ighe r b e n e f i t s t hen . U n f o r t u n a t e l y , such dramat ic changes in economic c o n d i t i o n s are norma l l y a s s o c i a t e d w i th t e c h n o l o g i c a l i nnova t i ons and imposs i b l e to p r e d i c t w i th any degree of c e r t a i n t y . R e a l i s t i c a l l y , i t i s d i f f i c u l t to g i ve much weight to economic p r e d i c t i o n s over an extended time h o r i z o n s i n c e the re are so many f a c t o r s which i n t e r r e l a t e to determine economic c o n d i t i o n s . Of ten these f a c t o r s are g l o b a l in nature and comp le te l y beyond any s o r t of l o c a l c o n t r o l . A s u s t a i n e d y i e l d p o l i c y w i l l t h e o r e t i c a l l y ensure tha t the f u tu r e p r o d u c t i v i t y of the f o r e s t l and base (as measured by t o d a y ' s c r i t e r i a f o r ' p r o d u c t i v i t y ' ) w i l l not be d i m i n i s h e d by present management a c t i o n s . Whether t h i s i s a l o g i c a l approach to t imber management d e c i s i o n s depends on what f u tu r e b e l i e f s a r e , the s t r e n g t h w i th which they are h e l d , the cos t of i n c o r r e c t d e c i s i o n s and the a t t i t u d e of the d e c i s i o n maker towards r i s k . 5.1.4 S e l e c t i o n of the Timber Supply Model (s ) Complex mathemat ica l models of long-term t imber supp ly are 70 i n t e r e s t i n g from a t h e o r e t i c a l s t andpo in t and u s e f u l f o r p r o v i d i n g an unders tand ing of the u n d e r l y i n g system, but are of l i m i t e d p r a c t i c a l va lue to the d e c i s i o n maker un l ess they are a n a l y t i c a l l y t r a c t a b l e . S i m p l i f i c a t i o n s to such models are necessary to ensure t r a c t a b i l i t y . The u n c e r t a i n t y a s s o c i a t e d w i th the a p p l i c a b i l i t y of a s o l u t i o n of a t imber supp ly model i s p a r t l y dependent upon the assumpt ions r e q u i r e d to make i t t r a c t a b l e . As such , i t i s r e l a t e d to the k ind of model employed as we l l as to the i n f o rma t i on requ i rements of the model . In o rder to p rov ide an example of how model form can i n t roduce u n c e r t a i n t y , r e f e r e n c e w i l l be made to Timber RAM. T h i s model was chosen because i t has been w ide ly a p p l i e d over the l a s t decade. The i n t e n t i s to i l l u s t r a t e how c e r t a i n model s t r u c t u r e s can i n t e r j e c t a degree of u n c e r t a i n t y i n t o the a p p l i c a b i l i t y of the model r e s u l t s , not to s i n g l e out Timber RAM as e i t h e r a p a r t i c u l a r l y bad or a p a r t i c u l a r l y good model . P r o p o r t i o n a l i t y : Timber RAM, as a l i n e a r programming mode l , r e q u i r e s an assumption of p r o p o r t i o n a l i t y in order f o r a s o l u t i o n to be d e r i v e d . T h i s means tha t average t imber y i e l d , c o s t s and revenues per u n i t a rea must be cons tan t fo r each a c t i v i t y r e g a r d l e s s of the s i z e of a rea managed w i th t h i s a c t i v i t y (Navon 1971, Chappe l l e et a l • 1976). T h i s i s not a v a l i d assumpt ion fo r average revenues and c o s t s and i t can i n t roduce some b i as to the e s t i m a t i o n of p e r i o d i c i npu t s and outputs and in the s e l e c t i o n of the op t ima l combina t ion of a c t i v i t i e s . The r e p e r c u s s i o n s of t h i s problem are not too 71 seve re , i f ca re i s taken to es t ima te the average c o s t s and revenues fo r the a reas to be managed w i th each a c t i v i t y . More r i g o r o u s p rocedures are a l s o a v a i l a b l e which can g r e a t l y reduce the s i z e of t h i s e r r o r , but on ly at the expense of h ighe r computing c o s t s . Lack of F l e x i b i l i t y : The na ture of l i n e a r programming s o l u t i o n s to t imber management problems i s such that o p t i m i z a t i o n can on l y take p l a ce over the a l t e r n a t i v e s p r o v i d e d . In o rder to keep the model to a workable s i z e , c e r t a i n assumpt ions must be made in the f o r m u l a t i o n of a l t e r n a t i v e s , o f t e n q u i t e e x t e r n a l to the model s t r u c t u r e i t s e l f . One of the major drawbacks to the o r i g i n a l v e r s i o n of Timber RAM i s the s t a t i c format in which i t a c cep t s volume input data (Chappe l l e et a l . 1976). Once the t imber c l a s s e s are set by the user and the volumes of e x i s t i n g and regenera ted t imber are e s t a b l i s h e d , the volumes e s s e n t i a l l y become s t a t i c . The volume ha r ves t ed from a p a r t i c u l a r t imber c l a s s at a p a r t i c u l a r age i s i n f l e x i b l e to p o t e n t i a l management a c t i v i t i e s which may take p l a c e . T h i s d i f f i c u l t y may be overcome, at l e a s t p a r t i a l l y , by genera t ing , a l t e r n a t i v e s in a d i f f e r e n t manner. I t i s p o s s i b l e , a l t hough time consuming and c o s t l y , to generate a l t e r n a t i v e s by hand. The 1975 v e r s i o n of Timber RAM (Navon 1975b) i s much l e s s r i g i d than the o r i g i n a l s i n ce i t p r o v i d e s fo r more a l t e r n a t i v e s fo r r egenera ted t imbe r . In g e n e r a l , any techn ique which r e s u l t s in the use of growth f u n c t i o n s r a the r than i n d i v i d u a l c l a s s y i e l d s would h e l p a l l e v i a t e the s t a t i c nature of the mode l . A c l o s e l y r e l a t e d d i f f i c u l t y i s a s s o c i a t e d w i th the 72 t reatment of regenera ted l a n d s . Once the r egene r a t i on c y c l e has begun fo r an a rea the model becomes f i x e d on t h i s c y c l e . No p r o v i s i o n i s p rov ided to d i r e c t l y account fo r some of the l and not be ing f u l l y regenera ted or be ing regenera ted to d i f f e r i n g degrees (Chappe l l e et a l . 1976). T h i s d i f f i c u l t y can be handled in a d e t e r m i n i s t i c manner by employ ing average s t o c k i n g l e v e l s fo r each t imber c l a s s and a d j u s t i n g the y i e l d of the regenera ted t imber a c c o r d i n g l y . The s e n s i t i v i t y of the s o l u t i o n to the average s t o c k i n g l e v e l s c o u l d be checked by pos t-op t ima l a n a l y s i s . If s t o c h a s t i c e lements c o u l d be i n t r oduced to the model then d i f f e r e n t s t o c k i n g l e v e l s c o u l d be d i r e c t l y i n c o r p o r a t e d . Such a mode l , however, would q u i c k l y become q u i t e complex and would l o se many of the computa t i ona l advantages a s s o c i a t e d wi th t r a d i t i o n a l l i n e a r programming models . Lack of S p a t i a l Components: Timber RAM can be d e s c r i b e d as a ' p o i n t ' model s i n ce i t does not i n c o r p o r a t e s p a t i a l components (Chappe l l e et a l . 1976). P r o s p e c t i v e a c t i v i t i e s are genera ted assuming tha t each t imber c l a s s e x i s t s in one homogeneous and con t i guous un i t r a the r than d i s t r i b u t e d over the whole f o r e s t a r e a . T h i s p r e c l u d e s e x p l i c i t c o n s i d e r a t i o n of l o c a t i o n , magnitude of s p e c i f i c area components and a c c e s s i b i l i t y which u l t i m a t e l y determines the f e a s i b i l i t y of h a r v e s t i n g p a r t i c u l a r a r e a s . T h i s can impose an a d d i t i o n a l burden on the c l a s s i f i c a t i o n system i f a reas c o n s i d e r e d c u r r e n t l y i nope rab l e a re to be i d e n t i f i e d and exc luded from the e f f e c t i v e t imber l and base . 73 The l a ck of s p a t i a l components i s not a problem of model s t r u c t u r e s i n c e l i n e a r programming can q u i t e e a s i l y i n c o r p o r a t e s p a t i a l components, but r a the r a problem of s o l u t i o n economy. I n c l u s i o n of s p a t i a l c h a r a c t e r i s t i c s would g r e a t l y i n c r ease the number of t imber c l a s s e s which must be c o n s i d e r e d in the model and hence the number of a c t i v i t i e s gene ra t ed . For an area of s u f f i c i e n t s i z e to warrant a t imber supp ly p r o j e c t i o n , the computa t iona l c a p a b i l i t y of even the l a r g e s t computers would be exceeded. The l a ck of s p a t i a l components means tha t there i s no mechanism fo r d i r e c t l y imposing p r o s p e c t i v e t r a n s p o r t a t i o n systems (p lus a host of o ther f o r e s t management i s s u e s which are i n h e r e n t l y s p a t i a l ) as c o n s t r a i n t s on f e a s i b l e s o l u t i o n s a l though the the model a ccep t s a c c e s s i b i l i t y i n d i c e s fo r the v a r i o u s t imber c l a s s e s . If t r a n s p o r t a t i o n l i m i t a t i o n s are a major c o n s i d e r a t i o n in de te rm in ing t imber supp ly then i t i s important tha t they be i n c o r p o r a t e d in some manner. D i r e c t i n c o r p o r a t i o n of s p a t i a l c o n s i d e r a t i o n s c r e a t e s the ' s o l u t i o n economy' problem mentioned p r e v i o u s l y , but i n d i r e c t i n c o r p o r a t i o n i s p o s s i b l e though l i n k a g e s w i th s p a t i a l l y s e n s i t i v e models such as Roading RAM (Navon 1975a). R e s o l u t i o n : Problem s i z e r e s t r i c t i o n s a l s o n e c e s s i t a t e the aggrega t ion of many i n i t i a l l y d e f i n e d stands i n t o r e l a t i v e l y few t imber c l a s s e s which causes a l ack of r e s o l u t i o n . The g rea te r the agg rega t i on which must take p l a c e , the l a r g e r the p o t e n t i a l l o s s of i n f o r m a t i o n . 74 Whi le i t i s p o s s i b l e to group t imber c l a s s e s on the b a s i s of p e r s o n a l e x p e r i e n c e , such an approach tends to be q u i t e a r b i t r a r y . A more r i g o r o u s approach suggested by W i l l i ams and Yamada (1976) i s to use c l u s t e r a n a l y s i s to group the o r i g i n a l l and u n i t s i n t o an a p p r o p r i a t e number of c l a s s e s . The f i n a l c l u s t e r s w i l l be most a p p l i c a b l e i f the d e s c r i p t i v e v a r i a b l e s chosen to d e s c r i b e the o r i g i n a l l and u n i t s are the most important to the model s t r u c t u r e as ev idenced by i t s s t a t e v a r i a b l e s . In t h i s manner the l e a s t amount of i n f o rma t i on important to the model i s l o s t . U s u a l l y there i s no obv ious c h o i c e f o r the optimum number or d e f i n i o n of t imber c l a s s e s . T r a d e o f f s must be made between the e f f e c t s of agg rega t i on e r r o r and the i n c r ease in computing c o s t s wi th i n c r e a s i n g numbers of c l a s s e s . 5 .1.5 Fo rmu la t i on of Model O b j e c t i v e s Timber supply models based on mathemat ica l programming approaches must have some c r i t e r i a f o r a l l o c a t i n g l and to v a r i o u s a c t i v i t i e s . G e n e r a l l y on l y t i m b e r - r e l a t e d c r i t e r i a are c o n s i d e r e d . The extent to which these c r i t e r i a r e f l e c t the o v e r a l l management o b j e c t i v e s fo r the f o r e s t a f f e c t s the a p p l i c a b i l i t y of the s o l u t i o n r e s u l t s . T r a d i t i o n a l l i n e a r programming approaches are l i m i t e d to a s i n g l e o b j e c t i v e f u n c t i o n . An o b j e c t i v e of max imiz ing volume ha r ve s t ed would l i k e l y produce a d i f f e r e n t mixture of a c t i v i t i e s and a d i f f e r e n t p i c t u r e of t imber supp ly over t ime than an o b j e c t i v e of maximiz ing revenue or m i n i m i z i n g c o s t . The d e c i s i o n maker must dec ide which o b j e c t i v e to use , or whether to look at 75 the r e s u l t s of s e v e r a l ana l y ses based on d i f f e r e n t o b j e c t i v e s . The i s sue becomes even more complex i f the d e c i s i o n of how much to cut i s a d m i n i s t r a t i v e l y separa ted from the d e c i s i o n of how to manage the f o r e s t . One p o s s i b l e means of overcoming t h i s d i f f i c u l t y would be to employ mathemat ica l programming t e chn iques such as m u l t i p l e - o b j e c t i v e l i n e a r programming or goa l programming in an attempt to approximate the m u l t i p l e o b j e c t i v e s g e n e r a l l y a s s o c i a t e d wi th f o r e s t management. (See F i e l d et a l . 1980b and Steur and Schu le r 1978 fo r examples . ) However, t h i s does not remove the d i f f i c u l t y a s s o c i a t e d wi th s p e c i f y i n g and we igh t ing the o b j e c t i v e s of f o r e s t management d i s c u s s e d in s e c t i o n 5.1.1 or of i n c o r p o r a t i n g p o s s i b l e p o l i t i c a l c o n s t r a i n t s mentioned in s e c t i o n 5 . 1 . 2 . Fur thermore , m u l t i p l e o b j e c t i v e mathemat ica l programming techn iques g e n e r a l l y l a ck the computa t i ona l e f f i c i e n c y of l i n e a r programming. Whi le f o r m u l a t i o n of an a p p r o p r i a t e o b j e c t i v e f u n c t i o n or f u n c t i o n s i s not an _ e x p l i c i t pa r t of c o n s t r u c t i n g s imu l a t i on-based t imber supp ly mode ls , i t does have i m p l i c i t e f f e c t s . T h i s i s p a r t i c u l a r l y ev iden t in the s e l e c t i o n of a p p r o p r i a t e management a c t i o n s to t e s t in such mode ls . The l e v e l of t imber which i s expected to be a v a i l a b l e remains t i e d to the management a c t i o n s expected to o c c u r . These in tu rn are r e l a t e d to the o v e r a l l f o r e s t management o b j e c t i v e s . 76 5.2 U n c e r t a i n t y A r i s i n g from Model In format ion Requirements U n c e r t a i n t y en te r s i n t o the t imber supp ly model s o l u t i o n through l a ck of complete i n f o r m a t i o n on p resen t and fu tu re c o n d i t i o n s r e q u i r e d fo r s o l u t i o n of the model . S ince the q u a l i t y and q u a n t i t y of i n f o rma t i on a v a i l a b l e d i f f e r g r e a t l y between present and f u t u r e c o n d i t i o n s and the p o t e n t i a l impacts of e r r o r s a l s o d i f f e r , a d i s t i n c t i o n w i l l be made between them in the subsequent d i s c u s s i o n . 5.2.1 U n c e r t a i n t y Regard ing Present C o n d i t i o n s In fo rmat ion on present l e v e l of t imber r e se r ve i s p rov i ded by f o r e s t i n v e n t o r i e s of some v a r i e t y or o t h e r . I f the i n ven to r y i s conducted a c c o r d i n g to some s t a t i s t i c a l l y a c c e p t a b l e sampl ing system and measurement e r r o r i s kept to a minimum through enforcement of accuracy s t anda rds , the ma jo r i t y of the e r r o r present in the i nven to ry i n f o r m a t i o n shou ld be a t t r i b u t a b l e on l y to s amp l i ng . Po in t e s t ima tes can then be q u a l i f i e d w i th a p p r o p r i a t e con f i dence l i m i t s . U n c e r t a i n t y r ega rd ing p resen t f o r e s t c o n d i t i o n s can t h e o r e t i c a l l y be reduced to c e r t a i n t y by g a t h e r i n g a complete i n f o rma t i on s e t . P r a c t i c a l l y , t h i s i s not p o s s i b l e or even d e s i r a b l e , because of the vas t s i z e of the i n f o r m a t i o n base r e q u i r e d . The i d e a l l e v e l of i n f o r m a t i o n a c q u i s i t i o n occurs at that p o i n t where the cos t of a c q u i r i n g one a d d i t i o n a l u n i t of i n fo rma t i on i s j u s t e q u i v a l e n t to the va lue of tha t i n f o r m a t i o n . There i s d i f f i c u l t y in de t e rm in ing t h i s p o i n t in p r a c t i c e because of the many f a c t o r s which i n f l u e n c e the va lue of 77 i n f o r m a t i o n . G e n e r a l l y the amount of i n f o rma t i on ga thered co r responds to some predetermined s tandard based on e x p e r i e n c e . U n c e r t a i n t y r ega rd ing p resen t c o n d i t i o n s i s norma l l y a s s o c i a t e d w i th e s t i m a t i o n of the net volume per ha o b t a i n a b l e from the d i f f e r e n t age c l a s s e s of the v a r i o u s t imber c l a s s e s and the a reas a s s o c i a t e d w i th each of t he se . Spec i e s compos i t i on of the d i f f e r e n t t imber c l a s s e s , wh i le important fo r cut a l l o c a t i o n , i s of l e s s e r importance in m o d e l l i n g long-term t imber supp ly a l t hough deduc t i ons are u s u a l l y made fo r non-commercia l s p e c i e s g roups . At tempts at f i r m i n g up these es t ima tes might at f i r s t ' appear i n t r i n s i c a l l y a t t r a c t i v e s i n ce a d d i t i o n a l i n f o rma t i on can be ga the red to reduce the u n c e r t a i n t y . Cau t ion shou ld be t aken , however, to ana l yze the c o n t r i b u t i o n of t h i s source of u n c e r t a i n t y w i t h i n the con tex t of management of the t imber r esource and the f o r e s t as a whole. Present f o r e s t c o n d i t i o n s o b v i o u s l y have a l a r g e impact on shor t- te rm p l ann ing fo r cut a l l o c a t i o n s , but t h e i r impact on the long-term t imber supp ly p i c t u r e may not be as g r e a t . In B r i t i s h Columbia fo r example, the nature of the age c l a s s d i s t r i b u t i o n over much of the p r o v i n c e i s such tha t most r eg ions s t i l l have s i g n i f i c a n t vo lumes .o f mature and overmature t imber a v a i l a b l e a l though l o c a l shor tages may s t a r t to occur as e a r l y as 1985 ( M i n i s t r y of F o r e s t s 1980c) . S ince the c o n s t r a i n t s imposed by p resen t p o l i c y and f u t u r e assumpt ions on a t imber supp ly model are c o n s i d e r a b l e , the model s o l u t i o n can be r e l a t i v e l y i n s e n s i t i v e to p resen t i n v e n t o r y l e v e l s . P resent economic c o n d i t i o n s i n d i r e c t l y i n f l u e n c e the amount 78 of m a t e r i a l thought to be p resen t by a f f e c t i n g u t i l i z a t i o n s tandards and s p e c i e s u t i l i z a t i o n . T h i s has an obv ious impact on the expected r e tu rn both to the ope ra to r and to the owner wh ich , in tu rn a f f e c t s the amount of investment r e tu rned to the f o r e s t in the form of i n t e n s i f i e d management. 5.2.2 U n c e r t a i n t y Regard ing Future C o n d i t i o n s P l ann ing of any so r t r e q u i r e s assumpt ions about f u t u r e c o n d i t i o n s . G e n e r a l l y these assumpt ions are in the form of p r e d i c t i o n s based on past t r e n d s , p resent c o n d i t i o n s and perhaps expe r imen ta l e v i dence . The f u r t h e r i n t o the f u t u r e p r o j e c t i o n s are made, the g r ea t e r the u n c e r t a i n t y a s s o c i a t e d wi th the p r o j e c t i o n s . Whereas u n c e r t a i n t y a s s o c i a t e d wi th p resen t c o n d i t i o n s can t h e o r e t i c a l l y be removed by i n f o r m a t i o n a c q u i s i t i o n , such i s not the case wi th f u t u r e c o n d i t i o n s . U n c e r t a i n t y c a n , however, be r educed . Research i n t o the b i o l o g i c a l and p h y s i c a l p rocesses of the f o r e s t system can i n c r ease unders tand ing of the response to p a r t i c u l a r management a c t i o n s . H i s t o r i c a l responses can be ana l yzed in the l i g h t of p resen t unders tand ing and w i l l p r o v i d e i n s i g h t i n t o p o t e n t i a l f u t u r e c o n d i t i o n s . Fu tu re requ i rements from the f o r e s t w i l l not be the same as the p r e s e n t . Economic c o n d i t i o n s , both i n t e r n a l and e x t e r n a l to the f o r e s t s e c t o r w i l l change. T h i s in tu rn w i l l i n f l u e n c e p e r c e p t i o n s of r e t u rn from the f o r e s t and a f f e c t the a l l o c a t i o n of f o r e s t l and to d i f f e r e n t r e sou rce use c a t e g o r i e s . Fu tu re demands fo r v a r i o u s t imber p roduc t s w i l l change as w i l l p o t e n t i a l markets fo r the p r o d u c t s . 79 H i s t o r i c a l t rends in consumption of d i f f e r e n t t imber p roduc ts w i l l p rov ide some i n s i g h t i n t o p o s s i b l e d i r e c t i o n s in the near f u t u r e . Much u n c e r t a i n t y remains wi th respec t to c o n d i t i o n s in the d i s t a n t f u t u r e s i n c e i t i s h i g h l y dependent on t e c h n o l o g i c a l i nnova t i ons and many other f a c t o r s imposs ib l e to p r e d i c t w i th any a c c u r a c y . P resent p o l i c y p r o v i d e s the manager wi th a p e r c e p t i o n of s t a b i l i t y w i th respec t to the f u t u r e . Such p e r c e p t i o n s are necessary to p rov ide a b a s i s f o r r a t i o n a l d e c i s i o n s at the present t ime . ' F a i t h ' p l a y s a l a r g e r o l e in p r o v i d i n g some s t a b i l i t y in the face of u n c e r t a i n t y (Duerr 1967, Duerr and Duerr 1975). S t r i c t l y speak ing , f u tu r e assumpt ions are seldom e x p l i c i t in p r o j e c t i o n of t imber s u p p l y . They are i m p l i c i t l y p r e s e n t , however, through e x i s t i n g and assumed p o l i c y which p rov ide the s t r u c t u r e f o r the t imber supp ly model employed. Without such i m p l i c i t assumpt ions no p r o j e c t i o n of f u tu re t imber supp ly would be p o s s i b l e . U l t i m a t e l y , the accu racy of t imber supply p r o j e c t i o n s and t h e i r a p p l i c a b i l i t y to the f o r m u l a t i o n of a p p r o p r i a t e f o r e s t management s t r a t e g y depends on how c l o s e l y the f u tu r e e n v i s i o n e d by f a i t h resembles the c o n d i t i o n s which w i l l o c c u r . T h i s we can not know. I t i s p o s s i b l e to ana l yze the impact of p resen t d e c i s i o n s under d i f f e r e n t f u t u r e c o n d i t i o n s , however. Whi le t h i s w i l l not i n d i c a t e whether p resen t p o l i c y and d e c i s i o n s are ' c o r r e c t ' , i t w i l l p rov ide some idea of p o s s i b l e r e p e r c u s s i o n s shou ld c e r t a i n c o n d i t i o n s a r i s e . T h i s shou ld h e l p the d e c i s i o n maker a c q u i r e a b e t t e r unde r s t and ing of the impact of h i s 80 c h o i c e s and hence a i d him in the d e c i s i o n p r o c e s s . The impact of assumpt ions conce rn ing f u tu r e f o r e s t c o n d i t i o n s g i ven p a r t i c u l a r management a c t i o n s now i s much more d i r e c t . The amount of t imber which w i l l be a v a i l a b l e at any t ime in the f u tu r e i s dependent upon two f a c t o r s , the t o t a l amount of f o r e s t e d l and a v a i l a b l e fo r t imber e x t r a c t i o n and the y i e l d from each of the t imber c l a s s e s compr i s i ng the l and base . P r e d i c t i o n s of the fu tu re l and base can be made from an unders tand ing of p resen t t e c h n o l o g i c a l c o n d i t i o n s and expected demands on the f o r e s t l and base from uses which are i n compa t ib l e wi th f o r e s t h a r v e s t i n g . In B r i t i s h Co lumbia , s p e c i f i c deduc t i ons are made from the e x i s t i n g l and base fo r low s i t e l a n d s , env i r onmen ta l l y s e n s i t i v e a r e a s , non-commercial t imber l a n d s , p r e d i c t e d l and a l i e n a t i o n and areas p r e s e n t l y i nope rab l e fo r t imber h a r v e s t i n g ( M i n i s t r y of F o r e s t s 1979; I980d) . Deduc t ions are norma l l y made p r i o r to t imber supp ly ana l y ses and are best e s t ima tes of l and not c o n s i d e r e d a v a i l a b l e fo r h a r v e s t i n g purposes based .on p resen t c o n d i t i o n s and a n t i c i p a t e d f u t u r e t r e n d s . Technology shou ld improve wi th t ime and t h i s may enab le the p r o f i t a b l e h a r v e s t i n g of l and p r e s e n t l y c o n s i d e r e d non-commercia l or i n a c c e s s i b l e . An i n c r ea se in the r e a l p r i c e of v a r i o u s t imber p roduc t s or the development of markets fo r p roduc t s based on s p e c i e s p r e s e n t l y c o n s i d e r e d non-commercial c o u l d have a s i m i l a r e f f e c t . A n t i c i p a t i n g such developments i s an important component in f o r e s t p l a n n i n g , but such c o n s i d e r a t i o n s can not be d i r e c t l y i n c o r p o r a t e d i n t o e x i s t i n g t imber supp ly mode ls . 81 E s t i m a t i o n of the y i e l d from d i f f e r e n t t imber c l a s s e s compr i s i ng the f o r e s t l and base i s based on an unders tand ing of f o r e s t dynamics . Y i e l d changes w i th time as a r e s u l t of complex i n t e r a c t i o n s between the b i o t i c and a b i o t i c components of the f o r e s t sys tem. Fu ture y i e l d i s a f u n c t i o n of p r e sen t s tand c o n d i t i o n s (both b i o t i c and a b i o t i c ) , response to any management a c t i o n s t aken , c l i m a t i c i n f l u e n c e s and the impact of damaging agents (pathogens , i n s e c t p e s t s , f i r e , et c e t e r a ) . See F i g u r e 4 fo r an i l l u s t r a t i o n of t h e i r r e l a t i o n s h i p s wi th one ano the r . The fundamental f a c t o r a f f e c t i n g fu tu re y i e l d from any s tand i s the present c o n d i t i o n of the stand i t s e l f . S ince the t r e e s are both the f a c t o r y and the product f o r t imber p r o d u c t i o n , the importance of p resen t i n ven to r y l e v e l i s o b v i o u s . The p h y s i c a l p r o p e r t i e s a s s o c i a t e d wi th a f o r e s t a r e a , no tab l y s i t e , p rov ide raw m a t e r i a l s fo r growth and l i m i t p r o d u c t i o n p o t e n t i a l . Management a c t i o n s i n f l u e n c e p r o d u c t i o n e i t h e r through a l t e r i n g the compos i t i on of the s tand ( s p a c i n g , t h i n n i n g , e_t c e t e r a ) or by a l t e r i n g the s i t e ( f e r t i l i z a t i o n , i r r i g a t i o n , et c e t e r a ) . Damaging agents are a n a t u r a l pa r t of the f o r e s t system. They a f f e c t f u t u r e y i e l d by a l t e r i n g the compos i t i on of the s t a n d . These agents work i n two b a s i c ways: (1) k i l l i n g or damaging s c a t t e r e d i n d i v i d u a l t r e e s throughout the l i f e of the s tand and (2) removing s i z a b l e amounts of i n ven to r y in a r e l a t i v e l y shor t p e r i o d of t ime ( c a t a s t r o p h i c m o r t a l i t y ) . The s u s c e p t a b i l i t y of a s tand to l o s s by damaging agents i s a f u n c t i o n of i t s c o n d i t i o n . Management a c t i o n s can a f f e c t l o s s to damaging agents by a c t i n g on the agents d i r e c t l y ( f o r example, 82 F i gu re 4: F a c t o r s A f f e c t i n g Fu ture Y i e l d . DAMAG AGENTS MANAGEMENT ACTIONS STAND CONDITIONS > .CLIMATIC .INFLUENCES FOREST DYNAMICS FUTURE STAND CONDITIONS by sp ray ing a f o r e s t a rea w i th p e s t i c i d e ) or i n d i r e c t l y through a l t e r i n g the c o n d i t i o n of the s t a n d . C l i m a t i c c o n d i t i o n s have d i r e c t and i n d i r e c t i n f l u e n c e s on f o r e s t dynamics . The d i r e c t e f f e c t i s through a l t e r i n g both the b i o t i c and a b i o t i c components of the f o r e s t . The i n d i r e c t e f f e c t i s through the impact of c l i m a t i c c o n d i t i o n s on the v a r i o u s damaging a g e n t s . Y i e l d p r o j e c t i o n s u s u a l l y at tempt to p r e d i c t ' a v e r age ' c o n d i t i o n s fo r a p a r t i c u l a r t imber c l a s s at some time i n the f u t u r e . The da ta which are used i n c a l i b r a t i n g such p r o j e c t i o n s a re based on o b s e r v a t i o n s of pas t growth of s i m i l a r s tands and/or o b s e r v a t i o n s of s i m i l a r s tands at v a r i o u s ages . Some 83 unders tand ing of f o r e s t dynamics i s g e n e r a l l y employed to s e l e c t a p p r o p r i a t e f u n c t i o n a l forms and to a i d in e x t r a p o l a t i n g r e s u l t s f o r management a c t i o n s wi th i n s u f f i c i e n t h i s t o r i c a l response d a t a . I n c i d e n t a l l o s s e s to damaging agents are norma l l y i n c o r p o r a t e d in the p r o j e c t e d v a l u e s . C a t a s t r o p h i c l o s s e s are norma l l y es t imated based on past t r ends and i n c o r p o r a t e d as a r e d u c t i o n in y i e l d from the v a r i o u s t imber c l a s s e s a c ros s the f o r e s t . U n c e r t a i n t y en t e r s i n t o the p r e d i c t i o n of f u tu r e y i e l d on a p a r t i c u l a r a rea as a r e s u l t of incomplete unders tand ing of the r e l a t i o n s h i p s which a f f e c t the dynamics of the s tand and as a r e s u l t of u n c e r t a i n f u tu re c o n d i t i o n s . Research i n t o the b i o l o g i c a l mechanism of change in a s tand can he lp e x p l a i n some of the r e l a t i o n s h i p s and a i d in p r e d i c t i o n , but cannot remove a l l the u n c e r t a i n t y . Future s tand c o n d i t i o n s become l e s s c e r t a i n the f a r t h e r i n t o the f u tu r e the p r o j e c t i o n i s made because of the feedback l oop i n v o l v e d in the growth p r o c e s s . In o ther words, the c o n d i t i o n of the s tand n p e r i o d s from now i s very much dependent on the c o n d i t i o n at p e r i o d n-1, which i s dependent on the c o n d i t i o n at p e r i o d n-2, and so on back to the p r e s e n t . The a p p l i c a b i l i t y of y i e l d p r e d i c t i o n s i s f u r t h e r comp l i c a t ed by incomplete unders tand ing of the e f f e c t s of d i f f e r e n t management p r a c t i c e s on f o r e s t dynamics . C o n s i d e r a b l e e f f o r t has been d i r e c t e d towards the e s t ab l i shment of managed s tand y i e l d e q u a t i o n s , - b o t h in t h i s p rov i n ce and e l sewhere , w i th some s u c c e s s . (See, f o r example, C u r t i s et a l . 1982; M i t c h e l l and Cameron 1982.) With the movement towards more i n t e n s i v e 84 management, f u tu r e t imber y i e l d s shou ld improve. The q u e s t i o n of how much they w i l l improve and how t h i s shou ld a f f e c t present l e v e l s of h a r v e s t i n g remains to be answered. The idea tha t i n c r e a s i n g the fu tu re y i e l d of t imber w i l l a l low a c o r r e s p o n d i n g i n c r ease in p resen t c u t t i n g l e v e l s , the s o - c a l l e d ' a l l o w a b l e cut e f f e c t ' ( Schwei tzer e_t a l . 1972) has been much d i s c u s s e d in the f o r e s t r y l i t e r a t u r e of the l a s t decade. It has been the sub jec t of c o n s i d e r a b l e c o n t r o v e r s y and s t rong economic arguments have been fo rmu la ted a g a i n s t i t s use fo r a l l o c a t i o n of funds . (See, f o r example, B e l l e_t a l . 1975, Lundren 1973 and Teeguarden 1973.) B a s k e r v i l l e (1978) p resen ted a p h y s i c a l l y based argument a g a i n s t the n o n - j u d i c i o u s a p p l i c a t i o n of t h i s e f f e c t and o u t l i n e d s e v e r a l p r e c a u t i o n s which he f e l t shou ld be taken p r i o r to a p p l y i n g the a l l owab l e cut e f f e c t to i n c r ease h a r v e s t i n g r a t e s . The crux of B a s k e r v i l i e ' s argument was tha t there i s c o n s i d e r a b l e u n c e r t a i n t y r ega rd ing f u tu r e y i e l d under any newly proposed management a c t i v i t y . He f e l t the a c t i v i t y shou ld be f u l l y implemented and a n t i c i p a t e d responses con f i rmed to the degree p o s s i b l e p r i o r to i n c o r p o r a t i n g t h i s e f f e c t in any p l ann ing a n a l y s i s . R e c o g n i t i o n of sources of u n c e r t a i n t y i s an important component in a r a t i o n a l d e c i s i o n p r o c e s s . However, r e c o g n i t i o n by i t s e l f i s not enough. Some e x p l i c i t or i m p l i c i t attempt to q u a n t i f y the u n c e r t a i n t y in the d e c i s i o n environment and/or to use t h i s i n f o r m a t i o n as a gu ide in making a d e c i s i o n i s necessa ry i f the d e c i s i o n maker i s to s e l e c t an a l t e r n a t i v e which i s c o n s i s t e n t wi th h i s p r e f e r e n c e s and b e l i e f s . 86 CHAPTER VI GENERAL PROCEDURES FOR DEALING WITH UNCERTAINTY AND POTENTIAL  APPLICATIONS TO TIMBER MANAGEMENT DECISIONS There are many ways of c l a s s i f y i n g the p rocedures which may be employed to i n c o r p o r a t e u n c e r t a i n t y in a d e c i s i o n s i t u a t i o n . The approach taken here i s to a r b i t r a r i l y d i v i d e the t echn iques i n t o pass i v e and a c t i v e s t r a t e g i e s . - P a s s i v e s t r a t e g i e s r e q u i r e no p r i o r knowledge of the u n c e r t a i n t y p resen t and i n vo l v e no a c t i v e i n f o rma t i on g a t h e r i n g . A c t i v e s t r a t e g i e s i n vo l v e some p r i o r knowledge of the amount of u n c e r t a i n t y p resen t and/or i n vo l v e some at tempts at i n f o r m a t i o n a c q u i s i t i o n . Arguments c o u l d be advanced conce rn ing the ass ignment of c e r t a i n of the s t r a t e g i e s . In a c t u a l d e c i s i o n s i t u a t i o n s i t i s not uncommon fo r s e v e r a l of these s t r a t e g i e s to be combined, but no d i s c u s s i o n of combined s t r a t e g i e s has been i n c l u d e d because of the l a r g e number of combina t ions p o s s i b l e . The d e s c r i p t i o n s of these t e chn iques were adapted from many s o u r c e s . At tempts were made to document these sources where a p p l i c a b l e , but o c c a s i o n a l l y d e s c r i p t i o n s from s e v e r a l sources were combined to form a d e s c r i p t i o n u n l i k e tha t found in any of the r e f e r e n c e s . In such i n s t a n c e s , the s p i r i t of the o r i g i n a l d e s c r i p t i o n s was p rese r ved to the ex tent p o s s i b l e . 6.1 Pass i ve S t r a t e g i e s Pass i ve s t r a t e g i e s are o f t e n used f o r d e a l i n g w i th u n c e r t a i n t y i n f o r e s t management d e c i s i o n s . Such s t r a t e g i e s , 87 when used by themse lves , are not very h e l p f u l . The p l ann ing h o r i z o n i s u s u a l l y too d i s t a n t and the d e c i s i o n environment too complex. C e r t a i n pas s i v e s t r a t e g i e s c o u l d prove q u i t e u s e f u l in a comprehensive d e c i s i o n system when i n t e g r a t e d w i th some a c t i v e component. Such i n t e g r a t i o n f a c i l i t a t e s the g a t h e r i n g of i n f o r m a t i o n and enab les the comp lex i t y of the d e c i s i o n environment to be r e cogn i zed and then reduced through m o d e l l i n g . 6.1.1 Game Theory S t r a t e g i e s These s t r a t e g i e s are w ide ly d e s c r i b e d in t e x t s d e a l i n g wi th game theory ( f o r example, Luce and R a i f f a 1957; Shubik 1964). F o r e s t r y p u b l i c a t i o n s which p rov ide some d e s c r i p t i o n of these s t r a t e g i e s i n c l u d e Dav is (1968) , B e l l and F i g h t (1976) and F i g h t and B e l l (1977) . Four t echn iques are u s u a l l y c o n s i d e r e d under the gene ra l term of game theory s t r a t e g i e s . There i s no b a s i s f o r s e l e c t i n g one approach over another other than the a t t i t u d e of the d e c i s i o n maker. Each of the game theory s t r a t e g i e s i n v o l v e c o n s t r u c t i o n of a d e c i s i o n mat r ix compr ised of the p o s s i b l e a l t e r n a t i v e s and s t a t e s of n a t u r e . The i n t e r a c t i o n of each a l t e r n a t i v e wi th each s t a t e of na ture (the outcome) must be r ep resen ted by some s i n g l e measure of p r e f e r e n c e . The i n d i v i d u a l s t r a t e g i e s are d e s c r i b e d below, assuming the outcomes are c o n s i d e r e d as l o s s e s . S i m i l a r approaches are a v a i l a b l e i f the outcomes are l i s t e d as p a y o f f s , but the names of the s t r a t e g i e s and the a c t u a l p rocedures i n v o l v e d may have to be r e v i s e d to some e x t e n t . 88 ( i ) Minimax C r i t e r i o n : T h i s approach i s recommended in game theory when p l a y i n g aga ins t a t h i n k i n g opponent , in a zero-sum game, who has the same p r i o r knowledge of the p a y o f f s as y o u r s e l f . In a game aga ins t an u n t h i n k i n g opponent ( na ture ) t h i s approach has p e s s i m i s t i c over tones s i n ce the b a s i c assumpt ion i s that the worst tha t c o u l d happen w i l l happen. G iven these c i r c u m s t a n c e s , the best procedure i s to s e l e c t the a l t e r n a t i v e whose maximum l o s s under any s t a t e i s the l e a s t amongst a l l the a l t e r n a t i v e s . ( i i ) Minimum C r i t e r i o n : T h i s approach assumes tha t the best s t a t e of na ture w i l l o c cu r . Hence, the best s t r a t e g y would be to s e l e c t the a l t e r n a t i v e which has the sma l l e s t p o t e n t i a l l o s s . O b v i o u s l y , t h i s s t r a t e g y r e q u i r e s an o p t i m i s t i c o u t l o o k . ( i i i ) L ap l a ce C r i t e r i o n : T h i s techn ique i s o c c a s i o n a l l y known as the c r i t e r i o n of r a t i o n a l i t y . S ince no knowledge i s assumed to be a v a i l a b l e conce rn i ng the p r o b a b i l i t y of the d i f f e r e n t s t a t e s , t h i s approach advocates a s s i g n i n g equa l p r o b a b i l i t i e s to each of the p o t e n t i a l s t a t e s . The a c t i v i t y which p r o v i d e s the l e a s t expected l o s s under these c o n d i t i o n s i s the one which shou ld be s e l e c t e d . ( i v ) Minimax Regret C r i t e r i o n : T h i s s t r a t e g y works s i m i l a r l y to that of minimax except that the p a y o f f s are expressed as r e g r e t s r a the r than as l o s s e s . Regrets are expressed f o r each a l t e r n a t i v e under a g iven s t a t e as the d i f f e r e n c e between the lowest p o s s i b l e l o s s under tha t s t a t e and the l o s s f o r tha t 89 a l t e r n a t i v e . The a l t e r n a t i v e which p r o v i d e s the maximum r eg r e t which i s lowest amongst the maximum r e g r e t s fo r a l l the a l t e r n a t i v e s would be the one to s e l e c t a c c o r d i n g to t h i s c r i t e r i o n . Game theory s t r a t e g i e s have l i m i t e d p o t e n t i a l f o r a p p l i c a t i o n in the cho i c e of t imber management s t r a t e g i e s . An important l i m i t i n g f a c t o r i s the requirement of a d e c i s i o n m a t r i x . In o rder to be u s e f u l , such a mat r ix must be of a workable s i z e . T h i s means a tremendous r e d u c t i o n in the number of a l t e r n a t i v e s which may be c o n s i d e r e d as we l l as an a r b i t r a r y s e p a r a t i o n of a con t inuous complex of e x t e r n a l and i n t e r n a l v a r i a b l e s which r ep resen t the s t a t e s of na ture and the management s t a t e v a r i a b l e s r e s p e c t i v e l y i n t o a r e l a t i v e l y sma l l number of mutua l l y e x c l u s i v e and c o l l e c t i v e l y exhaus t i v e p o t e n t i a l outcomes. P re f e rence measures must a l s o be a s s o c i a t e d w i th each of these outcomes, but t h i s i s common to many approaches . Reduct ion of a l a r g e number of a l t e r n a t i v e s to a r e l a t i v e l y sma l l number of c and ida te a l t e r n a t i v e s may not be too d i f f i c u l t depending on e x i s t i n g p o l i c y r e s t r i c t i o n s . L i n e a r programming may be used to generate f e a s i b l e a l t e r n a t i v e s as can e x p l o r a t i o n through s i m u l a t i o n p r o c e d u r e s . Past expe r i ences and/or p resen t commitment l e v e l s can a l s o l i m i t the number of a l t e r n a t i v e s c o n s i d e r e d . I t i s the s e p a r a t i o n of the cont inuum of v a r i a b l e s which determine the response of the f o r e s t to a p a r t i c u l a r a l t e r n a t i v e , and g i ven a p a r t i c u l a r c o n d i t i o n , p r e d i c t i o n of the r e sponse , which c r e a t e s d i f f i c u l t y . 90 Another source of concern i n v o l v e s the cho i c e of an a p p r o p r i a t e procedure from w i t h i n the game theory s t r a t e g i e s a v a i l a b l e . The p o s i t i o n that the d e c i s i o n maker, who on p u b l i c l and i s u l t i m a t e l y the agent of the p u b l i c , shou ld take i s a sub jec t which can l ead to c o n s i d e r a b l e p h i l o s o p h i c a l deba te , but no c l e a r answer. However, the u l t i m a t e drawback of game theory s t r a t e g i e s in p a r t i c u l a r and p a s s i v e s t r a t e g i e s in gene ra l i s tha t they e s s e n t i a l l y ignore whatever i n f o rma t i on ( e i t h e r s u b j e c t i v e or o b j e c t i v e ) the d e c i s i o n maker may have r ega rd ing the l i k e l i h o o d of v a r i o u s s t a t e s . They a l s o p r e c l ude the p o s s i b i l i t y of i n c o r p o r a t i n g any a d d i t i o n a l i n f o rma t i on which may be a v a i l a b l e . 6 .1 .2 S t r a t e g i e s fo r Reducing Pe r c ep t i ons of U n c e r t a i n t y The s t r a t e g i e s d e s c r i b e d under t h i s heading are o f t en used by d e c i s i o n makers but not o f t e n advoca ted . U n c e r t a i n t y i s not d e a l t w i th e x p l i c i t l y , but r a the r the whole i s sue i s s i de s t epped t e m p o r a r i l y . U n f o r t u n a t e l y , u n c e r t a i n t y s t i l l i n f l u e n c e s the outcome of the a l t e r n a t i v e s e l e c t e d a l t hough i t i s reduced or exc luded from the d e c i s i o n env i ronment . Complete d e s c r i p t i o n s of these t e chn iques are a v a i l a b l e in MacCrimmon and T a y l o r (1976) and c e r t a i n of them d i s c u s s e d in MacCrimmon (1974b) . ( i ) Ignore U n c e r t a i n t y : T h i s approach i n v o l v e s r e f u s i n g to e x p l i c i t l y r e c o g n i z e the sources of u n c e r t a i n t y and r i s k in the d e c i s i o n env i ronment . The s t a t e which the d e c i s i o n maker assumes i s most l i k e l y to occur i s s imp ly assumed to o c c u r . T h i s reduces 91 the d e c i s i o n environment to one of c e r t a i n t y and makes the s e l e c t i o n of an a l t e r n a t i v e much e a s i e r , e s p e c i a l l y in complex d e c i s i o n s i t u a t i o n s . ( i i ) Reduce to C e r t a i n t y : Rather than ignore u n c e r t a i n t y comp le t e l y t h i s approach i n v o l v e s a c t i n g as i f u n c e r t a i n events are more c e r t a i n than they r e a l l y a r e . Of ten such a s t r a t e g y i s employed a f t e r a p a r t i c u l a r d e c i s i o n has been made. In such s i t u a t i o n s the d e c i s i o n maker tends to conv ince h imse l f tha t f a v o r a b l e events w i l l o c c u r . T h i s can i n f l u e n c e f u tu r e d e c i s i o n s in the same a r e a . ( i i i ) De l a y : Some u n c e r t a i n t y may be removed by d e l a y i n g d e c i s i o n s . However, such a s t r a t e g y i s a p p l i c a b l e on ly to a l i m i t e d number of s i t u a t i o n s . No a c t i o n i s i t s e l f a d e c i s i o n a l t e r n a t i v e and the d e c i s i o n maker must be p repared to accep t the l o s s a s s o c i a t e d wi th any d e l a y . ( i v ) Absorb U n c e r t a i n t y : Large o r g a n i z a t i o n s tend to absorb u n c e r t a i n t y . U n l i k e other approaches , t h i s does not occur as a s p e c i f i c p o l i c y , but r a the r because of the nature and s t r u c t u r e of the o r g a n i z a t i o n . In fo rmat ion o f t e n appears more c e r t a i n as i t i s passed a l ong to d i f f e r e n t d e c i s i o n making u n i t s in an o r g a n i z a t i o n and i t s i n i t i a l u n c e r t a i n t y g r a d u a l l y d i s a p p e a r s . I f p r e c i s e i n f o r m a t i o n i s r e q u i r e d , ca re must be taken to ensure tha t the use rs know the degree of u n c e r t a i n t y i n v o l v e d . 92 Ignor ing u n c e r t a i n t y , or at l e a s t f a i l i n g to e x p l i c i t l y c o n s i d e r u n c e r t a i n t y and r i s k in the d e c i s i o n env i ronment , i s a s tandard approach in t imber supp ly m o d e l l i n g . U s u a l l y the assumpt ion i s made tha t the outcome c o n s i d e r e d most l i k e l y to o c c u r , w i l l o c c u r . The i n t e n t i o n beh ind t h i s approach i s to t r y to s i m p l i f y the d e c i s i o n environment at l e a s t w i th regards to the m o d e l l i n g of t imber s u p p l y . It i s f e l t tha t u n c e r t a i n t y can be i m p l i c i t l y c o n s i d e r e d when making the f i n a l c h o i c e of t imber management s t r a t e g y . Whi le such an approach was c e r t a i n l y j u s t i f i e d in the p a s t , the advent of h i gh speed computers and the advance of d e c i s i o n theory no longer r e q u i r e s such s i m p l i f y i n g a ssumpt ions . In f a c t , f a i l u r e to e x p l i c i t l y r e cogn i ze the u n c e r t a i n t y i n vo l v ed removes an important c r i t e r i o n when c o n s i d e r i n g a c h o i c e among s e v e r a l t imber management s t r a t e g i e s and can l ead to some of the d i f f i c u l t i e s c o n s i d e r e d below. Reduct ion to c e r t a i n t y c an , and does , occur f o l l o w i n g t imber management d e c i s i o n s . Subsequent d e c i s i o n s , e i t h e r on the pa r t of the government or on the pa r t of the i n d u s t r i a l use rs of the f o r e s t , may be based on the premise that the t imber management s t r a t e g y s e l e c t e d w i l l enab le the h a r v e s t i n g p a t t e r n chosen to be f o l l o w e d i n d e f i n i t e l y . T h i s i s not n e c e s s a r i l y the c a s e . The b i o l o g i c a l f ounda t i on u n d e r l y i n g p r o j e c t i o n s of t imber supply i s not comp le t e l y unde r s tood , the amount of l and a l l o c a t e d fo r t imber p r o d u c t i o n may v a r y , f u t u r e t e c h n o l o g i c a l changes may a f f e c t both the fu tu re demand and supp ly of t imbe r , et c e t e r a . In s h o r t , f u t u r e ha rves t l e v e l s are t e n t a t i v e at b e s t . 93 U s u a l l y government a g e n c i e s , through implementat ion of v a r i o u s p o l i c i e s , t r y to p rov i de some sense of s t a b i l i t y . C u t t i n g l e v e l s are set f o r a s p e c i f i c p e r i o d , t enures of v a r i o u s forms are o f f e r e d and other i n c e n t i v e s are p r o v i d e d to encourage investment by p r i v a t e i n d u s t r y based on a r i g h t to a c e r t a i n p o r t i o n of the t imber a v a i l a b l e on p u b l i c f o r e s t l a n d . Whi le such government assurances are important inducements to investment and deve lopment , they do not remove a l l the r i s k p r e s e n t . Ra the r , a c o n s i d e r a b l e p o r t i o n of the r i s k i s s h i f t e d onto the government, and u l t i m a t e l y back to the p u b l i c to which the f o r e s t r e sou rce b e l o n g s . In view of the c o n s i d e r a b l e amount of r i s k i n v o l v e d there i s a d e f i n i t e need to study the wea l th of r i s k sha r i ng l i t e r a t u r e a v a i l a b l e and to examine government p o l i c i e s in l i g h t of p o t e n t i a l r i s k . s h a r i n g s t r a t e g i e s . P r i o r to such an u n d e r t a k i n g , however, i t would be prudent to a c q u i r e a b e t t e r unde rs t and ing of the amount and sources of u n c e r t a i n t y p resen t in f o r e s t management d e c i s i o n s . Delay i s of l i t t l e va lue as a f o r e s t management s t r a t e g y . A l l owab l e c u t t i n g l e v e l s are r e q u i r e d on a p e r i o d i c b a s i s and pos tpon ing a d e c i s i o n on h a r v e s t i n g l e v e l i n v o l v e s an ex tens ion of the s t a t u s quo which i s in i t s e l f a d e c i s i o n . E s t a b l i s h i n g a morator ium on t imber h a r v e s t i n g u n t i l more i n f o r m a t i o n i s p resent i s seldom a v i a b l e a l t e r n a t i v e over an e x t e n s i v e a rea s i n ce there are u s u a l l y demands fo r e x i s t i n g t imber and commitment l e v e l s to be met. U n c e r t a i n t y does tend to be absorbed as the d e c i s o n p rocess proceeds from the a n a l y s i s of t imber supp ly to the f i n a l c h o i c e of a h a r v e s t i n g p a t t e r n and s e l e c t i o n of a management s t r a t e g y . 94 T h i s l eads to a r educ t i on to c e r t a i n t y and the a s s o c i a t e d d i f f i c u l t i e s mentioned above. T h i s i s , in p a r t , a product of f a i l i n g to e x p l i c i t l y r e cogn ize the u n c e r t a i n t y i n v o l v e d which i s a common f a u l t of a l l p a s s i v e s t r a t e g i e s employed without the b e n e f i t of a s s o c i a t i o n wi th any a c t i v e s t r a t e g y . 6 .1 .3 Gene ra t i on of A l t e r n a t i v e s U s u a l l y the d e c i s i o n maker r e q u i r e s not on ly more a l t e r n a t i v e s , but a l s o more c r e a t i v e a l t e r n a t i v e s . Techniques such as B r a i n s to rm ing (Osborn 1941) and S y n e c t i c s (Gordon 1961; P r i n ce 1968) have been deve loped to a i d in f o rmu l a t i ng a l t e r n a t i v e s in a group s e t t i n g and have been w ide l y a p p l i e d . Other l e s s e r known techn iques ( e . g . goa l f o c u s i n g , c h e c k l i s t s , e l i m i n a t i o n approach) may a l s o prove u s e f u l in gene ra t i ng a l t e r n a t i v e s in both i n d i v i d u a l and group d e c i s i o n s i t u a t i o n s . These and o ther approaches were d e s c r i b e d Olson (1980) . A l though a l t e r n a t i v e gene ra t i on w i l l reduce u n c e r t a i n t y through i n c r e a s i n g the i n s i g h t the d e c i s i o n maker has about the prob lem, i t does not a l l e v i a t e the u n c e r t a i n t y connected w i th the outcomes of the v a r i o u s a l t e r n a t i v e s . In order to be e f f e c t i v e , a l t e r n a t i v e gene ra t i on must be supplemented by some means of t e s t i n g the e f f e c t s of the d i f f e r e n t a l t e r n a t i v e s . One d i r e c t approach would be s i m u l a t i o n . However, in order to c o n s t r u c t a s i m u l a t i o n model of an u n c e r t a i n s i t u a t i o n , some knowledge about the range of u n c e r t a i n t y p resen t must be a v a i l a b l e . 95 Genera t ion of the necessa ry a l t e r n a t i v e s i s g e n e r a l l y not a problem in t imber management d e c i s i o n s . As ment ioned p r e v i o u s l y in t h i s s e c t i o n , d i f f i c u l t y i s more o f t e n a s s o c i a t e d wi th r educ ing the number of a l t e r n a t i v e s c o n s i d e r e d to a workable number than w i th gene r a t i ng them. P o l i c y , p resen t techno logy l e v e l s and c a p i t a l l i m i t a t i o n s in most cases r e a d i l y suggest a c and ida te set of t imber management s t r a t e g i e s from which to s e l e c t a course of a c t i o n . On the other hand, i f the much broader i s sue of f o r e s t management i s c o n s i d e r e d , there i s d e f i n i t e l y a g r ea t e r need fo r new and more c r e a t i v e a l t e r n a t i v e s and a l t e r n a t i v e gene ra t i on t e chn iques c o u l d be a u s e f u l a i d . 6 .1 .4 S t r a t e g i e s fo r Changing Adverse Consequences These approaches a l l ow the d e c i s i o n maker to cope wi th u n c e r t a i n t y by r educ ing the r i s k i n v o l v e d in commit t ing a l l h i s r e s o u r c e s . S t r a t e g i e s such as d i v e r s i f i c a t i o n , c o n t r a c t u a l arrangement and insurance a l l f a l l under t h i s head ing . Another o f t e n a p p l i e d techn ique which can be c o n s i d e r e d w i th t h i s group of s t r a t e g i e s i s a d a p t a t i o n . I f p r o p e r l y a p p l i e d , adap t a t i on may be a good approach , but too o f t e n the c a p a c i t y to adapt i s b u i l t up at the expense of e x p l i c i t l y d e a l i n g w.ith u n c e r t a i n t y . A more complete d e s c r i p t i o n of these s t r a t e g i e s i s found in MacCrimmon and T a y l o r (1976) . Of the approaches ment ioned above, a d a p t a t i o n i s the most p e r t i n e n t to the s e l e c t i o n of an a p p r o p r i a t e t imber management s t r a t e g y . In an environment known to c o n t a i n as much u n c e r t a i n t y 96 as the f o r e s t system, the need to adapt in l i g h t of f u t u r e i n f o r m a t i o n and changing needs i s o b v i o u s . The s t r a t e g y of a d a p t a t i o n can be f u r t h e r s u b d i v i d e d i n t o f requent r e p l a n n i n g and m a i n t a i n i n g o p t i o n s . F requent r ep l ann ing i s a n e c e s s i t y in an u n c e r t a i n env i ronment . Timber management p l ans are u s u a l l y c o n t i n u o u s l y rev iewed and harves t l e v e l s r e c a l c u l a t e d at p e r i o d i c i n t e r v a l s in o rde r to keep abreas t of c u r r e n t c o n d i t i o n s . Rep l ann ing , however, i s not of much b e n e f i t un l e s s the manager has o p t i o n s a v a i l a b l e to h im. In terms of managing the t imber r e s o u r c e , the number of o p t i o n s may be kept l a r g e by m a i n t a i n i n g h igh l e v e l s of i n v e n t o r y . 6 .1 .5 N o n d e l i b e r a t e d D e c i s i o n s These are d e c i s i o n s which are made a c c o r d i n g to a r u l e or set of r u l e s . Of ten the r o u t i n e nature or the comp lex i t y of the problem r e q u i r e tha t some f i r m r u l e s or p o l i c i e s be a p p l i e d to so l v e the problem r a the r than d e l i b e r a t e about the d e c i s i o n . I f c e r t a i n problems were not hand led in t h i s manner, the d e c i s i o n maker would be swamped wi th many l a r g e , d i f f i c u l t to so l ve p rob lems . T h i s approach can c r e a t e a d d i t i o n a l p rob lems , however, i f the d e c i s i o n r u l e s are not c r i t i c a l l y e va l ua t ed p e r i o d i c a l l y to ensure that they are s t i l l a p p r o p r i a t e fo r the s i t u a t i o n . Fu r the r d i s c u s s i o n of the s t r a t e g i e s i n v o l v e d and the advantages and shor tcomings of t h i s approach may be found in Duerr (1974b), Duerr and Duerr (1975) and Marquis (1975) . 97 Nonde l i be r a t ed d e c i s i o n r u l e s are p e r v a s i v e in f o r e s t management. Some premises must be taken as g i ven in order tha t a d e c i s i o n may be reached wi th as l i t t l e d i f f i c u l t y as p o s s i b l e . In management of p u b l i c f o r e s t l and these r u l e s are expressed as p o l i c i e s which govern the a l l o c a t i o n of l and amongst v a r i o u s uses and f u tu r e e x p e c t a t i o n s from the l a n d . N o n d e l i b e r a t e d d e c i s i o n r u l e s set the con tex t w i t h i n which t imber supp ly may be mode l led and a l l o w a b l e cut d e c i s i o n s made. Nonde l i be r a t ed d e c i s i o n r u l e s s h i f t u n c e r t a i n t y to a h igher h i e r a r c h i a l l e v e l . T h i s c r e a t e s an i l l u s i o n of c e r t a i n t y wi th regards to the a spec t s of the d e c i s i o n environment covered by such r u l e s . Care must be taken not to assume tha t the outcome a s s o c i a t e d wi th a d e c i s i o n made under these c o n d i t i o n s w i l l n e c e s s a r i l y o c c u r . N o n d e l i b e r a t e d d e c i s i o n r u l e s can be v i s u a l i z e d as a l l o w i n g d i f f e r e n t amounts of freedom for the d e c i s i o n maker to s e l e c t a t imber management s t r a t e g y fo r a p a r t i c u l a r a r e a . At one extreme r u l e s may be q u i t e minimal and p rov i de l i t t l e guidance beyond s t a t i n g who i s r e s p o n s i b l e fo r the d e c i s i o n . T h i s i s o b v i o u s l y not enough guidance in a d e c i s i o n environment as complex as tha t of f o r e s t management. On p u b l i c l a n d , the d e c i s i o n maker i s a c t i n g as an agent f o r the p u b l i c and there must be some r u l e s govern ing h i s d e c i s i o n s to ensure c o m p a t i b i l i t y w i th d e c i s i o n s fo r o ther a reas and fo r the same area in the f u t u r e . The p u b l i c needs some assurance that such d e c i s i o n s are not p u r e l y a r b i t r a r y and tha t t h e i r i n t e r e s t s are be ing p r o t e c t e d . The f o r e s t i n d u s t r y a l s o needs some assurance of a c o n t i n u i n g wood supp ly be fo re investments in manufac tu r ing of wood p roduc t s and 98 perhaps in management of the f o r e s t l ands are made. At the o ther extreme, n o n d e l i b e r a t e d d e c i s i o n r u l e s can be q u i t e c o n f i n i n g and s t a t e s p e c i f i c a l l y what the f o r e s t management s t r a t e g y shou ld be , g iven p a r t i c u l a r c o n d i t i o n s . At t h i s l e v e l s e l e c t i o n of a f o r e s t management s t r a t e g y ceases to become a d e c i s i o n and i s s imp ly a f u n c t i o n of the a s c e r t a i n e d c o n d i t i o n s . T h i s has the e f f e c t of e x p l i c i t l y removing u n c e r t a i n t y from present d e l i b e r a t i o n s , but not from fu tu re c o n d i t i o n s . Such a system of r u l e s would be i d e a l f o r a d e t e r m i n i s t i c system o p e r a t i n g w i t h i n a s t a t i c e x t e r n a l env i ronment , but not fo r s e l e c t i o n of a t imber management s t r a t e g y . Even i f the f o r e s t system i t s e l f were we l l enough unders tood tha t r u l e s c o u l d be e s t a b l i s h e d govern ing a l l p o s s i b l e c o n t i n g e n c i e s , l i m i t e d c o n t r o l e x i s t s over e x t e r n a l i n f l u e n c e s and any s i g n i f i c a n t change would r e q u i r e a new set of r u l e s . A c t u a l procedures f o r s e l e c t i n g a t imber management s t r a t e g y shou ld g e n e r a l l y f a l l somewhere between these two ext remes. Every p r o s p e c t i v e s i t u a t i o n can not be v i s u a l i z e d and a p p r o p r i a t e r u l e s p r o v i d e d . A l s o i t i s necessa ry to d e f i n e the scope of the problem and p r o v i d e the d e c i s i o n maker w i th a framework w i t h i n which to work. The exact demarcat ion between n o n d e l i b e r a t e d d e c i s i o n r u l e s and a c t u a l d e c i s i o n a n a l y s i s v a r i e s from j u r i s d i c t i o n to j u r i s d i c t i o n . As a gene ra l r u l e , the g rea te r the unders tand ing of the b i o l o g i c a l system and a p p r o p r i a t e t r a d e o f f s between d i f f e r e n t l e v e l s of r esource uses , the l e s s r e s t r i c t i v e w i l l be the set of n o n d e l i b e r a t e d d e c i s i o n r u l e s and the broader the boundar i e s of the d e c i s i o n a n a l y s i s . 99 6.2 A c t i v e S t r a t e g i e s A c t i v e s t r a t e g i e s have not seen widespread use in d e a l i n g wi th u n c e r t a i n t y fo r f o r e s t management pu rposes . The use of such s t r a t e g i e s i m p l i e s an e x p l i c i t r e c o g n i t i o n tha t u n c e r t a i n t y i s p resent and tha t i t can be q u a n t i f i e d to some e x t e n t . Such r e c o g n i t i o n u s u a l l y has been l a c k i n g in the s e l e c t i o n of t imber management s t r a t e g i e s in the p a s t . Reasons f o r t h i s i n c l ude the comp lex i t y of the .p rob lem and l a ck of knowledge about the f o r e s t system in gene ra l and about sources of u n c e r t a i n t y in pa r t i c u l a r . A c t i v e approaches a l low the d e c i s i o n maker to i n c o r p o r a t e h i s knowledge of the f o r e s t system and the u n c e r t a i n t i e s p resent i n t o the s e l e c t i o n of a t imber management s t r a t e g y . Whi le such procedures do not guarantee ' r i g h t ' answers (because the i n fo rma t i on w i l l not be p e r f e c t and there w i l l a lways be some element of r i s k i n v o l v e d ) , they do he lp ach ieve d e c i s i o n s which are c o n s i s t e n t w i th the b e l i e f s and p r e f e r e n c e s of the d e c i s i o n maker. F u r t h e r , such approaches can be used to a s c e r t a i n the va lue of p e r f e c t i n f o r m a t i o n . T h i s would suggest some bound on what shou ld be spent to a c q u i r e a d d i t i o n a l i n f o rma t i on to r e l i e v e some of the u n c e r t a i n t y p r e s e n t . 6.2.1 S t r a t e g i e s fo r M o d e l l i n g U n c e r t a i n t y The p rocess of m o d e l l i n g u n c e r t a i n t y i n v o l v e s i d e n t i f y i n g the sources of u n c e r t a i n t y in the d e c i s i o n environment and s y s t e m a t i z i n g any i n f o rma t i on which c o u l d l e a d to a b e t t e r unders tand ing of u n c e r t a i n t y . Two d i s t i n c t s i t u a t i o n s e x i s t . In the f i r s t the u n c e r t a i n v a r i a b l e occurs over t ime . The 100 techn iques employed i n vo l v e s ea r ch i ng fo r p a t t e r n s in the h i s t o r i c a l data and making p r e d i c t i o n s conce rn i ng the fu tu re on the b a s i s of these p a t t e r n s . The second s i t u a t i o n i n v o l v e s u n c e r t a i n t y in unique e ven t s . The approach in t h i s s i t u a t i o n would i n vo l v e a s s i g n i n g s u b j e c t i v e p r o b a b i l i t i e s to the d i f f e r e n t va lues that the event may r e p r e s e n t . The argument fo r us ing s u b j e c t i v e p r o b a b i l i t i e s i s that i f the d e c i s i o n maker has some b e l i e f s conce rn i ng the events which w i l l o c c u r , he w i l l use these to determine h i s c h o i c e s . E x p l i c i t acknowledgement of these b e l i e f s through assignment of s u b j e c t i v e p r o b a b i l i t y u s u a l l y causes the d e c i s i o n maker to r e f l e c t on h i s b e l i e f s and a l l ows him to c o r r e c t them fo r c o n s i s t e n c y . Seve ra l t echn iques have been deve loped to a i d the d e c i s i o n maker in a s s i g n i n g c o n s i s t e n t s u b j e c t i v e p r o b a b i l i t i e s to an event (Huber 1974, S p e t z l e r and S t a e l von H o l s t e i n 1975, MacCrimmon and T a y l o r 1976) . I t i s necessa ry to r e s t a t e at the ou t se t of a d i s c u s s i o n . regard ing the a p p l i c a b i l i t y of models i n c o r p o r a t i n g u n c e r t a i n t y i n the s e l e c t i o n of a t imber management s t r a t e g y that on ly the t imber resource component of the f o r e s t system on any s p e c i f i c a rea w i l l be e x p l i c i t l y c o n s i d e r e d in t h i s d i s s e r t a t i o n . The r e l a t i o n s h i p between t h i s component and other r esource components i s assumed to be s p e c i f i c a l l y set by e x i s t i n g p o l i c y ( non-de l i be r a t ed d e c i s i o n r u l e s ) . Many d e t e r m i n i s t i c models i l l u s t r a t i n g the p o t e n t i a l impacts of t imber management s t r a t e g i e s on f u t u r e wood supp ly e x i s t . A set of r u l e s govern ing the d e s i r e d s t r u c t u r e of the 101 fu tu re t imber resource opera tes e i t h e r i n t e r n a l or e x t e r n a l to the model to l i m i t p r o s p e c t i v e management s t r a t e g i e s and to suggest an a p p r o p r i a t e c h o i c e . These e x i s t i n g models p rov ide a conven ien t framework fo r the i n i t a l mode l l i ng of u n c e r t a i n t y . As i l l u s t r a t e d in Chapter IV, e f f e c t s of u n c e r t a i n t y can be e a s i l y c o n c e p t u a l i z e d in a t imber supp ly model through the i n c l u s i o n of s t o c h a s t i c components. P r a c t i c a l d i f f i c u l t i e s a r i s e from two b a s i c s o u r c e s : (1) de t e rm ina t i on of a p p r o p r i a t e p r o b a b i l i t y d i s t r i b u t i o n s and (2) s o l u t i o n of the r e s u l t a n t mode l . 6 .2 .2 S t r a t e g i e s I n vo l v i ng In fo rmat ion A c q u i s i t i o n The key to e f f e c t i v e dec i s ion-mak ing i s proper use of i n f o r m a t i o n (Richen 1968). Emphasis shou ld be p l a ced on the q u a l i t y and t i m e l i n e s s of the i n f o r m a t i o n r a the r than on the q u a n t i t y of i n f o rma t i on a v a i l a b l e (Uyl 1968). A c q u i r i n g and p r o c e s s i n g i n f o r m a t i o n can reduce u n c e r t a i n t y . Bayes ian p r o b a b i l i t y r e v i s i o n p rov i des a mechanism fo r upda t ing p r o b a b i l i t i e s on the b a s i s of f u r t h e r i n f o rma t i on us i ng Bayes ' Theorem. (See Luce and R a i f f a 1957, R a i f f a 1968, R a i f f a and S c h l a i f e r 1961 or any o ther d e c i s i o n theory t e x t . ) Techn iques e x i s t which a l l ow the expected va lue of p e r f e c t i n f o r m a t i o n to be found . T h i s p l a c e s an upper bound on the amount which shou ld be spent a c q u i r i n g a d d i t i o n a l i n f o r m a t i o n . The Theory of Teams was deve loped to p r o v i d e i n f o rma t i on s t r u c t u r e s and d e c i s i o n r u l e s f o r o r g a n i z a t i o n s (Marschalk and Radner 1972; MacCrimmon 1970;1974a) . More r e a l i s t i c but l e s s t r a c t a b l e t h e o r i e s fo r hand l i ng i n f o r m a t i o n in an o r g a n i z a t i o n a l s e t t i n g i n c l u d e Synd i ca te Theory (Rosing 1970, W i l son 1968) and 1 02 Agency Theory (Holmstrom 1979, Ross 1973, S h a v e l l 1979). Other i n f o r m a t i o n a l s t r a t e g i e s e x i s t , but the b a s i c concept remains the same. A c q u i r i n g u s e f u l i n f o rma t i on in an unders tandab le format can h e l p reduce the d e c i s i o n maker ' s u n c e r t a i n t y by expanding h i s knowledge of the d e c i s i o n env i ronment . Sources of u n c e r t a i n t y i n v o l v e d in the f o r m u l a t i o n and cho i ce of a p p r o p r i a t e management s t r a t e g i e s were d i s c u s s e d in Chapter V. A d d i t i o n a l i n f o rma t i on can reduce the u n c e r t a i n t y a s s o c i a t e d w i th some of these sources i n c l u d i n g those s p e c i f i c a l l y p e r t a i n i n g to t imber supply mode ls . Timber supp ly models r e q u i r e c e r t a i n k inds of i n f o r m a t i o n in order to r un . Less than p e r f e c t i n f o rma t i on u l t i m a t e l y r e s u l t s in some u n c e r t a i n t y a s s o c i a t e d w i th whatever c r i t e r i o n ( c r i t e r i a ) tha t i s (are) used to r ep resen t the e f f e c t of that management sequence. A d d i t i o n a l i n f o rma t i on w i l l remove some p o r t i o n of the u n c e r t a i n t y p resent and reduce the r i s k a s s o c i a t e d w i th implement ing any p a r t i c u l a r management s t r a t e g y and w i th any d e c i s i o n s based on the t imber supp ly s c e n a r i o a s s o c i a t e d w i th tha t s t r a t e g y , but such i n f o rma t i on i s a v a i l a b l e on ly at a c o s t . I f some monetary va lue c o u l d be a s s o c i a t e d w i th the r i s k i n v o l v e d i t would be t h e o r e t i c a l l y p o s s i b l e to a s c e r t a i n the optimum p r e c i s i o n l e v e l f o r the i n f o r m a t i o n which i s r e q u i r e d . R e a l i s t i c monetary v a lues a s s o c i a t e d w i th such r i s k s w i l l not be easy to d e r i v e and i n f o r m a t i o n r e q u i r e d by t imber supp ly models se rves o ther pu rposes . Fu r the rmore , the i n d i v i d u a l c o n t r i b u t i o n of v a r i o u s e r r o r sources to the u n c e r t a i n t y 1 03 a s s o c i a t e d w i th some o v e r a l l measure of t imber management s t r a t e g y e f f e c t w i l l be d i f f i c u l t to a s c e r t a i n . Desp i t e these p r a c t i c a l d i f f i c u l t i e s , o b t a i n i n g some i n s i g h t i n t o the s p e c i f i c e f f e c t s of d i f f e r e n t i n f o r m a t i o n l e v e l s remains a worthwhi le g o a l . Such i n s i g h t s can on l y be ob ta ined i f u n c e r t a i n t y i s s p e c i f i c a l l y i n c o r p o r a t e d i n t o the t imber supp ly mode l . W i th in the realm of t imber supp ly m o d e l l i n g there are two gene ra l i n f o r m a t i o n requ i rements whose q u a l i t y c o u l d be improved through a d d i t i o n a l monetary e x p e n d i t u r e s : (1) what i s p resent now and (2) what w i l l be p resen t in the f u tu r e g iven a p a r t i c u l a r sequence of a c t i o n s . These requ i rements are s u f f i c i e n t l y d i f f e r e n t to warrant some i n d i v i d u a l d i s c u s s i o n . I n fo rmat ion on the p resen t i n ven to r y no rma l l y r e q u i r e d by t imber supp ly models c o n s i s t s of the area p resen t in each r e c o g n i z e d management u n i t and the i nven to ry p resen t per un i t area fo r tha t u n i t . These are p roduc t s of the f o r e s t i nven to ry system in e f f e c t . As such , t h e i r a ccu racy c o u l d be improved by a more i n t e n s i v e sampl ing procedure in terms of number of samples and a t t r i b u t e s sampled. I f sample s i z e equa ls p o p u l a t i o n s i z e , the i n f o r m a t i o n shou ld be p e r f e c t . O b v i o u s l y the cos t of p roduc ing ' c e r t a i n ' i n f o rma t i on would be tremendous, and would p r e c l ude t h i s p o s s i b i l i t y . There w i l l , however, be some optimum l e v e l of sampl ing i n t e n s i t y w i th r e spec t to p r o d u c t i o n of a t imber supp ly model . I f t h i s l e v e l c o u l d be approximated i t would be of c o n s i d e r a b l e va lue in i n ven to r y d e s i g n . I n fo rmat ion on what w i l l be p resen t in the f u t u r e g iven a p a r t i c u l a r sequence of management a c t i o n s i s a product of some y i e l d p r o j e c t i o n system or sys tems. I f the t imber which 104 p r e s e n t l y e x i s t s in the un i t i s of n a t u r a l o r i g i n and no t reatment w i l l be a p p l i e d u n t i l the t ime of h a r v e s t , a y i e l d p r o j e c t i o n system fo rmu la ted from n a t u r a l ( e x i s t i n g ) s tand i n f o rma t i on would be a p p r o p r i a t e to p r e d i c t volume at r o t a t i o n age . In B r i t i s h Co lumbia , v a r i a b l e d e n s i t y y i e l d p r o j e c t i o n equa t i ons which form par t of the y i e l d p r o j e c t i o n system have been d e r i v e d f o r t h i s purpose ( M i n i s t r y of F o r e s t s 1982b;1983b) . If the t imber i s not of n a t u r a l o r i g i n and/or p a r t i c u l a r t rea tments w i l l be a p p l i e d in an attempt to a l t e r the compos i t i on of the s tand at h a r v e s t , a managed s tand p r o j e c t i o n system would be a p p r o p r i a t e . Growth (and the u l t ima t e compos i t i on of the stand) w i l l not n e c e s s a r i l y be the same as in un t r ea t ed s t a n d s . P r e s e n t l y , very l i t t l e i s a v a i l a b l e in terms of managed s tand p r o j e c t i o n systems s p e c i f i c to B r i t i s h Co lumb ia . Some success has been ach i eved wi th the i n c o r p o r a t i o n of c e r t a i n t reatment e f f e c t s i n t o a y i e l d p r o j e c t i o n system fo r managed C o a s t a l D o u g l a s - f i r (Pseudotsuga menz i e s i i (M i rb . ) F ranco) and work con t i nues on s e v e r a l o ther s p e c i e s ( M i t c h e l l and Cameron 1982; Cameron and M i t c h e l l 1983). Some i n fo rma t i on i s a v a i l a b l e from other l o c a l i t i e s but i n c o r p o r a t i o n of such r e s u l t s wi thout v a l i d a t i o n f o r l o c a l c o n d i t i o n s c r e a t e s c o n s i d e r a b l e u n c e r t a i n t y w i th regards to the u l t i m a t e e f f e c t on y i e l d . C o n s i d e r a b l e u n c e r t a i n t y s t i l l remains wi th r e spec t to the f i n a l y i e l d of s tands even i f good p r o j e c t i o n systems are a v a i l a b l e . C a t a s t r o p h i c o c cu r r ences of f i r e , i n s e c t s , d i s ea se and n a t u r a l d i s a s t e r s of v a r i o u s k inds e s s e n t i a l l y remove p o t e n t i a l l y u s e f u l l and a reas from a p a r t i c u l a r age c l a s s and 105 r e tu rn them to an unstocked s t a t e at v a r i o u s p o i n t s in t ime . The p r o b a b i l i t i e s of such occu r rences are dependent upon the management reg ime, age and compos i t i on of the s tand as we l l as e x t e r n a l v a r i a b l e s such as c l i m a t e and degree of human a c c e s s . In a d d i t i o n to t h i s p rob lem, there i s the impact of non-ca t a s t r oph i c l o s s e s from the same f a c t o r s to be c o n s i d e r e d . Such l o s s e s reduce the o v e r a l l y i e l d from a s tand but do not t o t a l l y remove the f o r e s t c o v e r . Incomplete u t i l i z a t i o n of an area due to the e x i s t e n c e of non-produc t i ve a reas (rock o u t c r o p s , swamps, roads) f u r t h e r reduces y i e l d . A s tandard approach fo r d e a l i n g wi th such p o t e n t i a l r e d u c t i o n s in y i e l d i s to reduce the o v e r a l l e s t imate of y i e l d by some pe r cen t age . A d d i t i o n a l r e s e a r c h i n t o the b i o l o g y of the f o r e s t system and o b s e r v a t i o n s of a c t u a l y i e l d r e d u c t i o n s as a f u n c t i o n of s tand t ype , r o t a t i o n age and management h i s t o r y would he lp c a l i b r a t e such a system and reduce , but never remove, the u n c e r t a i n t y su r round ing f i n a l p r e d i c t i o n s . The key f a c t o r , in terms of s e l e c t i n g an a p p r o p r i a t e management s t r a t e g y , i s the i n f l u e n c e of management on the p r o b a b i l i t i e s of these o c c u r r e n c e s . The f o r e s t manager can modify the s tand compos i t i on and s t r u c t u r e through v a r i o u s t r ea tmen t s , and hence a l t e r the p r o b a b i l i t i e s of such l o s s e s . I f enough i s unders tood r ega rd ing the e f f e c t of s tand c h a r a c t e r i s t i c s on these p r o b a b i l i t i e s , i t i s r easonab le to assume tha t s tand management w i l l be d i r e c t e d towards p roduc ing s tands w i th minimum p r o b a b i l i t i e s of l o s s . If t h i s i s indeed the c a s e , i n t e n s i f y i n g management shou ld reduce the u n c e r t a i n t y su r round ing es t ima tes of f i n a l y i e l d . Even i f such management 1 0 6 does not i n c r e a s e e s t ima tes ( i . e . expected or most l i k e l y va lue ) of f i n a l y i e l d s i g n i f i c a n t l y , r e d u c t i o n in u n c e r t a i n t y of t h i s es t imate i s some j u s t i f i c a t i o n fo r i n c r e a s e d e x p e n d i t u r e . However, u n t i l such time as t h i s r e d u c t i o n can be q u a n t i f i e d , i t i s imposs i b l e to e x p l i c i t l y i n c o r p o r a t e such an e f f e c t in the c h o i c e of an a p p r o p r i a t e t imber management s t r a t e g y . S ince u n c e r t a i n t y su r round ing f u tu r e e s t ima tes of y i e l d can never be comp le t e l y removed through the gene ra t i on of a d d i t i o n a l i n f o r m a t i o n , i t i s more d i f f i c u l t to a s s o c i a t e a va lue wi th such i n fo rma t i on than wi th i n f o r m a t i o n on the p resen t s t a t u s of the management a r e a . H e u r i s t i c a l l y , i t i s apparent that a b e t t e r unders tand ing of the b i o l o g y of the f o r e s t system w i l l l e ad to more p r e c i s e ( l e s s u n c e r t a i n ) p r e d i c t i o n s of f u tu r e management c o n d i t i o n s and that more i n t e n s i v e management, i n t e l l i g e n t l y a p p l i e d , shou ld have the same e f f e c t . Whi le i t i s p r e s e n t l y imposs ib l e to j u s t i f y the expend i tu res i n v o l v e d in the g a t h e r i n g of such i n f o r m a t i o n and w i th i n t e n s i f y i n g management s o l e l y on the b a s i s of a r e d u c t i o n in the u n c e r t a i n t y , i t i s important tha t such b e n e f i t s be c o n s i d e r e d . 1 07 CHAPTER VII ACTUAL TREATMENT OF UNCERTAINTY IN FOREST MANAGEMENT F i g h t and B e l l (1977) noted that l i t t l e e x p l i c i t r e c o g n i t i o n of u n c e r t a i n t y o c c u r r e d in t imber management p l a n n i n g by the U.S. Fo res t S e r v i c e . T h i s statement a l s o a p p l i e s to t imber management in B r i t i s h Columbia and throughout Canada. The l a s t decade or so has seen a number of e x p l i c i t t reatments suggested in the f o r e s t r y l i t e r a t u r e and the o p e r a t i o n a l a p p l i c a t i o n of some of the more rudimentary t e c h n i q u e s . However, there i s s t i l l a l a r g e gap between t h e o r e t i c a l developments and a c t u a l a p p l i c a t i o n s . The t echn iques a v a i l a b l e were, f o r the most p a r t , i n i t i a l l y deve loped f o r and a p p l i e d to o ther d i s c i p l i n e s . The inherent comp lex i t y of the t imber management d e c i s i o n environment and the long-term nature of t imber management p l a n n i n g can make the a p p l i c a t i o n of such t e chn iques imposs ib l e wi thout s u i t a b l e m o d i f i c a t i o n . Such m o d i f i c a t i o n i s o f t e n d i f f i c u l t . I m p l i c i t i n c o r p o r a t i o n of u n c e r t a i n t y , on the o ther hand, i s w idesp read . The o r g a n i z a t i o n a l h i e r a r c h y deve loped w i t h i n p u b l i c f o r e s t management agenc i es and the j u r i s d i c t i o n a l s e p a r a t i o n of the f o r e s t management problem i n t o resource components a r e , in p a r t , a r e c o g n i t i o n of the comp lex i t y of the prob lem. P l ann ing w i t h i n a r esource component i s shaped by p o l i c y o r i g i n a t i n g in l e g i s l a t i o n and f u r t h e r d e f i n e d and d i r e c t e d by the r e s p o n s i b l e agency . These n o n d e l i b e r a t e d d e c i s i o n r u l e s p rov ide ' t h e r u l e s of the game' and supp ly some 1 08 s t r u c t u r e to the d e c i s i o n env i ronment . W i th in t h i s s t r u c t u r e ' p a s s i v e ' s t r a t e g i e s such as i g n o r i n g u n c e r t a i n t y in the d e c i s i o n environment and a d a p t a t i o n , d i s c u s s e d in the p r e v i o u s c h a p t e r , a re commonly employed. I t would be t e c h n i c a l l y i n c o r r e c t to s t a t e tha t on l y ' p a s s i v e ' approaches to cop ing w i th u n c e r t a i n t y have ga ined o p e r a t i o n a l a c cep tance . Much i n f o r m a t i o n i s a v a i l a b l e and i s a c t i v e l y sought on most f o r e s t management p rob lems . In fo rmat ion a c q u i s i t i o n i s an ' a c t i v e ' s t r a t e g y . Such i n f o rma t i on i s used to he lp fo rmula te the d e c i s i o n p rob lem. Much of the b a s i c i n f o rma t i on which i s input i n t o t imber supp ly models i s p r o v i d e d by f o r e s t i n v e n t o r i e s and a d d i t i o n a l i n f o rma t i on i s a v a i l a b l e from many o the r s o u r c e s . N e v e r t h e l e s s , such approaches remain ' p a s s i v e ' . The i n f o rma t i on a v a i l a b l e i s used to fo rmula te the p rob lem, but no e f f o r t i s made to a ssess the amount of u n c e r t a i n t y remain ing or the va lue of a c q u i r i n g a d d i t i o n a l i n f o r m a t i o n . U s u a l l y the uns t a t ed assumpt ions are that the i n f o r m a t i o n used i s c o r r e c t and tha t no f u r t h e r i n f o r m a t i o n i s a v a i l a b l e or need be c o n s i d e r e d . C l e a r l y t h i s i s not the c a s e , and in t h i s sense the use of i n f o r m a t i o n can s t i l l be c o n s i d e r e d a ' p a s s i v e ' s t r a t e g y as d e f i n e d in Chapter V I . 7.1 Use of Most L i k e l y Va lues The t r a d i t i o n a l approach to f o r m u l a t i n g and s o l v i n g a t imber supp ly model , e s p e c i a l l y i f i t i s s t r u c t u r e d as a l i n e a r programming p rob lem, i n v o l v e s a s s o c i a t i n g a p a r t i c u l a r r e t u rn w i th each management sequence. T h i s i s ak in to making a d e c i s i o n 109 under c o n d i t i o n s of c e r t a i n t y s i n ce on ly one va lue i s a s s o c i a t e d wi th each management sequence. An a n a l y s i s of the a l l o c a t i o n of l and to each sequence i s made based on these va lues and the c o n t r i b u t i o n of each sequence towards s a t i s f y i n g the s p e c i f i e d c o n s t r a i n t s . A n a l y t i c a l l y , t h i s r e v e r t s to a bookkeeping prob lem, c o m p l i c a t e d by the f a c t tha t c o n s t r a i n t s e x i s t which d i c t a t e the compos i t i on of f e a s i b l e s t r a t e g i e s . Us ing l i n e a r programming to so l ve d e t e r m i n i s t i c t imber supp ly models o f f e r s many a n a l y t i c a l and computa t iona l advantages which make p o s s i b l e the gene ra t i on of many p o t e n t i a l management sequences and the s o l u t i o n of q u i t e l a r g e p rob lems . Desp i t e these advan tages , i g n o r i n g u n c e r t a i n t y and forming a d e t e r m i n i s t i c model can produce a s o l u t i o n which i s f a r from i d e a l g iven the d e c i s i o n maker ' s b e l i e f s and p re f e r ence s t r u c t u r e . A d e c i s i o n a n a l y t i c approach under u n c e r t a i n c o n d i t i o n s would suggest us ing expected va lues r a t he r than most l i k e l y v a l u e s . A problem fo rmu la ted in terms of most l i k e l y va lues i s r a r e l y go ing to y i e l d the same s o l u t i o n as one fo rmu la ted in terms of expected v a l u e s . In terms of a p r o b a b i l i t y d i s t r i b u t i o n , the most l i k e l y va lue r ep resen t s the mode, and the expected va lue the mean. They are i d e n t i c a l in a un imoda l , symmetr i ca l d i s t r i b u t i o n l i k e the normal , but o therw ise equ i va l ence no longer n e c e s s a r i l y h o l d s . If the d e c i s i o n maker i s r i s k averse i t i s u n l i k e l y tha t the d i s t r i b u t i o n of r e tu rns which he env i sages from any management s t r a t e g y c o n s i d e r e d i s s ymmet r i c a l . 110 Tab l e 1: An I l l u s t r a t i o n of the E f f e c t of Left-Skewness and D i s t r i b u t i o n Spread on the D i f f e r e n c e Between Expected Va lue and Most L i k e l y V a l u e . DISTRIBUTION 1a PROB. VALUE PROB.*VALUE .025 3.0 .075 .075 2.0 . 1 50 .200 1.0 .200 * .400 0.0 .000 .200 -1.0 - .200 .075 -2.0 - .150 .025 -3.0 - .075 EXPECTED VALUE 0.000 DISTRIBUTION 2a PROB. VALUE PROB.*VALUE .025 4.0 .100 .075 3.0 .225 .100 2.0 .200 .150 1.0 .150 * .300 0.0 .000 . 1 50 -1.0 - . 1 50 .100 -2.0 - .200 .075 -3.0 - .225 .025 -4.0 - .100 EXPECTED VALUE 0.000 DISTRIBUTION 1b PROB. VALUE PROB.*VALUE .025 1.5 .0375 .075 1.0 .0750 .200 0.5 .1000 * .400 0.0 .0000 .200 -2.0 -.4000 .075 -4.0 -.3000 .025 -6 .0 -.1500 -.6375 DISTRIBUTION 2b PROB. VALUE PROB.*VALUE .025 2.0 .0500 .075 1 .5 . 1 125 .100 1.0 .1000 .150 0.5 .0750 * .300 0.0 .0000 .150 -2.0 -.3000 .100 -4.0 -.4000 .075 -6 .0 -.4500 .025 -8.0 -.2000 -1.0125 * Most l i k e l y va lue i s 0 fo r a l l of these d i s t r i b u t i o n s . T h i s i s i l l u s t r a t e d by the s i m p l i f i e d d i s t r i b u t i o n s p resen ted in Tab le 1. D i s t r i b u t i o n s 1a and 2a are both s ymmet r i c a l , but d i s t r i b u t i o n 2a has a l a r g e r range of v a l u e s . The most l i k e l y v a l ues and the expected va lues a re equ i v a l en t i n each of these d i s t r i b u t i o n s and set at 0 f o r conven ience . D i s t r i b u t i o n s 1b and 2b are skewed to the l e f t . They are d e r i v e d 111 from d i s t r i b u t i o n s 1a and 2a r e s p e c t i v e l y by m u l t i p l y i n g r e tu rns g r e a t e r than the most l i k e l y va lue by a f a c t o r of .5 and those l e s s by 2 . 0 . Whi le these f a c t o r s a re comp le te l y a r b i t r a r y , they are i n d i c a t i v e of a s i t u a t i o n in which low r e t u r n s have more impact than h ighe r r e t u r n s of the same magnitude (a r i s k averse p o s i t i o n ) . The most l i k e l y va lue of both these d i s t r i b u t i o n s remains 0, but the expected va lues a s s o c i a t e d w i th d i s t r i b u t i o n s 1b and 2b drop to -.6375 and -1.0125 r e s p e c t i v e l y . The e f f e c t s of u s i n g most l i k e l y v a l ues in f o r m u l a t i n g t imber supp ly models a re not always o b v i o u s . Three s c e n a r i o s are p resen ted below in i n c r e a s i n g order of c o m p l e x i t y . The e f f e c t s of u s i ng the most l i k e l y va lue f o r u n c e r t a i n parameters r a the r than the expec ted va lue w i l l be p o s t u l a t e d f o r each . S c e n a r i o 1: The d e c i s i o n maker i s p resen ted wi th a f i n i t e number of t imber management s t r a t e g i e s which are deemed a c cep t ab l e under e x i s t i n g p o l i c y . He 'knows' the p r o b a b i l i t y d i s t r i b u t i o n f o r the r e t u r n s from each s t r a t e g y and the r e t u r n s have been a d j u s t e d to r e f l e c t h i s p r e f e r e n c e s t r u c t u r e and h i s a t t i t u d e towards r i s k . The r a t i o n a l c h o i c e i n t h i s s i t u a t i o n would be tha t s t r a t e g y which y i e l d s the h ighes t expected r e t u r n (or the lowest expec ted l o s s ) . S y m b o l i c a l l y , h i s d e c i s i o n problem becomes: F i n d S e (S , . . . , S } 1 n such tha t E (U(S*) ) i s maximum Sub jec t t o : {S , . . . , S } s a t i s f y i n g a l l manager ia l c o n s t r a i n t s 1 n 112 where S i s the ' b e s t ' of the t imber management s t r a t e g i e s c o n s i d e r e d . U (S* ) i s the p r o b a b i l i t y f u n c t i o n a s s o c i a t e d it with the a d j u s t e d r e t u r n s from S . E(U(S*) ) i s the expec ted va lue of the r e tu rns from S . Choos ing a s t r a t e g y w i th the h ighes t most l i k e l y va lue ( S m l ) would r e s u l t in some expec ted l o s s i f Sm^ was not equa l to S . The expected l o s s can be c a l c u l a t e d a s : E (U(S*) ) - E ( U ( S m 1 ) ) . Even i f Sm^ i s equa l to S* t he re i s a p o t e n t i a l f o r o ther d i f f i c u l t i e s . Us ing the most l i k e l y va lue i gno res the remainder of the d i s t r i b u t i o n s . I f the d e c i s i o n maker i s r i s k a v e r s e , i t i s r easonab le to expect tha t the h i g h e s t most l i k e l y va lue i s g r e a t e r than the l a r g e s t expec ted v a l u e . I f most l i k e l y v a l ues a re used , the d e c i s i o n maker would tend to a s s o c i a t e a h ighe r r e t u r n w i th the s t r a t e g y s e l e c t e d . T h i s c o u l d r e s u l t in the a l l o c a t i o n of more funds to t imber management than c o u l d be e c o n o m i c a l l y j u s t i f i e d g i ven h i s a t t i t u d e towards r i s k . S c ena r i o 2: The d e c i s i o n maker must c o n s t r u c t h i s own f i n i t e set of f e a s i b l e management s t r a t e g i e s . There i s some u n c e r t a i n t y a s s o c i a t e d w i th the r e tu rn from any a c t i v i t y , but the response of the f o r e s t to any a c t i v i t y i s d e t e r m i n i s t i c . The d e c i s i o n problem faced by the d e c i s i o n maker has two l e v e l s . The f i r s t ' l e v e l c o n s i s t s of c o n s t r u c t i n g a set of p o t e n t i a l management s t r a t e g i e s . Each s t r a t e g y c o n s i s t s of a number of management a c t i o n s s e l e c t e d from d i f f e r e n t s e t s of p o s s i b l e management a c t i o n s . These s t r a t e g i e s shou ld be f e a s i b l e 1 13 g i ven the p o l i c y c o n s t r a i n t s i n e f f e c t . T h i s p o r t i o n of the d e c i s i o n problem can be r ep resen ted s y m b o l i c a l l y f o r any set of management a c t i o n s us ing the same n o t a t i o n and model form p resen ted in S e c t i o n s 4.3 and 4 .4 . F i n d S. = l a . } 1 1 U such tha t E(R^) i s o p t i m i z e d Sub jec t t o : g. (C. = 0 f o r j = 1 , . . . ,J J j u t h (V ,a •) = 0 fo r q = 1 , . . . , Q qu u i u u = 1 , . . . , U a £ A f o r u=1, . . . ,U i u t i u t t = 1 , . . . , T where S r e p r e s e n t s the optimum management s t r a t e g y i •f""h f o r the i se t of p o t e n t i a l management a c t i o n s c o n s i d e r e d (A. ). i u t E(R. ) r ep r e sen t s the expected va lue of the t o t a l 1 of the r e t u r n s from the management a c t i o n s . The second l e v e l of the d e c i s i o n problem i s e s s e n t i a l l y the same as the problem d e s c r i b e d i n S cena r i o 1. I t i n v o l v e s s e l e c t i n g a management s t r a t e g y from the se t of f e a s i b l e s t r a t e g i e s . In o rde r to make a r a t i o n a l cho i c e between s t r a t e g i e s , the d i s t r i b u t i o n of p o t e n t i a l r e t u r n s (or t h e i r expected va lue ) must be known. T h i s i n v o l v e s combin ing the d i s t r i b u t i o n of r e t u r n s from each of the proposed a c t i v i t i e s i n t o a d i s t r i b u t i o n f o r the s t r a t e g y as a whole. Some r e c o g n i t i o n of the u n c e r t a i n t y a s s o c i a t e d w i th the r e tu rn from each management s t r a t e g y i s o b v i o u s l y r e q u i r e d . Such r e c o g n i t i o n can be made e i t h e r be fo re or a f t e r the 1 14 management s t r a t e g i e s have been c o n s t r u c t e d . In o rder to ensure the f o rmu l a t i on of op t ima l s t r a t e g i e s in accordance wi th the d e c i s i o n maker ' s b e l i e f s and p r e f e r e n c e s i t i s necessa ry to a s s o c i a t e expec t ed , r a the r than most l i k e l y , v a l ues w i th each a c t i v i t y . Use of most l i k e l y va lues in the c o n s t r u c t i o n of the s t r a t e g i e s can l e a d to sub-opt ima l s t r a t e g i e s . Land i s a l l o c a t e d to each a c t i v i t y on the b a s i s of the c o n t r i b u t i o n of tha t a c t i v i t y to the o v e r a l l r e t u rn and to s a t i s f y i n g the v a r i o u s c o n s t r a i n t s . S ince d i s t r i b u t i o n s of p o s s i b l e r e t u r n s from d i f f e r e n t a c t i v i t i e s are u n l i k e l y to be the same, the r e l a t i o n s h i p between the expected va lues of the a c t i v i t i e s i s not n e c e s s a r i l y the same as the r e l a t i o n s h i p between the most l i k e l y v a l u e s . T h i s be ing the c a s e , i t i s p o s s i b l e that the s t r a t e g y c o n s t r u c t e d us i ng most l i k e l y va lues would be d i f f e r e n t than i f expected va lues were used fo r the r e t u r n s from the v a r i o u s a c t i v i t i e s . T h i s i n d i c a t e s tha t every s t r a t e g y c o n s t r u c t e d wi th most l i k e l y v a l ues c o u l d be l e s s a p p r o p r i a t e fo r each set of p o t e n t i a l a c t i v i t i e s c o n s i d e r e d than the co r r e spond ing s t r a t e g y c o n s t r u c t e d us i ng expected v a l u e s . S cena r i o 3: The d e c i s i o n maker must c o n s t r u c t h i s own f i n i t e set of management s t r a t e g i e s . He i s unsure of r e t u r n s f rom, and response of the f o r e s t t o , v a r i o u s p o t e n t i a l a c t i v i t i e s . The d e c i s i o n maker shou ld s e l e c t a c t i v i t i e s to compr ise h i s s t r a t e g i e s on the b a s i s of t h e i r c o n t r i b u t i o n to o p t i m i z i n g r e tu rn and meet ing c o n s t r a i n t s . I f the consequences of not meet ing a c o n s t r a i n t exceed the consequences of more than meet ing that c o n s t r a i n t (p roduc ing some s l a c k ) , then i t would be 1 1 5 b e n e f i c i a l , g i ven equa l r e t u r n s , to a l l o c a t e more l and to those a c t i v i t i e s w i th l e s s u n c e r t a i n t y . When r e tu rns fo r d i f f e r e n t a c t i v i t i e s a re not e q u a l , the d e c i s i o n maker would l i k e l y be w i l l i n g to exchange some p o r t i o n of the p o t e n t i a l r e t u rn fo r g rea te r c e r t a i n t y . The use of most l i k e l y va lues in the f o r m u l a t i o n of the c o n s t r a i n t s i gnores t h i s p o s s i b i l i t y and hence c o u l d produce s t r a t e g i e s which are sub-opt ima l f o r the management a c t i o n s c o n s i d e r e d . One p o t e n t i a l s o l u t i o n to t h i s problem would be to i n c o r p o r a t e the u n c e r t a i n t y su r round ing the response to some a c t i v i t y i n t o the r e tu rn fo r tha t a c t i v i t y . E s s e n t i a l l y t h i s i n v o l v e s c o l l a p s i n g the u n c e r t a i n t y found throughout the problem s t r u c t u r e i n t o the o b j e c t i v e f u n c t i o n . I f t h i s can be done s u c c e s s f u l l y , the problem r e v e r t s to the two l e v e l problem d i s c u s s e d in S cena r i o 2. . S o l u t i o n would be p o s s i b l e us ing t r a d i t i o n a l mathemat ica l programming or s i m u l a t i o n t echn iques i n c o r p o r a t i n g expected va lues fo r the v a r i o u s r e t u r n s . In order to app ly t h i s techn ique o p e r a t i o n a l l y , i t would be necessa ry to deve lop an a c c e p t a b l e procedure fo r e f f e c t i v e l y c o l l a p s i n g the u n c e r t a i n t y . D i s c u s s i o n of t h i s p a r t i c u l a r approach w i l l be resumed in the next c h a p t e r . Other s o l u t i o n approaches are p o s s i b l e and have been a p p l i e d at l e a s t e x p e r i m e n t a l l y . The remainder of t h i s chapter w i l l be devoted to an e x p l o r a t i o n of these o ther p o s s i b i l i t e s . The manager 's d e c i s i o n problem remains s i m i l a r to tha t d e s c r i b e d fo r S cena r i o 3. Not on l y must he choose among p r o s p e c t i v e s t r a t e g i e s , he must a l s o fo rmu la te these s t r a t e g i e s 1 1 6 in the face of u n c e r t a i n t y . 7.2 S e n s i t i v i t y Ana l yses S e n s i t i v i t y ana l y ses examine the s e n s i t i v i t y of model r e s u l t s to changes in input pa ramete rs . L i n e a r programming s o l u t i o n a l g o r i t h m s , in p a r t i c u l a r , are q u i t e conduc ive to such ana l y ses as i n fo rma t i on p e r t a i n i n g to the range of c o n d i t i o n s over which the op t ima l s o l u t i o n ho lds i s g e n e r a l l y i nexpens i ve to o b t a i n once the op t ima l s o l u t i o n i s found . S e n s i t i v i t y ana l y ses are u s e f u l in i s o l a t i n g parameters which s i g n i f i c a n t l y i n f l u e n c e r e s u l t s . The d e c i s i o n maker can then attempt to gather more i n fo rma t i on conce rn ing these parameters or at l e a s t app ly the r e s u l t s w i th some degree of c a u t i o n i f the u n c e r t a i n t y su r round ing the parameter va lues can not be removed ( H i l l i e r and Lieberman 1980). R e cogn i t i on of sources of u n c e r t a i n t y which a f f e c t v a r i o u s a spec t s of t imber management has l e d to a number of s e n s i t i v i t y ana l y ses des igned to examine v a r i o u s a spec t s of the p rob lem. Some of these have d e a l t w i th s i n g l e parameters wh i le o the r s have examined s e v e r a l in the same s tudy . A p p l i c a t i o n s range from use wi th f o r e s t s e c to r models (Adams and Haynes 1980) to t e s t i n g the i m p l i c a t i o n s of v a r i ous y i e l d and i nven to r y assumpt ions in t imber supp ly mode l l i ng (Hatch et a l . 1976, Oregon S ta te F o r e s t r y Department 1979, Vomoc i l and Tedder 1983). S e n s i t i v i t y ana l y ses have a l s o been used to examine the e f f e c t of i n t e n s i v e management on ha rves t y i e l d s under d i f f e r e n t p o l i c y assumpt ions ( B e l l 1976, Beuter et a L 1976, USDA 1976). Other a p p l i c a t i o n s are p o s s i b l e . Most ana l y ses which dea l w i th t imber ha rves t 1 1 7 s c h e d u l i n g are q u i t e data s p e c i f i c and h i g h l y dependent upon the f o r e s t s t r u c t u r e assumed. S e n s i t i v i t y ana l y ses can be an important t o o l f o r examining the i n f l u e n c e of p a r t i c u l a r sources of u n c e r t a i n t y w i t h i n a t imber supp ly model . However, such sources may not be e c o n o m i c a l l y and b i o l o g i c a l l y s i g n i f i c a n t in the face of u n c e r t a i n t y sources e x t e r n a l to the f o r e s t model (Vomoci l and Tedder 1983). T h i s c a s t s some doubt on t h e i r b e n e f i t w i th r e spec t to t imber supp ly m o d e l l i n g . In terms of t imber management s t r a t e g y s e l e c t i o n , s e n s i t i v i t y ana l y ses can a i d in e s t a b l i s h i n g p o t e n t i a l r e t u r n s under d i f f e r e n t assumpt ions about f u tu re c o n d i t i o n s . T h i s i s b e n e f i c i a l to the d e c i s i o n p r o c e s s , but does not suggest which s t r a t e g y would be b e s t . If a s e n s i t i v i t y a n a l y s i s i s i n c o r p o r a t e d wi th a l i n e a r programming f o r m u l a t i o n of the t imber supp ly model , the range of a p p l i c a b i l i t y of d i f f e r e n t ' o p t i m a l ' s t r a t e g i e s formed under d i f f e r e n t c o n s t r a i n t c o n d i t i o n s can be determined and the r e t u r n from each of these s t r a t e g i e s n o t e d . As c o n s t r a i n t s are changed a p a r t i c u l a r s t r a t e g y most l i k e l y becomes not on l y non-opt imal but a l s o i n f e a s i b l e . T h i s makes i t d i f f i c u l t to determine the l o s s a s s o c i a t e d w i th f o l l o w i n g a g i ven s t r a t e g y under c o n d i t i o n s o ther than those fo r which i t was deve l oped . T h i s i s not a major d i f f i c u l t y w i th s i m u l a t i o n approaches . If a l i m i t e d number of a l t e r n a t i v e s t r a t e g i e s are examined fo r a f i n i t e number of a l t e r n a t i v e f u t u r e s , s e n s i t i v i t y ana l y se s c o u l d be used in c o n j u n c t i o n wi th one of the game theory s t r a t e g i e s ment ioned in S e c t i o n 6 . 1 . Such an approach would be 1 1 8 sub jec t to a l l the l i m i t a t i o n s noted in that s e c t i o n however. Another p o t e n t i a l approach would be to a s s o c i a t e a s u b j e c t i v e p r o b a b i l i t y d i s t r i b u t i o n wi th each of the f u t u r e s examined. T h i s would l ead to a d i s t r i b u t i o n of p o t e n t i a l r e t u r n s from any s t r a t e g y . A r i s k p r o p e n s i t y c o u l d be i n c o r p o r a t e d i n t o each d i s t r i b u t i o n and the expected u t i l i t y of each s t r a t e g y c a l c u l a t e d . T h e o r e t i c a l l y the a p p l i c a t i o n would be s t r a i g h t f o r w a r d , but the a c t u a l c o n s t r u c t i o n of an a p p r o p r i a t e l y r e f l e c t i v e s u b j e c t i v e p r o b a b i l i t y d i s t r i b u t i o n i s not an easy t a s k . In summary, s e n s i t i v i t y ana l y ses are u s e f u l e x p l o r a t o r y t o o l s fo r t imber ha rves t s c h e d u l i n g and t imber management s t r a t e g y s e l e c t i o n . U n c e r t a i n t y o u t s i d e of the t imber supp ly model may negate much of the b e n e f i t a s s o c i a t e d w i th t imber ha rves t s c h e d u l i n g . S e n s i t i v i t y ana l y ses can p rov ide i n f o r m a t i o n to a i d in the development of r e t u r n s fo r v a r i o u s s t r a t e g i e s under d i f f e r e n t assumpt ions , but r e q u i r e amalgamation w i th an e x t e r n a l d e c i s i o n model be fo re c o n s t i t u t i n g an a n a l y t i c a l methodology to a i d the c h o i c e of t imber management s t r a t e g i e s . I t i s impor t an t , t h e r e f o r e , that e f f o r t be d i r e c t e d towards development of an a p p r o p r i a t e d e c i s i o n model , r a the r thanto the p r o d u c t i o n of s e n s i t i v i t y ana l y se s which are more d e t a i l e d than cu r r en t d e c i s i o n models can accomodate. 7.3 Other Methods A p p l i e d to F o r e s t Management D e c i s i o n s L i t e r a t u r e on cop ing w i th u n c e r t a i n t y in f o r e s t management d e c i s i o n s i s not p l e n t i f u l . Whi le the l i t e r a t u r e c i t e d below i s 119 not e x h a u s t i v e , i t shou ld p rov ide a good c r o s s - s e c t i o n of approaches which have been exp lo r ed in r e l a t i o n to some aspec t s of f o r e s t management. Other d i s c i p l i n e s a s s o c i a t e d wi th management and a l l o c a t i o n of n a t u r a l r e s o u r c e s , no tab l y f i s h e r i e s management and a g r i c u l t u r e , c o n t a i n a wea l th of i n f o r m a t i o n on dec i s i on-mak ing under u n c e r t a i n t y . Management s c i e n c e and a p p l i e d s c i e n c e l i t e r a t u r e a l s o c o n t a i n r e f e r e n c e s to s p e c i f i c a p p l i c a t i o n of t echn iques fo r e x p l i c i t i n c o r p o r a t i o n of u n c e r t a i n t y in d e c i s i o n s . However, the long-term nature of f o r e s t management and the comp lex i t y of the d e c i s i o n environment g e n e r a l l y makes i n c o r p o r a t i o n of the t echn iques a p p l i e d i n f e a s i b l e wi thout major a l t e r a t i o n s and s i m p l i f i c a t i o n s . Hool (1966) a p p l i e d a dynamic programming - Markov cha in approach to f o r e s t p roduc t i on c o n t r o l in a s t a n d . The a p p l i c a b i l i t y of t h i s approach to f o r e s t l e v e l management i s l i m i t e d because c o o r d i n a t i o n of s tand l e v e l management a c t i o n s to p rov ide a r e g u l a t e d f low of t imber at the f o r e s t l e v e l was not p r o v i d e d . Such c o o r d i n a t i o n i s the essence of t imber supp ly m o d e l l i n g . Fu r the rmore , use of Markov cha ins i m p l i e s a s t r i n g e n t l y s i m p l i s t i c p r o b a b i l i t y s t r u c t u r e which would not g e n e r a l l y ho ld in r e a l i s t i c s i t u a t i o n s . Thompson and Haynes (1971) d i s c u s s e d a p a r t i a l l y s t o c h a s t i c l i n e a r programming model f o r d e a l i n g w i th the u n c e r t a i n t y i n v o l v e d in a l e a s t - c o s t wood procurement schedu le fo r a p a r t i c u l a r f i r m . T h i s approach i n v o l v e d r e p l a c i n g po in t e s t ima tes of r i gh t-hand s ide va lues i n a l i n e a r programming model w i th s u b j e c t i v e p r o b a b i l i t y d i s t r i b u t i o n s . A number of s o l u t i o n s were s imu l a t ed and the number of f e a s i b l e s o l u t i o n s 1 20 no ted . They f e l t that the pr imary b e n e f i t of t h i s approach was the added i n s i g h t i t p rov i ded the d e c i s i o n maker on the nature of the p rob lem. T h i s t echn ique i s l i m i t e d in that i t on ly a l l owed an e x p l o r a t i o n of the e f f e c t s of u n c e r t a i n t y on the r i gh t-hand s i de va lues in the l i n e a r programming model . B e t t e r s and Schaefer (1981) d i s c u s s e d a Monte C a r l o s i m u l a t i o n model f o r use in d e c i s i o n r i s k a n a l y s i s and i l l u s t r a t e t h e i r d i s c u s s i o n wi th a Dutch elm d i s e a s e c o n t r o l example. They s t a t e d tha t t h i s procedure c o u l d be a u s e f u l t o o l fo r " a n a l y z i n g a l t e r n a t i v e management s t r a t e g i e s where u n c e r t a i n t y e x i s t s r ega rd ing the outcome of management a c t i v i t i e s and e v e n t s " . Harvest s c h e d u l i n g was l i s t e d among the a p p l i c a t i o n s in which they thought t h i s approach might be u s e f u l . However, as i t s t ands , t h i s t echn ique can not be r e a d i l y combined w i th the r i g i d l i n e a r programming s t r u c t u r e o f t en employed in t imber supp ly models . The gene ra l s t o c h a s t i c t imber supp ly model i l l u s t r a t e d in S e c t i o n 4.5 can be fo rmu la ted fo r s o l u t i o n by a number of s t o c h a s t i c programming approaches . (See K o l b i n (1977) , Sengupta (1972) , or any o ther s t o c h a s t i c programming tex t f o r a d e s c r i p t i o n of the s t o c h a s t i c programming t e chn iques a v a i l a b l e . ) These t e chn iques have not been a p p l i e d to f o r e s t resource a l l o c a t i o n models due to l i m i t a t i o n s imposed by problem s i z e (Dixon and Howit t 1979). There are a few examples of a t tempts to app l y approximate s t o c h a s t i c p rocedures to f o r e s t management mode ls . Dixon (1976) and Dixon and Howitt (1979) a p p l i e d a s t o c h a s t i c c o n t r o l approach to a n a t u r a l r e source a l l o c a t i o n p rob lem. A techn ique 121 known as the L i nea r-Quad ra t i c -Gauss i an (LQG) c o n t r o l method was a p p l i e d to keep the a c t u a l e v o l u t i o n of the system ' c l o s e ' to a set of p rede te rmined l e v e l s . Hoganson (1981) r e f o rmu l a t ed a l i n e a r programming model of t imber supp ly p r o j e c t i o n w i t h i n a s i m u l a t i o n framework to i n c o r p o r a t e the s t o c h a s t i c na ture of f u tu re h a r v e s t i n g l e v e l s . H is p rocedure schedu les management a c t i o n s in such a manner that p o t e n t i a l l o s s e s under d i f f e r e n t l e v e l s of f u t u r e ha rves t requ i rements are m in im ized . C o s t i (1983) compared the e s s e n t i a l l y open-looped s t r u c t u r e of Type I and Type II models of t imber supp ly (Johnson and Scheurman 1977) wi th the c l o s e d - l o o p s t r u c t u r e of Dixon and Howitt (1979) . He noted tha t a t r a d e o f f e x i s t s between the a b i l i t y to handle a l a rge-d imens ioned s t a t e in the former wi th the feedback a b i l i t y and p o s s i b l i t y of i n c o r p o r a t i n g s t o c h a s t i c components in the l a t t e r . C a s t i exp lo r ed a l t e r n a t i v e s o l u t i o n procedures i n c l u d i n g imbedding l i n e a r programming w i t h i n an o v e r a l l dynamic programming framework to a i d in h a n d l i n g d i m e n s i o n a l i t y . The s p e c i f i c problem of f o r m u l a t i n g a p p r o p r i a t e management s t r a t e g i e s r e q u i r e s a h igh l e v e l of d i m e n s i o n a l i t y i f a s u i t a b l y l a r g e c and ida t e set of p o t e n t i a l a c t i v i t i e s i s e x p l o r e d . T h i s i m p l i e s the need fo r a s t r i c t l i n e a r programming s t r u c t u r e fo r f o r m u l a t i n g management s t r a t e g i e s p r o v i d i n g r e l e v a n t u n c e r t a i n t y can be i n c o r p o r a t e d in some manner. F l o r a (1964) suggested c a t e g o r i z i n g types of u n c e r t a i n t y and e l i m i n a t i n g from the d e c i s i o n environment those c a t e g o r i e s which do not p e r t a i n to the immediate d e c i s i o n . T h i s i s the 1 22 i n t en t of the a n a l y t i c a l s epa r a t i on suggested between the t imber ha rves t p a t t e r n d e c i s i o n and the t imber management s t r a t e g y d e c i s i o n . The next chapte r p r e s e n t s h e u r i s t i c arguments suppo r t i ng t h i s s e p a r a t i o n and p r e s e n t s a methodology fo r f o r m u l a t i n g t imber management s t r a t e g i e s which i n c o r p o r a t e s the r i s k a s s o c i a t e d w i th response to p o t e n t i a l management a c t i v i t i e s . Whi le such an approach l a cks the mathemat ica l e legance of C a s t i ' s f o r m u l a t i o n , i t does appear to be c o n s i d e r a b l y e a s i e r to implement and to p rov i de a good s o l u t i o n to the d e c i s i o n problem add res sed . A feedback loop would appear to be s u p e r f l u o u s in de te rm in ing the s p e c i f i c s of a t imber management s t r a t e g y u n t i l the u n c e r t a i n t y o u t s i d e of the immediate d e c i s i o n environment i s b e t t e r unde r s tood . 1 23 CHAPTER VII I  DEVELOPMENT OF A DECISION METHODOLOGY The f i r s t seven chap te r s of t h i s d i s s e r t a t i o n have i n t r o d u c e d the f o r e s t management problem and e s t a b l i s h e d a r e l a t i o n s h i p between t h i s l a r g e r problem and the t imber management subproblem. Management of the f o r e s t system as a whole or of any of the s p e c i f i c resource use c a t e g o r i e s which compr ise the f o r e s t system was c o n s i d e r e d as a d e c i s i o n prob lem. The d e c i s i o n problem i n v o l v e s s e l e c t i n g a set of management a c t i o n s (a management s t r a t e g y ) to app ly to the resource base in order to maximize the owner 's p e r c e p t i o n of r e t u r n . The d e c i s i o n p rocess i s comp l i c a t ed by the comp lex i t y of the d e c i s i o n env i ronment , and c o n s i d e r a b l e u n c e r t a i n t y su r round ing the p resen t s t a t e of the sys tem, the d e s i r e d f u t u r e s t a t e of the system and responses of the system to any management a c t i o n s t aken . P a r t i c u l a r sources of u n c e r t a i n t y were examined in some d e t a i l as were gene ra l and s p e c i f i c s t r a t e g i e s fo r a i d i n g d e c i s i o n s under c o n d i t i o n s of u n c e r t a i n t y . T h i s chapte r w i l l p l a c e the concepts p r e v i o u s l y i n t roduced i n t o a gene ra l methodology f o r f o r m u l a t i n g and s e l e c t i n g t imber management s t r a t e g i e s . Arguments w i l l be p r e sen ted to support the methodology s e l e c t e d . T h i s methodology w i l l be shown to ma in ta in l i n k a g e s between the mode l led p o r t i o n of the t imber management subproblem and o ther a spec t s of the subproblem, as w e l l as the f o r e s t management problem as a whole . 124 8.1 R a t i o n a l e f o r the M o d e l l i n g Context Models of some p o r t i o n of the f o r e s t system a i d the d e c i s i o n maker in p r o j e c t i n g the impacts of p resen t and a n t i c i p a t e d f u t u r e a c t i o n s on the p o r t i o n m o d e l l e d . If the d e s i r e d f u t u r e s t a t e of the f o r e s t system i s known, mode l l i ng can be used to h e l p c o n s t r u c t a s t r a t e g y which i s expected to a l l ow the f o r e s t system to a t t a i n t h i s d e s i r e d s t a t e . It i s r easonab le to expect the d e c i s i o n maker to change h i s management s t r a t e g y over t ime as responses of the system to v a r i o u s a c t i o n s taken become known or as the d e s i r e d f u tu r e s t a t e of the system ( i . e . management goa l s ) change. There i s a bas i c c o n f l i c t p resen t in any s o l u t i o n approach to the f o r e s t management problem which r e q u i r e s m o d e l l i n g in some form or o t h e r . The problem i s o f t e n too complex to model as a whole in s u f f i c i e n t d e t a i l to a l l ow m o d e l l i n g to p rov ide a u s e f u l t o o l in the development of s p e c i f i c management s t r a t e g i e s fo r the d i f f e r e n t f o r e s t r e s o u r c e s . Consequen t l y , the f o r e s t management problem has o f t e n been d i v i d e d both c o n c e p t u a l l y and j u r i s d i c t i o n a l l y i n t o resource use ca t ego ry subprob lems. Each of these subproblems has , in t u r n , o f t e n been f u r t h e r d i v i d e d g e o g r a p h i c a l l y as warranted by the s i z e and the d i s t r i b u t i o n of the l and a rea i n v o l v e d . T h i s h i e r a r c h i c a l approach by resource agenc i es to the f o r e s t management problem has p e r m i t t e d the use of more d e t a i l e d mode l l i ng and enhanced the u s e f u l n e s s of models as a i d s in the f o rmu l a t i on and implementat ion of s p e c i f i c management s t r a t e g i e s . In the case of t imber management, r a the r e l a b o r a t e m o d e l l i n g systems have e vo l ved to a s s i s t the manager. E x i s t i n g p o l i c y has p rov ided the l i n k a g e s between the d i f f e r e n t 1 25 s u b d i v i s i o n s of the f o r e s t management p rob lem. C o n s i d e r a b l e u n c e r t a i n t y e x i s t s at a l l l e v e l s of the f o r e s t management p rob lem. No matter how the problem i s decomposed, a d e c i s i o n model at any l e v e l can on l y d i r e c t l y i n c o r p o r a t e the u n c e r t a i n t y which e x i s t s at that l e v e l . U n c e r t a i n t y which e x i s t s at h ighe r h i e r a r c h i a l l e v e l s must be assumed to be addressed through p o l i c y ( nonde l i be r a t ed d e c i s i o n s ) . In terms of t imber supply m o d e l l i n g t h i s means that on l y sources of u n c e r t a i n t y d i r e c t l y encountered when e s t i m a t i n g model parameters can be e x p l i c i t l y mode l l ed . Some p o l i c y must be assumed to p rov ide s t r u c t u r e fo r the mode l . T h i s i s not to say tha t t imber supp ly models can not be used to t e s t the i m p l i c a t i o n s of d i f f e r e n t p o l i c i e s , but r a the r tha t to use such models to a i d in deve l op ing t imber management s t r a t e g i e s fo r a p a r t i c u l a r a r e a , some p o l i c y s t r u c t u r e must be g i v e n . In o rder to deve lop a comprehensive model or models which can i n c o r p o r a t e the major sources of u n c e r t a i n t y , the f o r e s t management problem must be c o n s i d e r e d h o l i s t i c a l l y . T h i s c o n f l i c t must be addressed in the development of a d e c i s i o n methodology to a i d in the f o r m u l a t i o n and s e l e c t i o n of t imber management s t r a t e g i e s . In o rder fo r the methodology to be u s e f u l i t must encompass s u f f i c i e n t l y d e t a i l e d m o d e l l i n g of the t imber r e sou r ce on any s p e c i f i e d g e o g r a p h i c a l a rea to be a u s e f u l d e c i s i o n t o o l . In order fo r the methodology to be a p p r o p r i a t e f o r the f o r e s t management problem as a whole , i t must p r o v i d e f o r i m p l i c i t or e x p l i c i t r e c o g n i t i o n of u n c e r t a i n t y e x t e r n a l to any mode l l i ng procedure employed. A n a l y t i c s e p a r a t i o n of the t imber management problem 1 26 p r o v i d e s one means of a d d r e s s i n g t h i s c o n f l i c t . T h i s concept was i n t r o d u c e d b r i e f l y in Chapter III when t imber management was d e s c r i b e d as be ing compr ised of two i n t e r r e l a t e d d e c i s i o n s : (1) the c h o i c e of a h a r v e s t i n g p a t t e r n and (2) the s e l e c t i o n of a t imber management s t r a t e g y . S epa ra t i on a l l ows the d e c i s i o n model deve loped to a i d in the s e l e c t i o n of a t imber management s t r a t e g y to be c o n s i d e r a b l y s i m p l i f i e d . T h i s , in t u r n , f a c i l i t a t e s e x p l i c i t c o n s i d e r a t i o n of some sources of u n c e r t a i n t y in the d e c i s i o n mode l . I t must be s t r e s s e d tha t the two components shou ld be i n t e g r a t e d in the development of any t imber management p l a n . The degree to which t h i s i n t e g r a t i o n occu rs i s a f u n c t i o n of the p l a n n i n g system in e f f e c t and the q u a n t i t y and q u a l i t y of i n f o r m a t i o n a v a i l a b l e . A t imber supp ly model r e q u i r e s i npu ts of management s t r a t e g y , h a r v e s t i n g p a t t e r n and some p o l i c y s t r u c t u r e to p r e d i c t f u tu r e t imber s u p p l y . If two of these components are taken as g i v e n , the t h i r d can be v a r i e d and the e f f e c t on the mode l l ed problem obse r ved . I f s e l e c t i o n of a h a r v e s t i n g p a t t e r n and c h o i c e of a t imber management s t r a t e g y are c o n s i d e r e d s e p a r a t e l y , i t can be shown tha t they d i f f e r in t h e i r scope and in the sources and amount of u n c e r t a i n t y p resen t in the d e c i s i o n p r o c e s s . The c h o i c e of a ha r ves t p a t t e r n and the d e t e r m i n a t i o n of a p p r o p r i a t e p o l i c y p e r t a i n to the d e s i r e d f u tu r e s t a t e of the f o r e s t sys tem. The c h o i c e of a d e s i r e d f u t u r e s t a t e r e q u i r e s c o n s i d e r a t i o n of r e sou rce use c a t e g o r i e s o ther than t imber and i n c l u d e i n f o rma t i on sources beyond the bounds of the f o r e s t 127 system. T h i s p r e c l u d e s e f f e c t i v e m o d e l l i n g to a i d in the c h o i c e s o l e l y at the l e v e l of the t imber supply model . Any models employed f o r t h i s purpose must, of n e c e s s i t y , be more macroscop ic in nature than t y p i c a l t imber supp ly models . The development and improvement of such models i s e s s e n t i a l to b e t t e r management of the f o r e s t system in the f u t u r e , but i s beyond the bounds of t h i s d i s s e r t a t i o n . S e l e c t i n g a harves t pa t t e rn e s s e n t i a l l y i n v o l v e s i m p l i c i t or e x p l i c i t s e l e c t i o n of a f u tu r e d e s i r e d s t a t e fo r the f o r e s t system. It i s at t h i s l e v e l tha t l i n k a g e s are ma in ta ined wi th the other r esource use c a t e g o r i e s which compr ise the system. T r a d i t i o n a l l y the d e s i r e d s t a t e of the p o r t i o n of the system a l l o c a t e d to t imber p roduc t i on has been a f u l l y r e g u l a t e d f o r e s t and the ha r ves t pa t t e rn was s e l e c t e d to ach ieve such a s t a t e over some time p e r i o d sub jec t to c e r t a i n r e s t r i c t i o n s . T h i s concept can be extended to i n c l u d e any d e s i r e d s t a t e and to opera te under a v a r i e t y of p o l i c y sys tems. A h a r v e s t i n g pa t t e rn may be s e l e c t e d fo r s p e c i f i c a reas w i t h i n the t o t a l area managed by a p a r t i c u l a r agency. Any p a t t e r n , wh i l e s e n s i t i v e to l o c a l c o n d i t i o n s , w i l l l i k e l y be sub jec t to the same broad p o l i c y parameters (based on some agency-wide v i s i o n o fa d e s i r e d f u t u r e s t a t e of the f o r e s t resource ) as p a t t e r n s chosen fo r o ther a reas w i t h i n the same j u r i s d i c t i o n . There i s c o n s i d e r a b l e u n c e r t a i n t y i n v o l v e d in a c h o i c e of a h a r v e s t i n g p a t t e r n . The u n c e r t a i n t y i s p r i n c i p a l l y c e n t r e d on the l e v e l of demand fo r v a r i o u s f o r e s t p roduc t s in the d i s t a n t f u t u r e . T h i s a f f e c t s the a l l o c a t i o n of the f o r e s t l and base 1 28 among c o n f l i c t i n g uses as we l l as the d e s i r e d s t r u c t u r e of the f o r e s t f o r p roduc ing wood p r o d u c t s . The cho i c e of a ha rves t pa t t e rn i s t i e d to management s t r a t e g i e s and p resen t f o r e s t i nven to ry in so f a r as i t shou ld be ' a c h i e v a b l e ' g i ven p resen t t e chno logy , fund ing l e v e l s and a v a i l a b l e growing s t o c k . Hence management s t r a t e g y p o s s i b i l i t i e s l i m i t the cho i c e of proposed harves t p a t t e r n s , but do not set the p a t t e r n . In a s i m i l a r manner, the cho i c e of a harves t p a t t e r n gu ides the c h o i c e of a t imber management s t r a t e g y , but does not make the c h o i c e . Cho ice of a t imber management s t r a t e g y shou ld be dependent upon the h a r v e s t i n g p a t t e r n d e s i r e d over t ime . I t i s more of an i n d i v i d u a l management un i t d e c i s i o n than the s e l e c t i o n of a h a r v e s t i n g p a t t e r n . The d e c i s i o n s on d i f f e r e n t u n i t s are not t o t a l l y independent because there w i l l l i k e l y be a common source of fund ing and other input requ i rements which may be l i m i t e d . P o l i c y c o n s t r a i n t s may a l s o be q u i t e b i n d i n g in terms of which management a c t i o n s are c o n s i d e r e d s u i t a b l e fo r any management un i t . U n c e r t a i n t y en te r s i n t o the c h o i c e through p r o j e c t i o n of t imber supp ly under the assumed s t r a t e g y . I f the proposed h a r v e s t i n g p a t t e r n i s to be a t t a i n e d , the growing s tock must be of a s u i t a b l e s i z e and d i s t r i b u t i o n to ' a l l o w ' the p r o j e c t e d h a r v e s t i n g l e v e l at v a r i o u s p o i n t s in the f u tu r e under e x i s t i n g p o l i c y . As long as a h a r v e s t i n g p a t t e r n does not r e q u i r e a growth r a te and a f o r e s t s t r u c t u r e which i s p h y s i c a l l y imposs ib l e fo r the f o r e s t to a t t a i n , i t shou ld be p o s s i b l e to f o l l o w the p a t t e r n w i th some t imber management s t r a t e g y . Whether such a s t r a t e g y i s r e c o g n i z e d , or the c o s t of a p p l y i n g such a 129 s t r a t e g y i s p r o h i b i t i v e , i s an e n t i r e l y d i f f e r e n t q u e s t i o n . The key p o i n t i s tha t o v e r - c u t t i n g i s not n e c e s s a r i l y a matter of s e t t i n g a h a r v e s t i n g l e v e l which i s too h i g h , but a matter of not s e l e c t i n g or implementing a management s t r a t e g y which causes the f o r e s t to respond in the manner a n t i c i p a t e d . The r i s k i n v o l v e d in the c h o i c e of a t imber management s t r a t e g y , g i ven a h a r v e s t i n g p a t t e r n , in the sepa ra ted t imber management problem p e r t a i n s on ly to whether the s t r a t e g y w i l l enable t h i s a p r i o r i p a t t e r n of h a r v e s t . T h i s r i s k i s caused by u n c e r t a i n t y su r round ing f u tu r e l e v e l s and d i s t r i b u t i o n s of growing s tock g i ven a p a r t i c u l a r management s t r a t e g y . Such u n c e r t a i n t y i s caused by imper fec t i n f o r m a t i o n conce rn ing p resen t i n ven to r y l e v e l s , d i f f e r e n t p o s s i b l e responses to p a r t i c u l a r management a c t i o n s and the i n f l u e n c e of f a c t o r s i n t e r n a l or e x t e r n a l to the f o r e s t system whole ly or p a r t i a l l y beyond the d e c i s i o n maker ' s c o n t r o l . The e x i s t e n c e of a p a r t i c u l a r h a r v e s t i n g p a t t e r n and p o l i c y s t r u c t u r e can be c o n s i d e r e d as pa r t of the p r i o r b e l i e f s of the d e c i s i o n maker from a d e c i s i o n a n a l y t i c v i e w p o i n t . The s e l e c t i o n of a management s t r a t e g y c o u l d then be made w i t h i n e x i s t i n g c o n s t r a i n t s assuming a p a r t i c u l a r h a r v e s t i n g p a t t e r n . Cho ice among p r o s p e c t i v e s t r a t e g i e s , under these c o n d i t i o n s , shou ld be made on the b a s i s of cos t of a p p l i c a t i o n and the degree of r i s k i n v o l v e d i n not p roduc ing a f o r e s t s t r u c t u r e which w i l l ' a l l o w ' the h a r v e s t i n g p a t t e r n p roposed . 1 3 0 8.2 R e l a t i o n s h i p Between the Mode l l ed and Non-model ied Aspec ts  of the Problem Sepa ra t i on of the t imber management problem a l l ows the d e c i s i o n maker to view t imber management s t r a t e g y f o r m u l a t i o n and s e l e c t i o n wi thout e x p l i c i t c o n s i d e r a t i o n of the o ther a spec t s of the f o r e s t management p rob lem. However, i f the s t r a t e g y i s to be a p p r o p r i a t e , some l i n k a g e s must be ma in ta ined between the s p e c i f i c problem of choos ing a t imber management s t r a t e g y and the more macroscop ic i s sues of the f o r e s t management p rob lem. E x i s t i n g p o l i c y s t r u c t u r e has been mentioned p r e v i o u s l y as one mechanism fo r m a i n t a i n i n g such r e l a t i o n s h i p s . From an a n a l y t i c a l p e r s p e c t i v e , the key component i s the t imber supp ly m o d e l l i n g p rocedure . There i s no need fo r the t imber supply models employed to be the same f o r both a spec t s of the t imber management p rob lem. In f a c t , t he re are d i s t i n c t advantages to employ ing d i f f e r e n t mode l l i ng approaches . A t imber supply model p r o v i d e s on l y one source of i n f o rma t i on r e q u i r e d fo r s e l e c t i n g a h a r v e s t i n g p a t t e r n . (See F i g u r e 5.) I t can be used to moni tor the p o t e n t i a l e f f e c t s of d i f f e r e n t p o l i c i e s and h a r v e s t i n g p a t t e r n s on p r o j e c t e d t imber supp ly and f o r e s t s t r u c t u r e . Whi le i t i s important tha t some l i n k a g e be ma in ta ined wi th the p resen t s t a t e of the f o r e s t r e s o u r c e , more emphasis shou ld be p l a ced on the d e s i r e d fu tu re s t a t e of the f o r e s t system and p o l i c y f o r m u l a t i o n . Some assumptions conce rn i ng t imber management s t r a t e g i e s must be made in such a n a l y s e s , but the s t r a t e g i e s assumed shou ld be kept g e n e r a l . 131 F i g u r e 5: Schematic I l l u s t r a t i o n of the Role of Timber Supply M o d e l l i n g in Harves t P a t t e r n D e c i s i o n s . EXTERNAL INFORMATION SOURCES -ECONOMIC FORECASTS -PUBLIC OPINIONS -INDUSTRY OPINIONS -POLITICAL REALITY DESIRED FUTURE STATE OF THE FOREST SYSTEM POLICY FORMULATION CHOICE OF HARVESTING PATTERN TIMBER SUPPLY MODEL PRESENT STATE OF THE TIMBER RESOURCE ON THE MANAGEMENT UNIT S i m u l a t i o n would be an i d e a l mode l l i ng approach fo r t imber supp ly under these c i r c u m s t a n c e s . I t would a l l ow the examinat ion of many 'what i f q u e s t i o n s wi thout f o r c i n g the problem i n t o some r i g i d s t r u c t u r e to a l l ow mathemat ica l s o l u t i o n . The idea of 132 F i gu re 6 : Schematic I l l u s t r a t i o n of the Role of Timber Supply M o d e l l i n g in Fo rmu la t i on of Timber Management S t r a t e g i e s . HARVESTING PATTERN PRESENT STATE OF THE TIMBER RESOURCE ON A MANAGEMENT UNIT TIMBER SUPPLY MODEL MANAGEMENT STRATEGY POLICY CANDIDATE SET OF MANAGEMENT ACTIONS some ' o p t i m a l ' model s o l u t i o n i s a l i e n to t h i s so r t of d e c i s i o n p rob lem. In f a c t , the i n f o rma t i on sources i n v o l v e d make any formal d e c i s i o n methodology ext remely d i f f i c u l t , i f not i m p o s s i b l e , to f o r m u l a t e . A t imber supp ly model can be c o n s i d e r e d c e n t r a l to the p rocess of f o r m u l a t i n g a t imber management s t r a t e g y . (See F i g u r e 6 . ) I t p r o v i d e s the e s s e n t i a l l i n k a g e between what i s c u r r e n t l y p resen t on the g round , the h a r v e s t i n g p a t t e r n s e l e c t e d and the p o l i c y s t r u c t u r e in e f f e c t . Models used f o r t h i s purpose were l a b e l l e d as t imber management models i n Chapter I I . Fo rmu la t i on of management s t r a t e g i e s under d e t e r m i n i s t i c c o n d i t i o n s i s w e l l - s u i t e d to s o l u t i o n by mathemat ica l programming approaches . Such models w i l l p ro v i de a s t r a t e g y 133 which o p t i m i z e s some o b j e c t i v e f u n c t i o n c r i t e r i o n g i ven a c and ida t e se t of management a c t i o n s sub jec t to a d e s i r e d h a r v e s t i n g p a t t e r n and a p a r t i c u l a r p o l i c y s t r u c t u r e . Under r e a l c o n d i t i o n s i t i s reasonab le to assume some tempora l o v e r l a p between the d e c i s i o n p r o c e s s e s . I f t h i s i s indeed the c a s e , i t e r a t i o n between the m o d e l l i n g p rocesses would be p o s s i b l e . I n i t i a l h a r v e s t i n g p a t t e r n s c o u l d be r e v i s e d based on s p e c i f i c i n f o r m a t i o n ga thered du r i ng the f o r m u l a t i o n of management s t r a t e g i e s . T h i s in tu rn c o u l d l ead to changes in the p o t e n t i a l management s t r a t e g i e s , perhaps to f u r t h e r changes in the h a r v e s t i n g p a t t e r n , and so on u n t i l the h a r v e s t i n g p a t t e r n and the p o t e n t i a l t imber management s t r a t e g i e s appear c o m p a t i b l e . At t h i s p o i n t a d e c i s i o n must be made as to which management s t r a t e g y to f o l l o w . Obv ious l y any p o l i c y changes or changes in the a l l o c a t i o n of the f o r e s t l and base between compet ing uses would upset t h i s d e l i c a t e ba lance and s t a r t the p rocess i n mot ion once a g a i n . Such a procedure f a l l s under the realm of p l ann ing system d e s i g n . The p o s s i b i l i t y of i t e r a t i o n w i l l not be pursued f u r t h e r in t h i s d i s s e r t a t i o n . I t w i l l s u f f i c e to say tha t some i m p l i c i t or e x p l i c i t i t e r a t i v e procedure i s necessa ry in a f o r e s t p l a n n i n g system which i n v o l v e s separa te ana l y ses of the d e c i s i o n components. 8.3 Development of a Methodology fo r Fo rmu la t i on and S e l e c t i o n  of a Timber Management S t r a t egy The t imber management s t r a t e g y d e c i s i o n problem faced by the f o r e s t manager can be f o r m a l l y s t a t e d a s : F i n d S * e { S , . . . , S , . . . , S } 1 i n 134 such tha t E (V(S* ) ) i s o p t i m a l . Sub jec t t o : (1) A p a r t i c u l a r p a t t e r n of ha r ves t (2) P resent p o l i c y l i m i t a t i o n s where S * i s the ' b e s t ' management s t r a t e g y of the cand ida te se t c o n s i d e r e d . E (V(S* ) ) i s the expected va lue of some c r i t e r i o n ( c r i t e r i a ) used f o r choos ing between t imber management s t r a t e g i e s . The s o l u t i o n of such a problem can be decomposed i n t o two p a r t s : 1. Fo rmu la t i on of i n d i v i d u a l management s t r a t e g i e s which are thought to be f e a s i b l e . 2. S e l e c t i o n of one management s t r a t e g y thought to be the ' b e s t ' of the s t r a t e g i e s c o n s i d e r e d . These components may be c l o s e l y r e l a t e d depending on the method employed to fo rmula te c and ida t e s t r a t e g i e s . 8.3.1 Fo rmu la t i on of Timber Management S t r a t e g i e s A l l too f r e q u e n t l y t imber management s t r a t e g i e s are s e l e c t e d wi thout e x p l i c i t c o n s i d e r a t i o n of the broad management s t r a t e g i e s assumed d u r i n g p r o j e c t i o n of t imber s u p p l y . L i m i t a t i o n s in f u n d i n g , e x p e r t i s e and manpower can r e s u l t in the implementat ion of a s t r a t e g y q u i t e d i f f e r e n t from that env i saged in long-term t imber supp ly a n l a y s e s . T r a n s l a t i o n of fund ing i n t o s i l v i c u l t u r a l a c t i o n s on the ground i s o f t en not r e l a t e d to the expec ted impact on the t imber supp ly from the f o r e s t a rea ( E rd l e 1984). Such f a c t o r s can cause a d e v i a t i o n between the p lanned 1 35 harves t p a t t e r n and the a c t u a l h a r v e s t i n g ra te ' a l l o w e d ' at any t ime q u i t e apar t from any d i f f i c u l t i e s caused by u n c e r t a i n t y about f o r e s t response and d e s i r e d f u t u r e s t a t e s . A l though the methodology p resen ted r e q u i r e s a a n a l y t i c a l s e p a r a t i o n between the cho i ce of a h a r v e s t i n g p a t t e r n and the s e l e c t i o n of a t imber management s t r a t e g y , the d e c i s i o n s remain l i n k e d through the t imber supp ly m o d e l l i n g p rocedu re . Whatever the model form employed to a i d in the f o rmu l a t i on and s e l e c t i o n of the management s t r a t e g y , i t must be s t r u c t u r e d to r e f l e c t e x i s t i n g p o l i c y and the d e s i r e d ha rves t p a t t e r n . It i s a l s o important tha t the s t r a t e g i e s fo rmu la ted r e f l e c t the c r i t e r i o n ( c r i t e r i a ) which w i l l be employed to choose between them. If the t imber h a r v e s t i n g pa t t e rn has been s e t , an obv ious b a s i s f o r the cho i c e between s t r a t e g i e s would be the cos t a s s o c i a t e d w i th each s t r a t e g y . Return from the t imber resource i s a f u n c t i o n of the amount of v a r i o u s t imber p roduc t s s u p p l i e d by h a r v e s t i n g and the u n i t va lue of those p roduc t s over t ime . C o n s i d e r a t i o n of p o t e n t i a l r e t u rns from the t imber resource and o ther f o r e s t r e sou r ces i s an important c r i t e r i o n in the cho i c e of a t imber h a r v e s t i n g p a t t e r n , but not necessa ry to the cho i c e of a management s t r a t e g y g iven a p a r t i c u l a r h a r v e s t i n g p a t t e r n . Once a p a t t e r n has been chosen , s e l e c t i o n of a t imber management s t r a t e g y shou ld be made on the b a s i s of a c h i e v i n g the d e s i r e d h a r v e s t i n g p a t t e r n in the most e f f i c i e n t manner ( i . e . f o r the l e a s t c o s t ) . The c o s t a s s o c i a t e d wi th any s t r a t e g y w i l l be compr ised of d i r e c t and i n d i r e c t components. D i r e c t cos t i s dependent upon presen t and p r o j e c t e d c o s t s of a p p l y i n g the v a r i o u s t rea tments 1 3 6 compr i s i ng the s t r a t e g y on a u n i t a rea b a s i s . I n d i r e c t cos t i s a s s o c i a t e d w i th the r i s k of not p roduc ing a f o r e s t s t r u c t u r e at a p a r t i c u l a r p o i n t in t ime which w i l l enab le the h a r v e s t i n g r a te d e s i r e d . I t i s not important tha t the t o t a l cos t a s s o c i a t e d w i th any s t r a t e g y be the ' t r u e ' cos t of a p p l y i n g the s t r a t e g y . As long as the d i f f e r e n c e s between the c o s t s fo r the v a r i o u s s t r a t e g i e s are r e f l e c t i v e of the ' t r u e ' d i f f e r e n c e s , a r a t i o n a l cho i c e can be made. For example, i t i s not necessa ry to i n c o r p o r a t e the p o s s i b i l i t i e s of f u tu re changes to the t imber h a r v e s t i n g p a t t e r n i n t o the t o t a l c o s t of a management s t r a t e g y s i n ce most of the f a c t o r s which w i l l i n f l u e n c e t h i s change can e s s e n t i a l l y be c o n s i d e r e d to be independent of the management s t r a t e g y s e l e c t e d ( i . e . t e c h n o l o g i c a l i n o v a t i o n s , g l o b a l economic p a t t e r n s , et  c e t e r a ) . Any e f f e c t a p a r t i c u l a r management s t r a t e g y might have on fu tu re h a r v e s t i n g p a t t e r n s w i l l be r e f l e c t e d in the i n d i r e c t c o s t component. S i m i l a r l y , the l i k e l i h o o d of c a t a s t r o h p i c l o s s e s from sources comp le te l y beyond the f o r e s t manager 's c o n t r o l ( ea r thquakes , v o l c a n i c a c t i v i t y , et c e t e r a ) can be ignored because the i n f l u e n c e would be the same on any of the s t r a t e g i e s . E f f e c t s of p o t e n t i a l l o s s e s to o ther damaging agents ( i n s e c t s , d i s e a s e s , f i r e , et c e t e r a ) can not be i gnored e n t i r e l y s i n ce p a r t i c u l a r management a c t i o n s can a f f e c t the p r o b a b i l i t y of l o s s , and hence , f u t u r e f o r e s t y i e l d s . D i scount r a te must a l s o be c o n s i d e r e d s i n c e c o s t s a s s o c i a t e d w i th a l t e r n a t i v e s t r a t e g i e s w i l l be spread over time in d i f f e r e n t p a t t e r n s so the p resen t cos t a s s o c i a t e d w i th any s t r a t e g y w i l l be dependent upon the d i s c o u n t r a te employed. I t 137 i s beyond the scope of t h i s d i s s e r t a t i o n to specu l a t e on what the d i s c o u n t r a t e shou ld be . I t w i l l s u f f i c e to say that the p r o b a b i l i t y of f o l l o w i n g any p a r t i c u l a r s t r a t e g y i n i t i a l l y s e l e c t e d w i l l dec rease w i th time fo r any t imber h a r v e s t i n g p a t t e r n . Even i f the h a r v e s t i n g p a t t e r n remains unchanged, t e c h n o l o g i c a l deve lopments , a d d i t i o n a l i n f o r m a t i o n on response to p a r t i c u l a r management a c t i o n s and unforeseen changes to the f o r e s t s t r u c t u r e c o u l d change the compos i t i on of the management s t r a t e g i e s c o n s i d e r e d . T h i s would suggest some p o s i t i v e d i s coun t r a te w i th a n t i c i p a t e d c o s t s in the near f u t u r e c o n t r i b u t i n g a s i g n i f i c a n t l y h ighe r p r o p o r t i o n of the t o t a l cos t a s s o c i a t e d w i th any management s t r a t e g y than a n t i c i p a t e d c o s t s in the more d i s t a n t f u t u r e . A t imber management s t r a t e g y may be compr ised of a number of sequences of management a c t i o n s o r i g i n a t i n g at d i f f e r e n t p o i n t s in t ime . If a t imber ha rves t p a t t e r n i s thought to be a t t a i n a b l e w i th some management s t r a t e g y , the re are l i k e l y a number of v a r i a t i o n s of tha t management s t r a t e g y which would a l s o p r o v i d e f e a s i b l e s o l u t i o n s . The d e c i s i o n maker would wish to s e l e c t the s t r a t e g y which i s the ' b e s t ' of a l l the f e a s i b l e s t r a t e g i e s . A problem s t r u c t u r e d i n t h i s way can employ some type of mathemat ica l programming to c o n s t r u c t an ' o p t i m a l ' s t r a t e g y from the cand ida te set of management sequences ( a c t i v i t i e s ) sub j ec t to the c o n s t r a i n t s imposed by i n i t i a l f o r e s t s t r u c t u r e , d e s i r e d h a r v e s t i n g p a t t e r n and p o l i c y . In o rder fo r the s o l u t i o n of the mode l l ed problem to be a p p r o p r i a t e f o r the r e a l d e c i s i o n of what t imber management s t r a t e g y to s e l e c t , the c r i t e r i o n ( c r i t e r i a ) used in f o rmu l a t i ng 1 38 the s t r a t e g y in the model shou ld be the same as that which would be used to choose one s t r a t e g y from among s e v e r a l s t r a t e g i e s . I t has a l r e a d y been i n d i c a t e d tha t t o t a l cos t appears to be an a p p r o p r i a t e c r i t e r i o n p r o v i d i n g d i r e c t and i n d i r e c t c o s t s can be a s s i g n e d to the i n d i v i d u a l a c t i v i t i e s which w i l l compr ise the s t r a t e g y . 8 .3 .2 I n c o r p o r a t i o n of U n c e r t a i n t y The u n c e r t a i n t y of immediate concern to the d e c i s i o n maker i n v o l v e d in f o r m u l a t i n g a management s t r a t e g y i s a s s o c i a t e d wi th the expected response to any management sequence. Response can be measured as the expected volume of wood a v a i l a b l e fo r ha rves t on an average ha of l and at some p o i n t in time (expected y i e l d ) . The u n c e r t a i n t y su r round ing the response i s r e f l e c t e d by the d i s t r i b u t i o n of p o t e n t i a l y i e l d s which the d e c i s i o n maker a s s o c i a t e s w i th the management sequence. The c o n t r i b u t i o n of any sequence towards a c h i e v i n g the d e s i r e d h a r v e s t i n g p a t t e r n may be measured as the expected amount of wood a v a i l a b l e f o r ha r ves t on a per ha b a s i s t imes the number of ha managed a c c o r d i n g to tha t sequence. If the d e c i s i o n maker i s r i s k n e u t r a l , he would be conten t w i th t h i s f o r m u l a t i o n of the p rob lem, and c o n s t r u c t t imber management s t r a t e g i e s us ing on ly the d i r e c t c o s t s of the cand ida te management sequences as the c r i t e r i o n f o r i n c l u s i o n in the management s t r a t e g y . Such a s tance would a l l ow d e t e r m i n i s t i c s o l u t i o n s . I t has been i n d i c a t e d p r e v i o u s l y that f o r e s t managers, at l e a s t on p u b l i c l a n d , can be expected to be r i s k averse to some deg ree . A r i s k averse manager would be w i l l i n g to pay some 1 39 premium to reduce the r i s k of not a c h i e v i n g the d e s i r e d h a r v e s t i n g p a t t e r n . In terms p e r t i n e n t to the s e l e c t i o n of a management s t r a t e g y , t h i s means the manager would be w i l l i n g to s e l e c t a more expens ive management s t r a t e g y in terms of expected cos t of imp lementa t ion , i f the r i s k he a s s o c i a t e s with not be ing ab l e to ach ieve a p a r t i c u l a r h a r v e s t i n g l e v e l i s reduced to some e x t e n t . The amount by which he i s w i l l i n g to i n c r ease the expected cos t of implementat ion to reduce the a s s o c i a t e d r i s k by some un i t va lue i s d i c t a t e d by the degree of h i s r i s k a v e r s i o n . The a d d i t i o n of an i n d i r e c t cos t component to the d i r e c t cos t a s s o c i a t e d wi th any management sequence w i l l a l l ow the u n c e r t a i n t y a s s o c i a t e d w i th the response of t imber managed a c c o r d i n g to that sequence to be i n c o r p o r a t e d in the f o rmu l a t i on of a t imber management s t r a t e g y . Management sequences which are l e s s c e r t a i n (sequences which have a wider d i s t r i b u t i o n of p o t e n t i a l y i e l d s around the expected y i e l d ) shou ld have a h ighe r i n d i r e c t c o s t component than more c e r t a i n sequences . I f management sequences are s e l e c t e d f o r a management s t r a t e g y on the b a s i s of t h e i r c o n t r i b u t i o n to t o t a l c o s t , the i n d i r e c t cos t component w i l l ac t as a pena l t y cos t i n c r e a s i n g the t o t a l cos t of more u n c e r t a i n s t r a t e g i e s to a g r e a t e r ex ten t than the t o t a l cos t of more c e r t a i n s t r a t e g i e s . The r a m i f i c a t i o n of such an approach i s tha t i t a l l ows the u n c e r t a i n t y to be ' c o l l a p s e d ' i n t o the o b j e c t i v e f u n c t i o n of the mathemat ica l programming model a l l o w i n g the c o n s t r a i n t s to be t r e a t e d d e t e r m i n i s t i c a l l y . Fu r the rmore , i f the c o n s t r a i n t s are fo rmu la ted i n a l i n e a r f a s h i o n and the t o t a l c o s t s a s s o c i a t e d w i th any management sequence are t r e a t e d l i n e a r l y , t h i s approach 1 40 a l l ows the model to be s t r u c t u r e d in a manner conduc ive to s o l u t i o n by l i n e a r programming t e c h n i q u e s . S t r u c t u r i n g the model so that i t may be so l v ed us ing l i n e a r programming a l l ows s o l u t i o n s of l a r g e r problems than would be p o s s i b l e u s i n g other mathemat ica l programming models . There i s a t r a d e o f f between p o t e n t i a l e r r o r s i n v o l v e d in f o r c i n g the model i n t o a l i n e a r s t r u c t u r e ve r sus e r r o r s r e s u l t i n g from c o n s i d e r a b l y more agg rega t i on and examinat ion of fewer a l t e r n a t i v e s us i ng o t h e r , l e s s r e s t r i c t i v e t e c h n i q u e s . Given the l a r g e amount of u n c e r t a i n t y p resen t o u t s i d e of the d e c i s i o n environment e x p l i c i t l y i n c l u d e d in the t imber supp ly model , the need fo r p r e c i s e f o r m u l a t i o n of the model s t r u c t u r e pa l e s c o n s i d e r a b l y . 8 .3 .3 De te rm ina t i on of Expected Y i e l d The success of t h i s m o d e l l i n g approach in a i d i n g t imber management s t r a t e g y d e c i s i o n s i s con t i ngen t on the means chosen to c a l c u l a t e expected y i e l d s and i n d i r e c t c o s t s fo r t imber management sequences . These a spec t s tu rn out to be c l o s e l y r e l a t e d . The assumpt ion was made tha t a l l the u n c e r t a i n t y p e r t i n e n t to the c h o i c e of a t imber management s t r a t e g y c o u l d be expressed as p e r c e i v e d d i s t r i b u t i o n s of the y i e l d cu rves a s s o c i a t e d wi th v a r i o u s management sequences . The expec ted y i e l d of a management sequence at any po in t in t ime would s imp ly be the expected va lue of the d i s t r i b u t i o n of y i e l d s p e r c e i v e d at tha t p o i n t . Whi le such a d i s t r i b u t i o n would be c o n t i n u o u s , i t can be approximated by a d i s c r e t e d i s t r i b u t i o n of p o t e n t i a l y i e l d s . 141 It i s e a s i e r fo r the d e c i s i o n maker to v i s u a l i z e a f i n i t e number of d i s t i n c t outcomes fo r any management sequence and a s s o c i a t e a s u b j e c t i v e p r o b a b i l i t y w i th each than to attempt to d e s c r i b e the u n c e r t a i n t y he p e r c e i v e s as some con t inuous d i s t r i b u t i o n of y i e l d s . Each outcome can be d e f i n e d by some y i e l d curve a p p r o p r i a t e fo r an average ha . The expected y i e l d at any t ime can then be c a l c u l a t e d as the sum of the p roduc t s of the p o t e n t i a l y i e l d s t imes t h e i r s u b j e c t i v e p r o b a b i l i t y . 8 .3 .4 C a l c u l a t i o n of D i r e c t and I n d i r e c t Cos t s The d i r e c t cos t of any management sequence i s s imply the sum of the present va lues of a l l c o s t s a s s o c i a t e d wi th implement ing tha t sequence. There may be a p p r e c i a b l e u n c e r t a i n t y su r round ing fu tu re d i r e c t c o s t s , but t h i s shou ld have e s s e n t i a l l y the same impact on a l l the a c t i v i t i e s . Fu r the rmore , the impact of fu tu re cos t u n c e r t a i n t y on p resen t d e c i s i o n s w i l l be d i m i n i s h e d to a l a r g e extent by d i s c o u n t i n g f u t u r e c o s t s . I n d i r e c t cos t must be reasonab l y easy to c a l c u l a t e , r e a d i l y unders tandab le and capab le of be ing expressed on the same b a s i s as d i r e c t c o s t so that t o t a l cos t of any management sequence may be e a s i l y c a l c u l a t e d . For these r easons , no u t i l i t y f u n c t i o n i s fo rmula ted f o r the d e c i s i o n maker and i n d i r e c t cos t i s determined in such a way tha t degree of r i s k a v e r s i o n i s i m p l i c i t in the c a l c u l a t i o n . The r i s k a d e c i s i o n maker a s s o c i a t e s w i th a p a r t i c u l a r management sequence i s r e l a t e d to the d e v i a t i o n he p e r c e i v e s around the expected y i e l d f o r tha t sequence. P o s i t i v e and 142 nega t i ve d e v i a t i o n s from expected y i e l d are e q u a l l y l i k e l y by d e f i n i t i o n . There would l i k e l y be some b e n e f i t a s s o c i a t e d wi th p roduc ing more than the expected y i e l d per ha and some cos t a s s o c i a t e d wi th a c h i e v i n g l e s s than the expected y i e l d . The d i f f e r e n c e between b e n e f i t and cos t v a l ues a s s o c i a t e d wi th d e v i a t i o n s a c t s as a su r roga te fo r the d e c i s i o n maker ' s a t t i t u d e towards r i s k . If the b e n e f i t of a d e v i a t i o n of some magnitude equa l s the cos t of a s i m i l a r s i z e d d e v i a t i o n , then the d e c i s i o n maker i s r i s k n e u t r a l , at l e a s t f o r that s i z e of d e v i a t i o n , and the i n d i r e c t cos t shou ld be z e r o . When the c o s t a s s o c i a t e d wi th a nega t i ve d e v i a t i o n i s g r ea t e r then the b e n e f i t of a p o s i t i v e d e v i a t i o n , then the d e c i s i o n maker would be r i s k a v e r s e . There are a number of ways of measur ing d e v i a t i o n s from expected va lues and de t e rm in ing i n d i r e c t c o s t . The approach advocated here i n v o l v e s de t e rm in ing p o t e n t i a l d e v i a t i o n s from expected mean annual increment (MAI) and p e n a l i z i n g t hese . The assumpt ion i s made tha t c o s t s and b e n e f i t s of d e v i a t i o n s have a cons tan t va lue r e g a r d l e s s of the magnitude of the d e v i a t i o n . T h i s assumpt ion i s not necessa ry fo r s o l u t i o n , but g r e a t l y s i m p l i f i e s the mathematics and i s conduc ive to p roduc ing a l i n e a r o b j e c t i v e f u n c t i o n in the programming mode l . The i n d i r e c t cos t per ha per year f o r some management sequence can be c a l c u l a t e d by : 1) de t e rm in ing the d e v i a t i o n ( p o s i t i v e or nega t i ve ) a s s o c i a t e d w i th each of the p o t e n t i a l outcomes fo r tha t sequence; 2) • m u l t i p l y i n g the p o s i t i v e d e v i a t i o n s by the b e n e f i t per cub i c m per ha per year of exceed ing expec ted growth and the nega t i v e d e v i a t i o n s by the c o s t ; 143 3) we ight ing each of these p roduc t s by the s u b j e c t i v e p r o b a b i l i t y a s s i gned to the r e s p e c t i v e outcomes; and 4. summing the p r o d u c t s . If c o s t s exceed b e n e f i t s , then the r e s u l t i n g answer w i l l be n e g a t i v e . The magnitude of t h i s number w i l l i n d i c a t e the i n d i r e c t cos t a s s o c i a t e d w i th managing one ha fo r one year under that, management sequence. The cos t w i l l accrue each year fo r the d u r a t i o n of the time t h i s management sequence i s assumed to be f o l l o w e d ( t r a d i t i o n a l l y to the end of the p l a n n i n g h o r i z o n ) . The p resen t va lue of the i n d i r e c t cos t can be determined as the sum of a s e r i e s of y e a r l y c o s t s assuming some d i s c o u n t ra te fo r f u t u r e y e a r l y c o s t s . The p resen t va lue of i n d i r e c t cos t can be added to the present va lue of the d i r e c t cos t to y i e l d the t o t a l cos t of the management sequence. The t o t a l c o s t can then be a d j u s t e d to r e f l e c t the p e r i o d . i n which the management sequence w i l l be a p p l i e d . The r a t i o n a l e fo r employ ing a y e a r l y measure of p o t e n t i a l growth d e v i a t i o n s i s based on there be ing some r e l a t i o n s h i p between growth ra te and f o r e s t s t r u c t u r e , and the h a r v e s t i n g ra te a l l owed by p o l i c y . In a f u l l y r e g u l a t e d f o r e s t , the amount a l l owed f o r ha rves t under a s t r i c t s u s t a i n e d y i e l d p o l i c y would be equa l to the p e r i o d i c growth of the f o r e s t . I f the growth of on ly one age c l a s s in tha t f o r e s t i s underes t imated c o n s i s t e n t l y ( i . e . the t imber f o l l ows a lower y i e l d curve then e x p e c t e d ) , the f o r e s t i s be ing over-cut immed ia te l y , not j u s t when tha t age c l a s s comes to be h a r v e s t e d . The same idea extends to f o r e s t s which are not f u l l y r e g u l a t e d . Not a c h i e v i n g the growth ra te expec ted w i l l mean not be ing ab l e to produce the t imber ha rves t 1 44 p a t t e r n p r e s e n t l y d e s i r e d wi thout d e v i a t i n g from the s e l e c t e d management s t r a t e g y , v i o l a t i n g e x i s t i n g p o l i c y or bo th . A l though the t imber h a r v e s t i n g p a t t e r n w i l l undoubted ly change w i th time (as w i l l the compos i t i on of the t imber management s t r a t e g y ) , the d e c i s i o n maker can not a n t i c i p a t e such changes . The extent to which he b e l i e v e s he may be o v e r c u t t i n g fo r the t imber management s t r a t e g y fo l l owed w i l l r ep resen t some cos t to him now in terms of p o t e n t i a l f u tu re t imber h a r v e s t i n g o p p o r t u n i t i e s f o regone . 8 .3 .5 S e l e c t i o n of a Timber Management S t r a t egy Fo rmu la t i on of a management s t r a t e g y us ing mathemat ica l programming i m p l i e s that the op t ima l s t r a t e g y produced i s the ' b e s t ' of a l l the f e a s i b l e s t r a t e g i e s which c o u l d be produced g iven the cand ida te set of management sequences . If ca re i s taken to i n c l u d e a l l r e l e van t management sequences and to make the c r i t e r i a f o r s e l e c t i n g management sequences in the model agree wi th the c r i t e r i a f o r choos ing a management s t r a t e g y from among a set of c and ida te management s t r a t e g i e s , the d e c i s i o n maker shou ld choose the management s t r a t e g y fo rmu la ted i f he agrees wi th the i n d i r e c t c o s t s and d i s c o u n t r a t e i m p l i c i t in the model . Use of d i f f e r e n t d i s coun t r a t e s and/or the s e l e c t i o n of a d i f f e r e n t b e n e f i t / c o s t va lue s t r u c t u r e fo r p o t e n t i a l d e v i a t i o n s c o u l d change the compos i t i on of the fo rmu la ted s t r a t e g y . The c h o i c e between s t r a t e g i e s fo rmu la ted us i ng d i f f e r e n t d i s c o u n t r a t e s and/or b e n e f i t / c o s t s t r u c t u r e s w i l l depend on the p r e f e r e n c e s of the d e c i s i o n maker. O f ten the d e c i s i o n maker w i l l 1 45 not have a sound r a t i o n a l e fo r the c h o i c e . In such s i t u a t i o n s i t can be u s e f u l to examine the s t r a t e g i e s fo rmu la ted under d i f f e r e n t assumpt ions in some d e t a i l p r i o r to choos ing a management s t r a t e g y . The next chapte r i l l u s t r a t e s t h i s type of a n a l y s i s/examinat i o n . 146 CHAPTER IX AN EXAMPLE ILLUSTRATING THE FORMULATION OF TIMBER MANAGEMENT STRATEGIES An example i s p resen ted below to i l l u s t r a t e some of the p o t e n t i a l a p p l i c a t i o n s of the methodology d e s c r i b e d in the p r e v i o u s c h a p t e r . In order to keep the example s i m p l e , on ly one t imber c l a s s i s c o n s i d e r e d a long wi th three management o p t i o n s which can be a p p l i e d f o l l o w i n g h a r v e s t i n g of the s t and ing t imbe r . S t r a t e g i e s are fo rmu la ted fo r two d i f f e r e n t t imber h a r v e s t i n g p a t t e r n s under s e v e r a l d i f f e r e n t l e v e l s of r i s k a v e r s i o n . The f o r e s t i s h y p o t h e t i c a l , and the management o p t i o n s are s i m p l i f i e d . The i n t e n t i s not to p rov i de a r e a l i s t i c a n a l y s i s , but to i l l u s t r a t e the p o t e n t i a l a p p l i c a t i o n of the methodology. T h i s chapte r i s d i v i d e d i n t o two major s e c t i o n s : (1) d e s c r i p t i o n of the i n i t i a l f o r e s t and the approach taken and (2) p r e s e n t a t i o n and i n t e r p r e t a t i o n of the r e s u l t s . D i s c u s s i o n of the a p p l i c a b i l i t y of the techn ique in l i g h t of the r e s u l t s ob t a i ned fo r the example i s r e se r ved u n t i l the f o l l o w i n g c h a p t e r . 9.1 D e s c r i p t i o n of the Problem 9.1.1 D e s c r i p t i o n of the I n i t i a l Fo res t The f o r e s t c o n s i s t s of 5000 ha of good s i t e (SI 30 m at 50 years ) C o a s t a l D o u g l a s - f i r . The a rea i s d i v i d e d i n t o 12 10-year age c l a s s e s , w i th the m a j o r i t y of the a rea be long ing to the o l d e r age c l a s s e s . V a r i a b l e d e n s i t y y i e l d t a b l e s fo r C o a s t a l 1 47 D o u g l a s - f i r ( M i n i s t r y of F o r e s t s 1982b) were used to determine expected y i e l d per ha fo r the v a r i o u s age c l a s s e s assuming a d iameter l i m i t of 17.5 cm. The expec ted y i e l d was c a l c u l a t e d by we ight ing the y i e l d s a s s o c i a t e d w i th crown c l o s u r e s of 60, 75 and 90 pe rcen t by . 10 , .50 and .40 r e s p e c t i v e l y . Tab le 2 c o n t a i n s a summary of the i n i t i a l f o r e s t c o n d i t i o n . 9 .1 .2 Management Opt ions Cons ide red The three management o p t i o n s a v a i l a b l e f o l l o w i n g h a r v e s t i n g a r e : 1. P l an t 1500 s e e d l i n g s of ' n o r m a l ' s tock @ $0.85 per s e e d l i n g . DIRECT COST: $1275.00 per ha ( A c t i v i t i e s p r e f i x e d by A) 2. P l an t 1500 s e e d l i n g s of ' improved ' s tock @ $1.00 per s e e d l i n g . DIRECT COST: $1500.00 per ha ( A c t i v i t i e s p r e f i x e d by B) 3. N a t u r a l r e g e n e r a t i o n . DIRECT COST: $0.00 ( A c t i v i t i e s p r e f i x e d by C) I n d i v i d u a l a c t i v i t i e s c o n s i s t of combina t ions of i n i t i a l p e r i o d of a p p l i c a t i o n and o r i g i n a l age c l a s s t r e a t e d . In order to l i m i t the number of a c t i v i t i e s , any l and a s s i g n e d to a p a r t i c u l a r management o p t i o n was assumed to remain in tha t o p t i o n u n t i l the end of a 200 year p l a n n i n g h o r i z o n wi th a r e c u r r i n g ha r ves t every 70 yea rs f o l l o w i n g the i n i t i a l h a r v e s t . I n i t i a l h a r v e s t i n g was r e s t r i c t e d to t imber in at l e a s t i t s s i x t h decade (average age fo r any c l a s s ha r ves ted must be at l e a s t 60) and a l l of the o r i g i n a l t imber p resen t which w i l l be ha r ves ted must be cut be fo re i t en t e r s i t s s i x t e e n t h decade (average age of any age c l a s s ha r ve s t ed must be no more than 150 y e a r s ) . 148 Tab le 2: D e p i c t i o n of the I n i t i a l F o r e s t AGE CLASS AGE RANGE AREA VOL/HA MAI (YEARS) (HA) (OLDEST AGE) (OLDEST AGE) (M**3) (M**3/HA/YR) 1 1-10 500 .94 .094 2 1 1-21 500 29.29 1 .465 3 21-30 250 130.15 4.338 4 31-40 250 284.19 7. 105 5 41-50 200 441.85 8.837 6 51-60 200 572.51 9.542 7 61-70 300 668.81 9.554 8 71-80 300 735.20 9. 190 9 81-90 1000 779.27 8.659 10 91-100 1000 807.90 8.079 1 1 101-110 250 826.31 7.511 12 1 1 1-120 250 836.57 6.968 13 121-130 - 845.57 6.504 14 131-140 - 850.36 6.074 15 141-150 - 853.41 5.689 5000 As an example , an a c t i v i t y denoted as A1:12 has the f o l l o w i n g i n t e r p r e t a t i o n : "Cut t imber in the f i r s t decade (pe r iod ) which was in i t s t w e l f t h decade at the s t a r t of the p l a n n i n g h o r i z o n (age 120 at h a r v e s t ) . Regenerate the l and by p l a n t i n g ' n o r m a l ' s t o c k . Subsequent l y ha rves t the l a n d i n p e r i o d s 8 and 15 p l a n t i n g w i th ' n o r m a l ' s tock a f t e r each h a r v e s t . " An a c t i v i t y denoted as C3:10 shou ld be i n t e r p r e t e d a s : "Cut t imber in the t h i r d p e r i o d which was in i t s t e n t h decade at the s t a r t of the p l a n n i n g h o r i z o n (age 120 at h a r v e s t ) . A l l ow the l and to regenera te n a t u r a l l y f o l l o w i n g the h a r v e s t . Subsequent ly ha r ves t the l and in p e r i o d s 10 and 17 a l l o w i n g the l a n d to regenera te n a t u r a l l y on each o c c a s i o n . " A complete l i s t of the p o t e n t i a l a c t i v i t i e s i s p r o v i d e d in 149 Appendix I. Average response to any of the management o p t i o n s was c o n s i d e r e d to be u n c e r t a i n . A l i m i t e d number of d i s t i n c t outcomes were c o n s i d e r e d f o r each management o p t i o n and a s u b j e c t i v e p r o b a b i l i t y of occu r rence was a s s i g n e d to each . Y i e l d s were a s s o c i a t e d w i th each p o t e n t i a l outcome us ing the same v a r i a b l e d e n s i t y y i e l d t a b l e s employed f o r the s t and ing t imbe r . An aggregate (expected) y i e l d t a b l e was then c o n s t r u c t e d f o r each, management o p t i o n by we igh t ing the y i e l d s a s s o c i a t e d w i th the p o t e n t i a l outcomes by the s u b j e c t i v e p r o b a b i l i t y of the outcomes. S i n ce r o t a t i o n age was f i x e d at 70 yea rs a f t e r the i n i t i a l h a r v e s t , on l y the expected y i e l d at tha t age was used in the a n a l y s i s . The expected y i e l d s f o r each o p t i o n at age 70 and the c o r r e s p o n d i n g mean annual increment (MAI) v a lues are g i ven in Tab le 3. The complete y i e l d t a b l e s and s u b j e c t i v e p r o b a b i l i t i e s a s s o c i a t e d w i th each p o t e n t i a l outcome are p r o v i d e d in Appendix I I . Tab le 3: Expec ted Y i e l d s and MAI 's a t Ro t a t i on Age f o r the D i f f e r e n t Management Op t ions MANAGEMENT OPTION A MANAGEMENT OPTION B EXPECTED YIELD AT ROTATION AGE (M**3/HA) 668.81 715.37 EXPECTED MAI AT ROTATION AGE (M**3/HA/YEAR) 9.55 10.22 MANAGEMENT OPTION C 587.88 8.40 150 9 .1 .3 Timber H a r v e s t i n g P a t t e r n s Two t imber h a r v e s t i n g p a t t e r n s were examined. The ob j ec t was not to determine which p a t t e r n was ' b e s t ' , but r a the r to i l l u s t r a t e change in s t r a t e g y w i th a change i n the d e s i r e d harves t p a t t e r n . As noted in a p r e v i o u s c h a p t e r , i t would be p o s s i b l e to use the i n f o r m a t i o n gathered in a management s t r a t e g y d e c i s i o n p rocess such as t h i s to he lp r e v i s e the t imber harves t p a t t e r n i n i t i a l l y s e l e c t e d ( i . e . i n c o r p o r a t e the a n a l y s i s in some p l ann ing p r o c e s s ) . The f i r s t t imber ha r ves t p a t t e r n (THP1) r e q u i r e s 490,000 cub i c m to be ha r ves t ed in the f i r s t 10-year p e r i o d , 500,000 p lus or minus f i v e percent to be ha r ves t ed in the second p e r i o d and 510,000 p l u s or minus ten pe rcen t to be ha r ves t ed in subsequent p e r i o d s . The second t imber h a r v e s t i n g p a t t e r n (THP2) i s more r e s t r i c t i v e . It r e q i r e s 490,000 cub i c m to be ha r ves t ed in the f i r s t p e r i o d , 500,000 in the second , 510,000 in the t h i r d and 510,000 p l u s or minus f i v e pe rcen t in subsequent p e r i o d s . The two p a t t e r n s are i l l u s t r a t e d g r a p h i c a l l y in F i g u r e 7. 9 .1 .4 Cos t s A c t i v i t i e s were s e l e c t e d to form a management s t r a t e g y on the b a s i s of m i n i m i z i n g the t o t a l cos t of management sub jec t to ' a l l o w i n g ' the ha r ves t l e v e l s s p e c i f i e d by the ha r ves t p a t t e r n chosen . The t o t a l cos t a s s i g n e d to each a c t i v i t y i s a f u n c t i o n of the d i r e c t cos t of the management o p t i o n , the c o s t a s s o c i a t e d wi th the p o s s i b i l i t y of making an e r r o r of a s p e c i f i c magnitude wi th r espec t to an assumed response ( i n d i r e c t c o s t ) and the p e r i o d of i n i t i a l a p p l i c a t i o n of the management a c t i v i t y . 151 F i gu re 7: D e p i c t i o n of the Two Timber Ha r ves t i ng Pa t t e rns THP1 — r -600 PERIODIC VOLUME TO BE HARVESTED (1000 M**3) 0 5 10 15 20 PERIODS The c u r r e n t d i r e c t c o s t s assumed fo r the v a r i o u s management o p t i o n s were g i ven in S e c t i o n 9 . 1 . 2 . A d i s coun t r a te of .03 was assumed and used to express the c o s t s fo r a l l a c t i v i t i e s on a p resen t va lue b a s i s . P e r i o d c o s t s are expressed as an average of the d i s c o u n t e d c o s t s over the 10-year d u r a t i o n of the p e r i o d . P resent va lue of d i r e c t c o s t s f o r a c t i v i t i e s i n v o l v i n g more than one p e r i o d where c o s t s are i n c u r r e d are c a l c u l a t e d as the sum of the average d i s c o u n t e d p e r i o d c o s t s . The d i r e c t c o s t s a s s o c i a t e d w i th p l a n t i n g ' n o r m a l ' s tock and ' improved ' s tock f o r v a r i o u s p e r i o d s of i n i t i a l ha r ves t a re g i ven i n Tab le 4. The n a t u r a l 152 Tab le 4: D i s coun ted D i r e c t Cos t s of Management by P e r i o d of I n i t i a l H a r v e s t . PERIOD OF DISCOUNTED DIRECT COST INITIAL HARVEST (DOLLARS) * * PNS PIS 1 1242.31 1461.54 2 924.90 1087.53 3 687.84 809.23 4 511.82 602.14 5 384.84 448.05 6 283.38 339.39 7 207.92 244.61 8 154.71 182.01 9 115.12 135.44 10 85.66 100.78 1 1 63.74 74.99 12 47.43 55.80 13 35.29 41 .52 14 23.32 27.43 15 17.35 20.41 * PNS r ep r e sen t s P l a n t i n g 'Norma l ' Stock PIS r ep r e sen t s P l a n t i n g ' Improved ' Stock r e g e n e r a t i o n o p t i o n i s not l i s t e d because no d i r e c t cos t i s assumed to i n c u r . The expec ted average growth r a t e under any of the management o p t i o n s i s r ep resen ted by the MAI at r o t a t i o n age a s s o c i a t e d w i th the expected y i e l d . Long term d e v i a t i o n s from t h i s growth r a t e w i l l occur i f the responses to the management o p t i o n s a re not as expec t ed . The outcomes l i s t e d in Appendix II a re assumed to be the on l y responses p o s s i b l e . The b e l i e f s of the d e c i s i o n maker w i th r espec t to the p o s s i b i l i t y of t h e i r occu r rence are r e f l e c t e d by the s u b j e c t i v e p r o b a b i l i t y a s s i gned to them when c o n s t r u c t i n g the expec ted y i e l d t a b l e s . 153 Constant b e n e f i t / c o s t v a l ues are assumed fo r p o s i t i v e / n e g a t i v e d e v i a t i o n s from the expected growth r a t e . The spread of p o s s i b l e average growth r a t e s around the expected average growth r a t e and the magnitude of the d i f f e r e n c e between the b e n e f i t and cos t v a l ues determine the i n d i r e c t c o s t in t h i s example, not the a c t u a l v a l ues assumed. Rega rd l e ss of the spread of p o s s i b l e growth r a t e s around the expec ted growth r a t e , i f the b e n e f i t a s s o c i a t e d w i th a p o s i t i v e d e v i a t i o n i s equa l to the c o s t a s s o c i a t e d w i th a nega t i ve d e v i a t i o n , then the i n d i r e c t cos t component of the t o t a l cos t would be z e r o . I n c r ea s i ng the c o s t of a nega t i ve d e v i a t i o n over the b e n e f i t of a p o s i t i v e d e v i a t i o n i n t r o d u c e s a p o s i t i v e i n d i r e c t c o s t and i n d i c a t e s tha t the d e c i s i o n maker i s r i s k a v e r s e . The magnitude of the d i f f e r e n c e i s r e f l e c t i v e of the degree of r i s k a v e r s i o n . I n d i r e c t c o s t s are assumed to accumulate on a y e a r l y b a s i s once e x i s t i n g t imber i s h a r v e s t e d . The formulae employed to c a l c u l a t e the y e a r l y i n d i r e c t cos t a s s o c i a t e d w i th a p a r t i c u l a r management o p t i o n a r e : J = i[(Expected MAI - MAI ) * p * b e n e f i t ] i = l i i f o r a l l outcomes where a c t u a l MAI exceeds expected MAI. (Note : J w i l l be n e g a t i v e . ) n k K = z [ ( E x p e c t e d MAI - MAI ) * p * c o s t ] i = l i i f o r a l l outcomes where expec ted MAI exceeds a c t u a l MAI. (Note: K w i l l be p o s i t i v e . ) YEARLY INDIRECT COST = J + K where b e n e f i t i s the d o l l a r va lue a s s o c i a t e d with exceed ing the expec ted average growth r a t e by 1 m**3/ha/year c o s t i s the d o l l a r va lue a s s o c i a t e d wi th f a l l i n g below the expected average 154 growth r a t e by 1 m**3/ha/year Expected MAI i s the mean annual increment a s s o c i a t e d w i th the expected y i e l d J i s the weighted sum of the b e n e f i t s ( nega t i ve c o s t s ) a s s o c i a t e d wi th exceed ing expected MAI K i s the weighted sum of the c o s t s a s s o c i a t e d w i th f a l l i n g below expected MAI MAI. i s the mean annual increment of 1 outcome i n. i s the number of outcomes where the J average growth r a te exceeds the expec ted MAI n i s the number of outcomes where the * average growth r a te f a l l s below the expected MAI p i s the p r o b a b i l i t y of outcome i i The p resen t va lue of an n term s e r i e s of i n d i r e c t c o s t s was then determined by the f o l l o w i n g formula ( C l u t t e r et a l . (1983 ) ) : l - r n S ' a l * " I T 1 where a = YEARLY INDIRECT COST 1 (TfT) i i s the d i s c o u n t r a t e (.03 assumed) n i s the s e r i e s d u r a t i o n (200 assumed) 1 S i s the p resen t va lue of the s e r i e s The p resen t v a lues of the v a r i o u s s e r i e s were then a d j u s t e d to r e f l e c t the p e r i o d of i n i t i a l ha r ves t a s s o c i a t e d w i th each of the a c t i v i t i e s u s i n g a d i s c o u n t r a t e of . 0 3 . T h i s p l a c e d the i n d i r e c t c o s t s on the same b a s i s as the d i r e c t c o s t s and a l l owed the two c o s t components to be added to produce a t o t a l c o s t f o r 155 the v a r i o u s a c t i v i t e s . The i n d i r e c t c o s t s a s s o c i a t e d wi th p o t e n t i a l d e v i a t i o n s from the average expec ted growth r a t e under b e n e f i t / c o s t assumpt ions of $5/$10 and $5/$20 per c u b i c m per ha per year are g iven in Appendix III by management op t i on and time of i n i t i a l h a r v e s t . Management s t r a t e g i e s were fo rmu la ted fo r each of the ha r ves t p a t t e r n s under s e v e r a l t o t a l c o s t s c e n a r i o s . The combina t ions examined are d e s c r i b e d in Tab l e 5. The t o t a l c o s t s Tab l e 5: D e s c r i p t i o n of Cost S cena r ios A n a l y s e d . TIMBER HARVEST PATTERN THP1 SCENARIO (1) Ignore i n d i r e c t c o s t . T o t a l cos t = d i r e c t c o s t . (2) I n d i r e c t cos t c a l c u l a t e d assuming b e n e f i t / c o s t of $5/$l0 per m**3/ha/yr. T o t a l c o s t = d i r e c t c o s t + i n d i r e c t c o s t (3) Ignore d i r e c t c o s t s . I n d i r e c t c o s t s are as i n (2 ) . T o t a l cos t = i n d i r e c t c o s t . THP2 (4) Ignore i n d i r e c t c o s t . T o t a l cos t = d i r e c t c o s t . (5) I n d i r e c t c o s t s are as i n (2 ) . T o t a l c o s t = d i r e c t c o s t + i n d i r e c t c o s t (6) I n d i r e c t c o s t s c a l c u l a t e d assuming b e n e f i t / c o s t of $5/$20 per m**3/ha/yr. T o t a l c o s t = d i r e c t c o s t + i n d i r e c t c o s t (7) Ignore d i r e c t c o s t s . I n d i r e c t c o s t s a re as in (2 ) . T o t a l cos t = i n d i r e c t c o s t . 1 56 a s s o c i a t e d w i th each management o p t i o n by p e r i o d of i n i t i a l ha rves t are l i s t e d fo r each s c e n a r i o in Appendix IV. Note that the t o t a l cos t s t r u c t u r e i s the same fo r s c e n a r i o s (1) and (4 ) , (2) and (5 ) , and (3) and (7 ) . 9 .1 .5 Model S t r u c t u r e The model s t r u c t u r e employed can be c l a s s i f i e d as a Type I l i n e a r programming s t r u c t u r e (Johnson and Scheurman 1977), but the c o e f f i c i e n t mat r ix was generated wi thout the a i d of any formal t imber supp ly model . T h i s was done to a v o i d some of the i n f l e x i b i l i t y a s s o c i a t e d wi th the gene r a t i on of p o t e n t i a l a c t i v i t i e s and any e x p l i c i t t i e s to a p a r t i c u l a r p o l i c y s t r u c t u r e . A l though both of the t imber ha rves t p a t t e r n s examined r e f l e c t a r e l a t i v e l y cons tan t supply of t imber through t ime , the model would work fo r any h a r v e s t i n g p a t t e r n which was f e a s i b l e g i ven the c o n s t r a i n t s , the i n i t i a l f o r e s t s t r u c t u r e and the management o p t i o n s a v a i l a b l e . The c o n s t r a i n t s which f o r ce any t imber ha r ves t ed in p e r i o d t to be ha r ves t ed aga in in p e r i o d t+7 and subsequent l y managed a c c o r d i n g to the management o p t i o n chosen at p e r i o d t ( c o n s t r a i n t (5) in the model below) c o u l d be r e l a x e d . T h i s would a l low depar tu re from a s t a t i c h a r v e s t i n g p lan once the i n i t i a l s t and ing t imber has been h a r v e s t e d . The r e p e r c u s s i o n s of t h i s would be a tremendous i n c r ease in the number of a c t i v i t i e s c o n s i d e r e d in a Type I f o r m u l a t i o n . A Type II f o r m u l a t i o n would a l l ow such f l e x i b i l i t y w i th fewer a d d i t i o n a l a l t e r n a t i v e s , but would r e q u i r e a s u b s t a n t i a l i n c r ea se in the number of c o n s t r a i n t s . The p o s s i b i l i t y of f o l l o w i n g a Type II f o r m u l a t i o n was not pu r sued , but appears 157 q u i t e f e a s i b l e . The model s t r u c t u r e employed i s as f o l l o w s : F i n d a i = 1,2,3? t = 1 , . . . , 2 0 ; j = 1 , . . . , 1 2 i + i 20 x t J 3 12 such tha t E E Z C. . a . . = Z i s min imized i t j i t ] l t j Sub jec t to : ( D a . i t j (2) a i t j (3) a = 0 = 0 = 0 f o r i = 1 , 2 , 3 t = 1 , . . . , 5 i t j 3=1 , f o r i = 1 , 2 , t 5 / • • j=17-t fo r i=1 , t=16 j = 1 , . . , 6 - t 15 . . , 12 3 . . ,20 . , 12 (4) b. i t ( S ) b l t = 0 i , t -7 i , t -7 f o r i = 1 , 2 , 3 f o r i = 1 ,2 ,3 t = 8 , . . . , 2 0 f o r j = 1 , . . . , 12 (6) £ za < A i j i t j j (7) E E a v + E b v ' <;=;> V f o r t = 1 , . . . , 2 0 i j i t j i t j i i t i— — t (8) a. . > 0 f o r i=1 ,2 ,3 l t : 3 t = 1 , . . . , 2 0 j=1,•••,12 where a. . i s the number of ha of i n i t i a l age c l a s s j l t :J ha r ves ted in p e r i o d t and subsequent l y managed a c c o r d i n g to management o p t i o n i . A- i s the number of ha i n i t i a l l y p resen t i n age ^ c l a s s j . b. i s the number of ha i n i t i a l l y ha r ves t ed in x t p e r i o d t-7 and subsequent l y managed a c c o r d i n g to management o p t i o n i . C i s the p resen t va lue of the c o s t a s s o c i a t e d i t j w i t h managing l and i n i t i a l l y in age c l a s s j . i i s the number of the^ management o p t i o n c o n s i d e r e d , i < 3 by d e f i n i t i o n f o r t h i s p rob lem. 1 58 j i s the number of the i n i t i a l age c l a s s , j <_12 by d e f i n i t i o n fo r t h i s p rob lem. — t i s the number of the t ime p e r i o d . t <_ 20 by d e f i n i t i o n fo r t h i s p rob lem. v . . i s the volume per ha in c u b i c m a v a i l a b l e 1 - t J i n p e r i o d t on l and i n i t i a l l y in age c l a s s j and subsequent l y managed a c c o r d i n g to management op t i on i . v'. i s the volume per ha of 70 year o l d t imber 1 managed a c c o r d i n g to management o p t i o n i . V i s the r e q u i r e d volume f o r p e r i o d t . Note t tha t two va lues of V are r e q u i r e d fo r i n e q u a l i t y c o n s t r i a n t s at p e r i o d t . C o n s t r a i n t (1) ensures tha t no t imber younger than age 60 i s ha r ves t ed from the i n i t i a l age c l a s s e s . (Stands must be in at l e a s t t h e i r s i x t h decade . ) C o n s t r a i n t s (2) and (3) ensure tha t no t imber o l d e r than 150 years of age i s ha r ves t ed from the i n i t i a l age c l a s s e s . (Stands must not be ha r ves t ed a f t e r t h e i r f i f t e e n t h decade . ) The f i x e d r o t a t i o n p e r i o d of 70 years a f t e r i n i t i a l ha rves t i s r e f l e c t e d in c o n s t r a i n t s (4) and (5 ) . C o n s t r a i n t s (1) through (5) were i m p l i c i t l y i n c o r p o r a t e d f o r the g e n e r a t i o n of p o t e n t i a l a c t i v i t i e s in the a c t u a l problem s o l u t i o n so i t was not necessa ry to i n c l u d e these c o n s t r a i n t s in the fo rmu la ted p rob lem. C o n s t r a i n t (6) c o n t r o l s the area ha r ves t ed in any age c l a s s to some va lue l e s s than or equa l to tha t i n i t i a l l y p r e s e n t . Harves t r a t e s are l i m i t e d to those s p e c i f i e d in the t imber ha r ves t p a t t e r n by c o n s t r a i n t (7 ) . These two c o n s t r a i n t types are necessa ry i n the fo rmu la ted prob lem. C o n s t r a i n t (8) i s known as a ' n o n - n e g a t i v i t y ' c o n s t r a i n t . a n d i s i m p l i c i t l y i n c l u d e d in 159 any l i n e a r programming s o l u t i o n a l g o r i t h m . L i n e a r programming problems were fo rmu la ted us ing t h i s model s t r u c t u r e fo r s c e n a r i o s 1 through 7. These problems were so l v ed us i ng the l i n e a r programming s o l u t i o n a l g o r i t h m con t a i ned in the v e r s i o n of the MPSX (Mathemat ica l Programming System Extended) language a v a i l a b l e on the U n i v e r s i t y of B r i t i s h Columbia computing system. Documentat ion on the MPSX language i s a v a i l a b l e in IBM (1972) . I n fo rmat ion on how to use MPSX on the U n i v e r s i t y of B r i t i s h Columbia computing system i s a v a i l a b l e from the Computing C e n t r e . 9.2 R e s u l t s and I n t e r p r e t a t i o n A c t i v i t y va lues s e l e c t e d to so l ve the l i n e a r programming problems fo rmu la ted fo r s c e n a r i o s 1 through 7 are p resen ted in Tab l e s 6 through 12. Each of these s o l u t i o n s r ep re sen t s a management s t r a t e g y a p p r o p r i a t e f o r the c o n d i t i o n s assumed in the s c e n a r i o . Whi le the a c t u a l s o l u t i o n s in t h i s example are of secondary importance to the methodology employed, c e r t a i n t r ends w i l l be h i g h l i g h t e d . T h i s w i l l i l l u s t r a t e some of the a d d i t i o n a l i n f o r m a t i o n genera ted by t h i s approach which c o u l d a i d the d e c i s i o n maker in the c h o i c e of a management s t r a t e g y and perhaps in the r e v i s i o n of the t imber harves t p a t t e r n . 1 60 Tab le 6: Summary of S o l u t i o n fo r S cena r i o 1. RIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 C l :12/250/836 C l :11/250/826 C 1 : 1 0 / 92/808 2 475,000 C2:10/575/826 3 459,000 C3:10/333/836 C3:9 /218/826 4 459,000 C4 :9 /549/836 5 459,000 C5:9 /233/846 C5:8 /300/836 C5:7 / 14/826 6 459,000 B6:6 /138/826 B6:4 /112/779 B6:3 /204/735 C6:4 /138/779 7 459,000 B7:7 /286/846 B7:6 / 62/836 B7:5 /200/826 8 459,000 NR1 /592/588 B8:3 / 46/808 B8:2 / 95/779 9 474,659 NR2 /575/588 B9:2 /169/808 10 476,436 NR3 /551/588 B10:1/188/808 1 1 481 ,71 3 NR4 /549/588 B11:2/ l58/836 B11 :1/ 33/826 1 2 482,282 NR5 /547/588 B12:1/193/836 1 3 468,645 NR6 /138/588 PIS6 /454/715 B13 :1/ 74/846 1 4 459,000 PIS7 /548/715 C 1 4 : 2 / 78/853 1 5 459,000 PIS8 /141/715 NR8 /592/588 C l 5 : 1 / 12/853 16 459,000 PIS9 /I 69/715 NR9 /575/588 1 7 459,000 PIS10/188/715 NR10 /551/588 18 459,000 PIS11/191/715 NR11 /549/588 19 459,000 PIS12/193/715 NR12 /547/588 20 459,000 PIS13/528/715 NR13 /138/588 ALL AVAILABLE AREA IN EVERY AGE CLASS MANAGED TOTAL COST OF STRATEGY = $383741.34 161 Tab le 7: Summary of S o l u t i o n fo r S cena r i o 2. PERIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 CI :12/250/836 C1:11/250/826 C 1 : 1 0 / 92/808 2 475,000 C2:10/575/826 3 459,000 C3:10/333/836 C3:9 /218/826 4 •459,000 C4:9 /549/836 5 " 459,000 C5 :9 /233/846 C5:8 /300/836 C5:7 / 14/826 *6 459,000 B6:6 /200/826 B6:4 /186/779 B6:3 / 66/735 C6:3 /I 36/735 * 7 459,000 B7:7 /286/846 B7:5 /200/826 B7:4 / 64/808 *8 459,000 NR1 /592/588 B8:3 / 48/808 B8:2 / 93/779 *9 *474,658 NR2 /575/588 B9:2 /169/808 *1 0 *479,405 NR3 /551/588 B10:2/161/826 B10 :1/ 27/808 *1 1 *480,142 NR4 /549/588 B11:1/191/826 *1 2 *482,281 NR5 /547/588 B12:1/193/836 *1 3 *469,097 PIS6 /452/715 NR6 /136/588 B13 :1/ 78/846 * 1 4 459,000 PIS7 /550/715 C 1 4 : 2 / 77/853 1 5 459,000 ' PIS8 /141/715 NR8 /592/588 C I5s1/ 12/853 1 6 459,000 PIS9 /I 69/715 NR9 /575/588 1 7 459,000 PIS10/188/715 NR10 /551/588 18 459,000 PIS11/191/715 NR11 /549/588 19 459,000 PIS12/193/715 NR12 /547/588 *20 459,000 PIS13/530/715 NR13 /136/588 ALL AVAILABLE AREA IN EVERY AGE CLASS MANAGED TOTAL COST OF STRATEGY = $534606.57 I nd i c a t e s change in volume ha rves ted and/or a change in the a c t i v i t i e s f o r a p e r i o d from s c e n a r i o 1. 162 Tab le 8: Summary of S o l u t i o n f o r S cena r io 3. PERIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 B1:12/250/836 B1:11/250/826 B1 :10/ 92/808 2 475,000 B2:10/575/826 3 459,000 B3:10/333/836 B 3 : 9 / 2 l 8 / 8 2 6 4 459,000 B4:9 /549/836 5 459,000 B5:9 /233/846 B5:8 /300/836 B5:7 / 14/826 6 459,000 B6:7 /286/836 B6:6 /200/826 B6:5 / 67/808 7 459,000 B7:5 /133/826 B7:4 /250/808 B7:3 /189/779 8 459,000 PIS1 /592/715 B8:3 / 44/808 9 463,267 PIS2 /575/715 B9:1 / 67/779 10 467,342 PIS3 /551/715 B 1 0 : 1 / 90/808 11 469,291 PIS4 /549/715 B11 :1/ 93/808 12 471,393 PIS5 /547/715 B12 :2/ 95/846 13 470,893 PIS6 /553/715 B13 :2/ 88/850 14 459,000 PIS7 /572/715 B14 :2/ 59/853 15 459,000 PIS8 /636/715 B I5 :1/ 5/853 16 459,000 PIS9 /642/715 17 459,000 PIS10/641/715 18 459,000 PIS11/642/715 19 459,000 PIS12/642/715 20 459,000 PIS13/641/715 THE FOLLOWING AREAS WERE LEFT UNMANAGED: 246 HA OF AGE CLASS 1 258 HA OF AGE CLASS 2 17 HA OF AGE CLASS 3 TOTAL COST OF STRATEGY = $95433.83 163 Tab le 9: Summary of S o l u t i o n fo r S cena r i o 4. RIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 CI :12/250/836 C1:11/250/826 C 1 : 1 0 / 92/808 2 500,000 C2:10/605/826 3 510,000 B3:9 /250/826 C3:10/303/836 C3:9 / 61/826 4 484,500 B4:9 /579/836 5 484,500 B5:9 /110/846 B5:7 /278/826 B5:6 /200/808 6 484,500 B6:4 /193/779 B6:3 /153/735 B6:2 /331/669 7 484,500 B7:8 /300/850 B7:7 / 22/846 B7:5 /200/826 B7:4 / 57/808 8 484,500 NR1 /592/588 B8:3 / 97/808 B8:2 / 75/779 9 496,003 NR2 /605/588 B9:1 /180/779 10 496,397 PIS3 /250/715 NR3 /364/588 B10:1/129/808 1 1 495,478 PIS4 /579/715 B1.1 : 2 / 12/836 B11 :1/ 86/826 1 2 495,265 PIS5 /588/715 B12 :1/ 89/836 1 3 484,500 PIS6 /677/715 1 4 484,500 PIS7 /579/715 C 1 4 : 2 / 83/853 1 5 484,500 PIS8 /172/715 NR8 /592/588 C 1 5 : 1 / 16/853 1 6 484,500 PIS9 /I 80/715 NR9 /605/588 17 484,500 PIS10/379/715 NR10 /364/588 18 484,500 PIS11/677/715 19 484,500 PIS12/677/715 20 484,500 PIS13/677/715 ALL AVAILABLE AREA IN EVERY AGE CLASS MANAGED TOTAL COST OF STRATEGY = $1266649.06 164 Tab le 10: Summary of S o l u t i o n fo r S cena r i o 5. PERIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 C1:12/250/836 C1:11/250/826 C 1 : 1 0 / 92/808 2 500,000 C2:10/605/826 *3 510,000 B3:10/251/836 C 3 : 1 0 / 52/836 C3:9 /311/826 4 484,500 B4:9 /579/836 *5 484,500 B5:9 /110/846 B5:8 /275/836 B5:6 /200/808 *6 484,500 B6:4 /195/779 B6:3 /150/735 B6:2 /332/669 *7 484,500 B7:8 / 25/850 B7:7 /300/846 B7:5 /200/826 B7:4 / 55/808 *8 484,500 NR1 /592/588 B8:3 /100/808 B8:2 / 72/779 * g *496,427 NR2 /605/588 B9:2 / 15/808 B9:1 /165/779 *1 0 *496,376 PIS3 /251/715 NR3 /363/588 B10:1/128/808 * 1 1 *495,363 PIS4 /579/715 B11 :1/ 98/826 *1 2 *495,665 PIS5 /585/715 B12 :1/ 92/836 1 3 484,500 PIS6 /677/715 *1 4 484,500 PIS7 /580/715 C 1 4 : 2 / 82/853 1 5 484,500 PIS8 /I 72/715 NR8 /592/588 CI5 s1/ 16/853 16 484,500 PIS9 /I 80/715 NR9 /605/588 17 484,500 PIS10/379/715 NR10 /363/588 18 484,500 PIS11/677/715 19 484,500 PIS12/677/715 20 484,500 PIS13/677/715 ALL AVAILABLE AREA IN EVERY AGE CLASS IS MANAGED TOTAL COST OF STRATEGY = $1406725.98 * I n d i c a t e s change in volume ha r ves t ed and/or a change in the a c t i v i t i e s f o r a p a r t i c u l a r p e r i o d from s c e n a r i o 4. 1 65 Tab le 11: Summary of S o l u t i o n fo r S cena r io 6. PERIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 C1:12/250/836 C l :11/250/826 C 1 : 1 0 / 92/808 2 500,000 C2:10/605/826 *3 510,000 B3:9 /256/826 C3:10/303/836 C3:9 / 54/826 4 484,500 B4:9 /579/836 *5 484,500' B5:9 /110/846 B5:8 /300/836 B5:7 /170/826 *6 484,500 B6:4 /198/779 B6:3 /250/735 B6:2 /219/669 *7 484,500 B7:7 /130/846 B7:6 /200/836 B7:5 /200/826 B7:4 / 52/808 8 484,000 NR1 /592/588 B8:2 /175/779 *g *496,003 NR2 /605/588 B9:1 /180/779 * 10 *496,288 PIS3 /256/715 NR3 /357/588 B10:1/127/808 1 1 495,620 PIS4 /579/715 B11 :2/ 26/836 B11 :1/ 72/826 * 1 2 *496,241 PIS5 /570/715 B12 :1/ 97/836 * 1 3 *485,844 PIS6 /667/715 B13 :1/ 10/836 * 1 4 484,500 PIS7 /582/715 C 1 4 : 2 / 80/853 * 1 5 484,500 PIS8 /I 7 5/715 NR8 /592/588 C l 5 s 1 / 13/853 1 6 484,500 PIS9 /180/715 NR9 /605/588 * 17 484,500 PIS10/383/715 NR10 /357/588 18 484,500 PIS11/677/715 1 9 484,500 PIS12/677/715 20 484,500 PIS13/677/715 ALL AVAILABLE AREA IN EVERY AGE CLASS MANAGED TOTAL COST OF STRATEGY = $1686678.48 * I n d i c a t e s a change in the volume to be ha rves ted and/or the a c t i v i t i e s f o r a p a r t i c u l a r p e r i o d from s c e n a r i o 4. 1 66 Tab le 12: Summary of S o l u t i o n f o r S cena r i o 7. PERIOD VOLUME TO ACTIVITY/NO. HA/VOL. PER HA BE HARVESTED (M**3) 1 490,000 B1 12/250/836 B1:11/250/826 B1 10/ 92/808 2 500,000 B2 10/605/826 3 510,000 B3 10/303/836 B3:9 /311/826 4 • 484,500 B4 9 /579/836 5 484,500 B5 9 /110/846 B5:8 /275/836 B5 6 /200/808 6 484,500 B6 8 / 25/846 B6:7 /300/836 B6 5 /200/808 B6:4 / 65/779 7 484,500 B7 4 /185/808 B7:3 /250/779 B7 2 /I 91/735 8 484,500 PIS1 /592/715 B8:2 / 78/779 9 491,178 PIS2 /605/715 B9:2 / 72/808 1 0 490,396 PIS3 /614/715 B10 :1/ 64/808 1 1 495,363 PIS4 /579/715 B11:1/198/826 1 2 496,524 PIS5 /585/715 B12 :2/ 92/846 1 3 495,932 PIS6 /590/715 B13 :2/ 23/850 B13 :1/ 64/846 1 4 484,500 PIS7 /626/715 B14 :2/ 43/853 1 5 484,500 PIS8 /670/715 B I5s1/ 6/850 1 6 484,500 PIS9 /676/715 1 7 484,500 PIS10/678/715 18 484,500 PIS11/677/715 19 484,500 PIS12/677/715 20 484,500 PIS13/677/715 ONLY 231 HA OUT OF 500 HA IN INITIAL AGE CLASS 1 ARE HARVESTED. ALL OTHER AGE CLASSES ARE HARVESTED COMPLETELY AND MANAGED. TOTAL COST OF STRATEGY = $100335.89 167 9.2.1 Comparison of S o l u t i o n s to S cena r ios 1, 2 and 3 S cena r i o 1 genera tes a management s t r a t e g y fo r THPl based on c o n s i d e r a t i o n of d i r e c t c o s t s of the management o p t i o n s a l o n e . T h i s i s ak in to s o l v i n g the problem under the assumpt ion that the expected response to any of the management o p t i o n s w i l l occur or that the dec i son maker i s r i s k n e u t r a l . Only a c t i v i t i e s compr i s i ng management o p t i o n C ( na tu r a l r egene ra t i on ) and management o p t i o n B ( p l a n t i n g ' improved ' s tock ) were s e l e c t e d . Not s u r p r i s i n g l y , the f i r s t s e v e r a l p e r i o d s c o n s i s t e d e n t i r e l y of n a t u r a l r egene r a t i on s i n ce the d i r e c t cos t of such a c t i v i t i e s i s z e r o . Management a c t i v i t i e s r e q u i r i n g p l a n t i n g of ' improved ' s tock predominated in the l a t e r p e r i o d s of c o n v e r s i o n of the e x i s t i n g f o r e s t to a managed f o r e s t when the h ighe r y i e l d a s s o c i a t e d wi th t h i s management op t i on was necessary to meet the t imber ha rves t p a t t e r n requ i rements once the i n i t i a l s t and ing i nven to ry was exhaus ted . T r a n s i t i o n between the management o p t i o n s o c c u r r e d du r i ng p e r i o d 6. S ince the o b j e c t i v e was to min imize the management cos t of meet ing the ha rves t p a t t e r n , most of the p e r i o d i c volume c o n s t r a i n t s tended to be at t h e i r lower l i m i t s . The excep t i ons were p e r i o d s 9 through 13 which represen t the t r a n s i t i o n from p r i m a r i l y h a r v e s t i n g the e x i s t i n g f o r e s t to p r i m a r i l y h a r v e s t i n g the regenera ted f o r e s t . S cena r i o 2 genera tes a management s t r a t e g y fo r THP1 based on both d i r e c t and i n d i r e c t c o s t s . The e f f e c t of add ing i n d i r e c t cos t i s to i n c r ea se the r e l a t i v e cos t of n a t u r a l r egene ra t i on w i th r espec t to e i t h e r of the p l a n t i n g o p t i o n s s i n ce i t i s the r i s k i e r u n d e r t a k i n g . P l a n t i n g ' imp roved ' s tock i n v o l v e s l e s s 168 r i s k than p l a n t i n g ' n o r m a l ' s tock so the dominance of the ' improved ' s tock op t i on apparent in s c e n a r i o 1 i s r e i n f o r c e d . Desp i t e the h igher r i s k , n a t u r a l r e g e n e r a t i o n remains the most a t t r a c t i v e op t i on d u r i n g the e a r l i e r t ime p e r i o d s s i n ce i t i s s t i l l the cheapest op t i on by f a r . Changes in the management s t r a t e g y begin to occur in p e r i o d 6, the time of t r a n s i t i o n from p r i m a r i l y n a t u r a l r egene ra t i on to p r i m a r i l y p l a n t i n g of ' improved ' s t o c k . The changes are g e n e r a l l y of a minor nature i n v o l v i n g some s h i f t i n g of age c l a s s e s and amounts to be ha r ves t ed in the i n i t i a l s t and ing t imbe r . P e r i o d i c volumes to be ha r ves t ed d i f f e r s l i g h t l y from s c e n a r i o 1 in p e r i o d s 9 through 13, the t ime of conve r s i on from p r i m a r i l y h a r v e s t i n g the i n i t i a l f o r e s t to p r i m a r i l y h a r v e s t i n g the regenera ted f o r e s t . D i r e c t c o s t s are ignored in s c e n a r i o 3 and the management s t r a t e g y i s fo rmula ted on the premise of m i n i m i z i n g i n d i r e c t cos t which i s ak in to m i n i m i z i n g r i s k . Not s u r p r i s i n g l y , the on l y management op t i on used was p l a n t i n g ' i m p r o v e d ' s tock which produced the h i ghes t y i e l d and had the lowest i n d i r e c t c o s t . Volumes to be ha r ves ted vary from s c e n a r i o s 1 and 2 on l y du r i ng the t r a n s i t i o n p e r i o d (pe r i ods 9 through 13) . Under the assumption of cons tan t cos t and b e n e f i t v a l u e s , chang ing the magnitude of the d i f f e r e n c e between these va lues ( i . e . chang ing the degree of r i s k a ve r s i on ) would not change the s o l u t i o n a l though i t would a l t e r the t o t a l c o s t a s s o c i a t e d wi th the s t r a t e g y . T h i s ho lds because the r e l a t i v e r e l a t i o n s h i p s between the i n d i r e c t c o s t s would-not change. S c ena r i o 3 can be c o n s i d e r e d to l i e at the o the r end of the spectrum from s c e n a r i o 1. Whi le s c e n a r i o 1 p roduces a s t r a t egy 1 69 A a p p r o p r i a t e fo r a r i s k n e u t r a l d e c i s i o n maker, s c e n a r i o 3 produces a s t r a t e g y a p p r o p r i a t e fo r a d e c i s i o n maker who i s so r i s k averse tha t the i n d i r e c t c o s t s t o t a l l y dominate d i r e c t c o s t s . In te rmed ia te s t r a t e g i e s such as tha t produced fo r s c e n a r i o 2 can be genera ted by v a r y i n g r i s k a v e r s i o n between these two ext remes . 9 .2 .2 Comparison of S o l u t i o n s to S cena r i o s 4, 5, 6 and 7. S cena r i o 4 genera tes a management s t r a t e g y fo r THP2 based on c o n s i d e r a t i o n s of d i r e c t c o s t s o n l y . T h i s i s comparable w i th s c e n a r i o 1 f o r THP1. The d i f f e r e n c e between the t o t a l c o s t s r ep resen t s the d i r e c t cos t of sw i t ch i ng from the volume r e g u l a t i o n s a s s o c i a t e d wi th THP1 to those a s s o c i a t e d w i th THP2. As in s c e n a r i o 1, on l y a c t i v i t i e s i n v o l v i n g n a t u r a l r egene ra t i on and p l a n t i n g ' improved ' s tock were s e l e c t e d . Aga in a c t i v i t i e s i n v o l v i n g n a t u r a l r e g e n e r a t i o n predominated in the e a r l i e r p e r i o d s . T i g h t e n i n g the volume r e g u l a t i o n s under THP2 had the e f f e c t of moving the t r a n s i t i o n from predominant l y n a t u r a l r e g e n e r a t i o n to p l a n t i n g forward from p e r i o d 6 to p e r i o d 3. The h ighe r volume requ i rements in l a t e r p e r i o d s under THP2 n e c e s s i t a t e d i n t r o d u c i n g the h ighe r y i e l d s a s s o c i a t e d w i th p l a n t i n g ' i m p r o v e d ' s tock at an e a r l i e r p o i n t in t ime . T r a n s i t i o n from h a r v e s t i n g p r i m a r i l y the o r i g i n a l f o r e s t to h a r v e s t i n g p r i m a r i l y a r egenera ted f o r e s t o c c u r r e d in p e r i o d s 9 through 12. A cons tan t ha rves t r a t e at the lower l i m i t a l l owed by the t imber ha rves t p a t t e r n i s a ch i e ved i n the o ther p e r i o d s . S cena r i o 5 genera tes a management s t r a t e g y fo r THP2 based on both d i r e c t and i n d i r e c t c o s t s . The i n d i r e c t c o s t s are based 170 on $5/$10 b e n e f i t / c o s t va lues of d e v i a t i n g from the expected growth r a t e . T h i s s c e n a r i o i s compat ib l e wi th s c e n a r i o 2 and the d i f f e r e n c e in t o t a l c o s t s r ep resen t s the cos t of sw i t ch i ng from THP1 to THP2 under the l e v e l of r i s k a v e r s i o n r ep resen ted by a $5.00 d i f f e r e n c e between the b e n e f i t and cos t v a l u e s . The i n t e r p r e t a t i o n of the management s t r a t e g y i s s i m i l a r to that p r o v i d e d fo r s c e n a r i o 2. The major d i f f e r e n c e i s tha t changes in s t r a t e g y compos i t i on as compared to the s t r a t e g y fo rmu la ted fo r d i r e c t cos t occur as e a r l y as p e r i o d 3. T h i s i s not too s u r p r i s i n g as p e r i o d 3 r ep re sen t s the t r a n s i t i o n in management from n a t u r a l r egene ra t i on to p l a n t i n g of ' improved ' s tock under THP2. Changes in p e r i o d i c volumes to be ha r ves ted are l i m i t e d to the t r a n s i t i o n between h a r v e s t i n g the i n i t i a l f o r e s t and h a r v e s t i n g the regenera ted f o r e s t as was the case fo r s c e n a r i o s examined under THP1. S cena r i o 6 d i f f e r s from s c e n a r i o 5 in that the b e n e f i t / c o s t v a l ues are changed to $5/$20. T h i s r ep r e sen t s a t r i p l i n g of the d i f f e r e n c e between b e n e f i t and cos t and hence i s i n d i c a t i v e of a more r i s k averse s tance on the pa r t of the d e c i s i o n maker. There are some minor changes between s c e n a r i o s 5 and 6 in terms of s c h e d u l i n g order and amount ha r ves t ed in any one year s t a r t i n g in p e r i o d 3. In tha t p e r i o d a few more ha are a l l o c a t e d to p l a n t i n g improved s tock than was the case in the l e s s r i s k averse s i t u a t i o n . Subsequent changes are a r e s u l t of b a l a n c i n g the f low of t imber over the remainder of the p l ann ing h o r i z o n . D i r e c t c o s t remains the dominant f a c t o r in the t o t a l cos t of the p l a n t i n g o p t i o n s and the d e c i s i o n maker ' s a v e r s i o n to r i s k must be q u i t e l a r g e to warrant any major change i n management 171 s t r a t e g y fo r the f i r s t few p e r i o d s . S cena r io 7 r ep resen t s a s i t u a t i o n where the i n d i r e c t cos t a lone d i c t a t e s f o rmu l a t i on of the management s t r a t e g y . As was the case in s c e n a r i o 3, the on ly management o p t i o n s e l e c t e d was p l a n t i n g ' improved ' s t o c k . T h i s o p t i o n had the lowest i n d i r e c t cos t and a l s o p rov ided the h i g h e s t expected y i e l d per ha so t h i s r e s u l t i s q u i t e expec t ed . B e n e f i t / c o s t va lues were set at $5/$10 so the d i f f e r e n c e in the t o t a l cos t of the management s t r a t e g i e s fo r s c e n a r i o s 3 and 7 i s a t t r i b u t a b l e on ly to the change in t imber ha rves t p a t t e r n s . 9 .2 .3 Comparison of Cos ts Tab le 13 c o n t a i n s a summary of the c o s t components a s s o c i a t e d w i th the management s t r a t e g i e s fo rmu la ted fo r c e r t a i n of the s c e n a r i o s . The cos t component employed in the f o r m u l a t i o n of the management s t r a t e g y i s i n d i c a t e d wi th an a s t e r i s k in each c a s e . The other cos t components were c a l c u l a t e d from the a c t i v i t i e s compr i s i ng the s t r a t e g y us i ng Tab le 4 fo r d i r e c t c o s t s and the t a b l e in Appendix III a s s o c i a t e d wi th a b e n e f i t / c o s t s t r u t u r e of $5/$l0 fo r i n d i r e c t c o s t s where a p p r o p r i a t e . Comparison of the cos t f i g u r e s w i t h i n a column p rov ide some i n d i c a t i o n of the e f f e c t of f o r m u l a t i o n us i ng d i f f e r e n t cos t components on the t o t a l cos t of the s t r a t e g i e s fo r t h i s example. Comparison of the cos t f i g u r e s w i t h i n a row p rov ide an i n d i c a t i o n of the change in the c o s t components a s s o c i a t e d w i th t i g h t e n i n g the volume requ i rements from those r e q u i r e d fo r THP1 to those r e q u i r e d f o r THP2. 172 Tab l e 13: Cost Components A s s o c i a t e d w i th V a r i o u s S cena r i o s Assuming a B e n e f i t / C o s t S t r u c t u r e of $5/$ l0 THP1 THP2 INCREASE IN COST COMPONENT SCENARIO 1 SCENARIO 4 DIRECT COST* $383,741. 34 $1 ,266 ,649 . ,06 $882,907. ,72 INDIRECT COST $150,884. 54 $ 140,213. ,91 -$ 10,670. ,63 TOTAL COST $534,625. 88 $1 ,406 ,862 . ,97 $872,237. ,09 SCENARIO 2 SCENARIO 5 DIRECT COST . $383,770. 24 $1 ,266 ,573 . .25 $882,803. .01 INDIRECT COST $150,836. 33 $ 140,152. .73 -$ 10,683. .60 TOTAL COST* $534,606. 57 $1 ,406 ,725 . .98 $872,119. .41 SCENARIO 3 SCENARIO 7 DIRECT COST $2,883,507 .33 $3,031,964, .01 $148,456, .68 INDIRECT COST* $ 95,433 .83 $ 100,335, .89 $ 4,902, .06 TOTAL COST $2,978,941 .16 $3 ,132,299, .90 $153,358, .74 * I n d i c a t e s which component was min imized I t i s apparent from comparing the c o s t components of s c e n a r i o s 1 and 4 w i th s c e n a r i o s 2 and 5 r e s p e c t i v e l y , tha t m i n i m i z i n g d i r e c t c o s t r e s u l t s i n a s t r a t e g y w i th t o t a l c o s t s l i t t l e d i f f e r e n t than the s t r a t e g y a s s o c i a t e d w i th m i n i m i z i n g t o t a l c o s t s assuming a b e n e f i t / c o s t s t r u c t u r e of $ 5 / $ l 0 . One would expect the d i r e c t c o s t s to be s l i g h t l y s m a l l e r and the t o t a l c o s t s s l i g h t l y l a r g e r i n s c e n a r i o s 1 and 4 than in s c e n a r i o s 2 and 5 because of the m i n i m i z a t i o n c r i t e r i a . T h i s i s indeed the case except tha t the d i r e c t c o s t i n s c e n a r i o 5 i s m a r g i n a l l y sma l l e r than tha t of s c e n a r i o 4. T h i s i s due to round ing e r r o r when c a l c u l a t i n g the d i r e c t c o s t component f o r 173 Tab le 14: Comparison of Cost Components fo r S cena r i o s 4 and 6 Assuming a $5/$20 B e n e f i t / C o s t S t r u c t u r e f o r I n d i r e c t C o s t s . SCENARIO 4 SCENARIO 6 CHANGE FROM 4 TO 6 DIRECT COST $1 ,266 ,649 .06* INDIRECT COST $ 420,641.73 TOTAL COST $1 ,687 ,290 .79 $1,266,959.31 $310.25 $ 419,719.17 -$922.56 $1 ,686 ,678 .48* -$612.31 I n d i c a t e s which component was min imized in s t r a t e g y f o r m u l a t i o n s c e n a r i o 5 manua l l y . The sma l l dec rease in t o t a l c o s t a s s o c i a t e d wi th i n t r o d u c i n g i n d i r e c t c o s t to r e f l e c t r i s k and then m i n i m i z i n g t o t a l c o s t i s a p roduct of the dominance of d i r e c t cos t in the t o t a l cos t w i th the b e n e f i t / c o s t s t r u c t u r e employed and the s t a b i l i t y of the management a c t i v i t i e s in the f i r s t s e v e r a l p e r i o d s . The l a t t e r i s a r e s u l t of the i n t e r a c t i o n of the i n i t i a l f o r e s t s t r u c t u r e , the h a r v e s t i n g p a t t e r n s examined and the management o p t i o n s c o n s i d e r e d . I n c r e a s i n g the l e v e l of r i s k a v e r s i o n w i l l i n c r ease the d i f f e r e n c e in t o t a l cos t between s t r a t e g i e s fo rmu la ted by m i n i m i z i n g d i r e c t cos t and those a s s o c i a t e d w i th m i n i m i z i n g t o t a l c o s t . To i l l u s t r a t e t h i s e f f e c t , the cos t components a s s o c i a t e d w i th s c e n a r i o 6 are compared to those a s s o c i a t e d w i th s c e n a r i o 4 i n Tab le 14. Note tha t the i n d i r e c t c o s t s f o r both s t r a t e g i e s a re c a l c u l a t e d us i ng b e n e f i t / c o s t v a l ues of $5/$20. S ince d i r e c t c o s t compr ises a l a r g e p r o p o r t i o n of the t o t a l c o s t of the v a r i o u s management o p t i o n s in t h i s example at low l e v e l s of r i s k a v e r s i o n , i g n o r i n g d i r e c t cos t and m i n i m i z i n g 174 i n d i r e c t c o s t s l eads to a s u b s t a n t i a l l y l a r g e r d i r e c t and t o t a l cos t f o r s c e n a r i o s 3 and 7 than f o r the o ther s c e n a r i o s . The d e c i s i o n maker would r e q u i r e an ext remely h igh a v e r s i o n to r i s k to j u s t i f y the l a r g e d i r e c t cos t components a s s o c i a t e d w i th the management s t r a t e g i e s fo rmula ted fo r s c e n a r i o s 3 and 7 under the two t imber h a r v e s t i n g p a t t e r n s examined. The a c t u a l cos t f i g u r e s may be of some h e l p to the d e c i s i o n maker i f he wants to choose between h a r v e s t i n g p a t t e r n s us ing management cos t c r i t e r i a . In o rder fo r the cos t f i g u r e s to be of v a l u e , however, the expected i n c r ea se in cos t must be compared to the expected i n c r ease in revenue. Expected i n c r e a s e in revenue would be d i f f i c u l t to e s t ima te wi th r e l i a b i l i t y s i n ce i t would i n vo l v e market f o r e c a s t i n g as we l l as supp ly p r o j e c t i o n . THP2 s t r a t e g i e s p r o v i d e d a lower i n d i r e c t c o s t component than the comparable s t r a t e g i e s under THP1 fo r s c e n a r i o s 1 and 2. T h i s p a r t i a l l y o f f s e t s the l a r g e i n c r ease in d i r e c t c o s t s a s s o c i a t e d wi th sw i t ch ing from THP1 to THP2. I f the d e c i s i o n maker i s r i s k a v e r s e , i t i s important that the t o t a l cos t d i f f e r e n c e between t imber ha rves t p a t t e r n s be examined, not j u s t the d i r e c t cos t component. The decrease in i n d i r e c t c o s t between THP1 and THP2 i s due to the nature of the management o p t i o n s c o n s i d e r e d . P l a n t i n g ' improved ' s tock was the most expens ive o p t i o n in terms of d i r e c t c o s t , but i t produced the h i ghes t expected y i e l d and was the l e a s t r i s k y of the o p t i o n s a v a i l a b l e . Sw i t ch ing from THP1 to THP2 r e q u i r e s h ighe r t imber y i e l d s a f t e r the f i r s t few management p e r i o d s . In order to s u s t a i n t h i s l e v e l of h a r v e s t , h ighe r y i e l d s from the regenera ted f o r e s t a re r e q u i r e d 1 75 n e c e s s i t a t i n g the i n c r e a s e d use of p l a n t i n g wi th ' improved ' s t o c k . The i n c r e a s e d use of t h i s op t i on subsequent l y lowers the i n d i r e c t c o s t . It i s apparent fo r t h i s example that i n c r e a s i n g the l e v e l of r i s k a v e r s i o n would decrease the t o t a l cos t a s s o c i a t e d w i th sw i t ch i ng from THP1 to THP2. I n c r e a s i n g a v e r s i o n to r i s k would r e s u l t in more a rea be ing p l a n t e d wi th ' improved ' s t o c k . S ince t h i s management o p t i o n produces h ighe r y i e l d s , the r e l a t i v e i n c r ease in p l a n t i n g r e q u i r e d to sw i t ch from THP1 to THP2 would be sma l l e r r e s u l t i n g in a lower t o t a l cos t i n c r e a s e . 176 CHAPTER X  IMPLICATIONS 10.1 D i s c u s s i o n of Methodology The c h o i c e of a management s t r a t e g y fo r the example p resen ted in the p r e v i ous chapter would not be a d i f f i c u l t p r o p o s i t i o n fo r e i t h e r of the t imber harves t p a t t e r n s examined. The management a c t i o n s fo r the f i r s t few p e r i o d s compr i s i ng the v a r i o u s s t r a t e g i e s fo rmu la ted were q u i t e s t a b l e fo r the l e v e l s of r i s k a v e r s i o n s p e c i f i c a l l y i n c o r p o r a t e d . Changes in the s t r a t e g y compos i t i on in more d i s t a n t p e r i o d s a s s o c i a t e d wi th d i f f e r e n t l e v e l s of r i s k a v e r s i o n do not a f f e c t what needs to be done in the p resen t i f any of the s t r a t e g i e s are implemented. Future r e v i s i o n of the t imber h a r v e s t i n g p a t t e r n , t echno logy changes , et c e t e r a w i l l undoubtably change the management a c t i o n s fo r f u tu r e p e r i o d s c o n s i d e r a b l y from what whould be chosen fo r those p e r i o d s now. C o n s i d e r a t i o n of the d i f f e r e n t l e v e l s of r i s k a s s o c i a t e d wi th cand ida te management o p t i o n s becomes more important when the management a c t i o n s s e l e c t e d fo r the f i r s t few p e r i o d s under d i f f e r e n t degrees of r i s k a v e r s i o n f l u c t u a t e g r e a t l y . Whether or not t h i s s i t u a t i o n occurs depends on the i n t e r a c t i o n of the i n i t i a l f o r e s t s t r u c t u r e , the h a r v e s t i n g p a t t e r n s e l e c t e d and the management o p t i o n s c o n s i d e r e d . Even in a s i m p l i s t i c problem the s t a b i l i t y of management a c t i o n s recommended fo r the f i r s t few p e r i o d s may not be apparent p r i o r to m o d e l l i n g . I f the a c t i v i t i e s a s s i g n e d to the f i r s t few p e r i o d s are not 177 s t a b l e , the d e c i s i o n f a c i n g the f o r e s t manager becomes more d i f f i c u l t . The cho i ce of a management s t r a t e g y , and i t s i m p l i c a t i o n s i n terms of r e q u i r e d management a c t i o n s , becomes more immediate and more dependent on the l e v e l of r i s k a v e r s i o n deemed a p p r o p r i a t e . The mathemat ica l s t r u c t u r e of the model ensures that the s o l u t i o n s , q u a l i t a t i v e l y , w i l l appear the way they have. I n c r ea s i ng r i s k a v e r s i o n and m i n i m i z i n g t o t a l cos t produced s t r a t e g i e s which were more expens ive to implement (h igher d i r e c t c o s t ) , but l e s s r i s k y than s t r a t e g i e s based on m i n i m i z a t i o n of d i r e c t c o s t s a l o n e . E s s e n t i a l l y , the d e c i s i o n maker a s s o c i a t e s some premium wi th r educ ing r i s k . The g rea te r the r e d u c t i o n in r i s k , the l a r g e r the premium. Employ ing a l i n e a r programming f o r m u l a t i o n a l l ows s o l u t i o n of l a r g e r problems more e f f i c i e n t l y than would be p o s s i b l e u s i ng o t h e r , more r i g o r o u s , mathemat ica l programming approaches . Problem s i z e cannot be i n c r e a s e d i n d e f i n i t e l y , however. A l though the a c t u a l model s t r u c t u r e employed f o r the example was q u i t e s i m p l i s t i c , i t c o u l d be e a s i l y expanded. R e a l i s t i c a p p l i c a t i o n s would c e r t a i n l y i n c l u d e more than one t imber c l a s s and c o u l d r e q u i r e i n t e r v a l c o n s t r a i n t s on expend i t u r e l e v e l s , maximum area to be managed by a p a r t i c u l a r management o p t i o n , et c e t e r a . The number of management o p t i o n s c o n s i d e r e d c o u l d be c o n s i d e r a b l y l a r g e r than the three a v a i l a b l e in the example. Whi le such c o m p l i c a t i o n s do not change the methodology from a t h e o r e t i c a l s tand p o i n t , they g r e a t l y i n c r e a s e the s i z e of the l i n e a r programming c o e f f i c i e n t m a t r i x . The n e c e s s i t y of c o n s t r a i n i n g the problem to a workable s i z e c o u l d c o n s i d e r a b l y l i m i t the 1 7 8 f l e x i b i l i t y of the p o t e n t i a l management a c t i v i t i e s c o n s i d e r e d . It i s not e s s e n t i a l that a c t u a l d i r e c t c o s t s be known fo r d i f f e r e n t management o p t i o n s , on l y r e l a t i v e d i f f e r e n c e s in c o s t , i f m i n i m i z a t i o n of d i r e c t c o s t s (a r i s k n e u t r a l s tance) i s to be the c r i t e r i o n fo r management s t r a t e g y f o r m u l a t i o n . I f the d e c i s i o n maker i s r i s k a v e r s e , then i t i s important that d i r e c t c o s t s be c l o s e to t h e i r proper v a l u e s . T h i s i s necessa ry because the r e l a t i v e magnitude of the i n d i r e c t cos t component to the d i r e c t cos t component i n f l u e n c e s the impact that r i s k a v e r s i o n , r ep resen ted by a p a r t i c u l a r d i f f e r e n c e between b e n e f i t and cos t v a l u e s , w i l l have on s t r a t e g y f o r m u l a t i o n . The i n t e r e s t r a te assumed in the example was not of any r e a l importance s i n c e i t d i d not i n f l u e n c e s t r a t e g y f o r m u l a t i o n . T h i s was a r e s u l t of the cand ida te management.opt ions a l l hav ing d i r e c t c o s t s which occu r r ed at the same p o i n t in time (upon es t ab l i shmen t ) and s i m i l a r i n d i r e c t cos t s t r u c t u r e s . If the t im ing of the c o s t components d i f f e r e d , then the d i s c o u n t ra te assumed c o u l d i n f l u e n c e the f o r m u l a t i o n of the management s t r a t e g y . For t h i s methodology, i t i s the p resen t va lue of the c o s t s which are important to the cho i c e between cand ida te management o p t i o n s , not the a c t u a l magnitude of the c o s t . P o t e n t i a l d e v i a t i o n of growth r a te from expected growth r a te appears to be a reasonab le b a s i s f o r i n t r o d u c t i o n of i n d i r e c t c o s t s fo r d i f f e r e n t management o p t i o n s as o u t l i n e d in Chapter V I I I . Other p o s s i b i l i t i e s e x i s t . For example, p o t e n t i a l d e v i a t i o n from expec ted y i e l d at the time of ha rves t c o u l d be p e n a l i z e d r a the r than d e v i a t i o n from expected annual growth r a t e . 179 It would be t h e o r e t i c a l l y p o s s i b l e to a s s o c i a t e an i n d i r e c t cos t w i th h a r v e s t i n g t imber a l r e a d y e s t a b l i s h e d at the s t a r t of the management p e r i o d . Y i e l d s c u r r e n t l y a s s o c i a t e d wi th p a r t i c u l a r age and t imber c l a s s e s a re more c e r t a i n now then they w i l l be in f u tu r e p e r i o d s . I f the d e c i s i o n maker i s r i s k a v e r s e , he might be w i l l i n g to fo rego f u t u r e ga in and harves t s tands at an e a r l i e r age i f i t reduces the r i s k he p e r c e i v e s . T h i s i s p a r t i c u l a r l y t rue i f there i s an e s c a l a t i n g p r o b a b i l i t y of heavy m o r t a l i t y the longer a stand i s l e f t . An i n d i r e c t cos t c o u l d b e ' a s s o c i a t e d wi th each age c l a s s s u i t a b l e fo r h a r v e s t i n g based on p o t e n t i a l d e v i a t i o n s from expected y i e l d under a spectrum of p o s s i b l e outcomes. The expected y i e l d shou ld be c o n s t r u c t e d as a weighted average (based on a s s i gned s u b j e c t i v e p r o b a b i l i t i e s ) of the y i e l d curves a s s o c i a t e d w i th each of the p o t e n t i a l outcomes. The i n d i r e c t cos t c o u l d be c a l c u l a t e d on a p e r i o d by p e r i o d b a s i s depending on p o t e n t i a l d e v i a t i o n s in any p e r i o d and the b e n e f i t / c o s t va lues per cub i c m of exceed ing/not a c h i e v i n g expected y i e l d per ha . B e n e f i t / c o s t va lues were t r e a t e d as cons t an t s i n t h i s example to a l l ow s o l u t i o n of the problem u s i n g l i n e a r programming. It i s q u i t e c o n c e i v a b l e tha t the b e n e f i t / c o s t of exceed ing/not a c h i e v i n g the expected growth ra te would not have a cons tan t va lue fo r each cub i c m per ha per y ea r . The magnitude of the b e n e f i t / c o s t c o u l d depend on the t o t a l p o t e n t i a l y e a r l y d e v i a t i o n in growth ra te which would be r e l a t e d to the number of ha a s s i gned to a p a r t i c u l a r a c t i v i t y . I t i s reasonab le to expect tha t the c o s t a s s o c i a t e d w i th u n d e r e s t i m a t i n g growth r a te by 1 180 cub i c m per ha per year on 100 ha would be more than 100 t imes g r ea t e r than that a s s o c i a t e d w i th a s i m i l a r d e v i a t i o n fo r on l y one ha . S i m i l a r l y , the b e n e f i t of exceed ing the growth r a te by one cub i c m per ha per year c o u l d dec rease as the excess growing s tock accumu la tes . While v a r i a b l e b e n e f i t / c o s t v a l ues c o u l d be accommodated, i t would comp l i c a t e the s o l u t i o n p r o c e d u r e . U n t i l more i n f o r m a t i o n i s a v a i l a b l e on the b e n e f i t s / c o s t s of d e v i a t i n g from expected growth r a t es under d i f f e r e n t management o p t i o n s and h a r v e s t i n g s c h e d u l e s , i t was thought best to keep the va lues as s imple as p o s s i b l e . The use of s u b j e c t i v e p r o b a b i l i t i e s and s e p a r a t i o n of what shou ld be a con t inuous d i s t r i b u t i o n of p o s s i b l e y i e l d pathways i n t o a f i n i t e number of d i s c r e t e c l a s s e s may appear q u i t e a r b i t r a r y . I t i s , however, a necessa r y s tep towards s i m p l i f y i n g the s o l u t i o n p r o c e d u r e . Arguments were p resen ted in Chapter VII s uppo r t i ng the use of expected va lues r a the r than most l i k e l y v a l u e s . I f a f i n i t e number of outcomes are c o n s i d e r e d , each assuming a y i e l d curve c o r r e s p o n d i n g to the y i e l d of an average ha , a s s i g n i n g s u b j e c t i v e p r o b a b i l i t i e s as weights fo r each y i e l d curve p r o v i d e s a conven ien t means of a c q u i r i n g an expected y i e l d c u r v e . The same p r o b a b i l i t i e s can be used in de t e rm in ing the i n d i r e c t cos t component fo r each management op t i on assuming some l e v e l of r i s k a v e r s i o n on the p a r t of the d e c i s i o n maker. The e x e r c i s e of a s s i g n i n g s u b j e c t i v e p r o b a b i l i t i e s focuses the d e c i s i o n maker ' s a t t e n t i o n on the u n c e r t a i n t y of response he a s s o c i a t e s w i th p a r t i c u l a r management o p t i o n s . T h i s procedure i s o f t e n of b e n e f i t i n i t s e l f s i n c e i t r e q u i r e s the d e c i s i o n maker to c a r e f u l l y examine each of the management o p t i o n s a v a i l a b l e to 181 h im. The i n s i g h t t h i s p rov i des i s e s s e n t i a l to r each ing a d e c i s i o n which i s c o n s i s t e n t wi th h i s b e l i e f s and p r e f e r e n c e s . No p r o v i s i o n fo r ga the r i ng i n f o rma t i on i s e x p l i c i t l y i n c o r p o r a t e d i n t o the methodology p r e s e n t e d . Much of the i n f o r m a t i o n necessary to reduce u n c e r t a i n t y su r round ing responses to d i f f e r e n t management o p t i o n s i s not immediate ly a v a i l a b l e . Examinat ion of the u n c e r t a i n t y a s s o c i a t e d wi th p a r t i c u l a r management o p t i o n s w i l l p rov ide i n fo rma t i on on where most of the u n c e r t a i n t y l i e s . T h i s can p rov ide a d i r e c t i o n fo r a p p r o p r i a t e r e sea r ch which may be of b e n e f i t in subsequent t imber management s t r a t e g y d e c i s i o n s in f u t u r e management p l a n s . 10.2 Implementat ion of the Methodology A d d i t i o n a l work i s r e q u i r e d p r i o r to implementat ion of the methodology on an o p e r a t i o n a l s c a l e . Three a spec t s in p a r t i c u l a r warrant immediate a t t e n t i o n : 1. De te rm ina t i on of the s u i t a b i l i t y of the i n d i r e c t cos t approach employed in the example in more gene ra l s i t u a t i o n s . 2. Development of g u i d e l i n e s f o r de t e rm ina t i on of a p p r o p r i a t e b e n e f i t / c o s t l e v e l s . 3. C r e a t i o n of computer r o u t i n e s which w i l l s t r e am l i ne the gene ra t i on of a p p r o p r i a t e a c t i v i t i e s and c o s t s , c o n s t r u c t an input mat r ix fo r some l i n e a r programming s o l u t i o n a l g o r i t h m and p rov ide a s tandard a n a l y s i s of the l i n e a r programming s o l u t i o n to f a c i l i t a t e i n t e r p r e t a t i o n of the management s t r a t e g y gene ra t ed . 182 10.2.1 De te rm ina t i on of the S u i t a b i l i t y of the I n d i r e c t  Cost Approach Employed The use of some c o s t to p e n a l i z e the s e l e c t i o n of l e s s c e r t a i n a c t i v i t i e s i s not a new concep t . However, f o r such an approach to produce r e s u l t s which are r e f l e c t i v e of the d e c i s i o n maker ' s t rue a v e r s i o n to r i s k , a mean ingfu l b a s i s fo r e s t ab l i shment of a pena l t y cos t must e x i s t . H e u r i s t i c arguments suppo r t i ng the use of d e v i a t i o n s from expected average growth ra te are p rov ided in Chapter V I I I . T h i s approach has i n t u i t i v e appea l under a s u s t a i n e d y i e l d p o l i c y where there i s a s t rong l i nkage i m p l i e d between f o r e s t s t r u c t u r e and h a r v e s t i n g r a t e . If there i s no p o l i c y r e q u i r i n g some l i n k between f o r e s t s t r u c t u r e and h a r v e s t i n g ra te then d e v i a t i o n from expec ted growth r a te l o s e s much of i t s i n t e r p r e t a t i o n . Under such c o n d i t i o n s another b a s i s f o r pena l t y c o s t s ( d e v i a t i o n from expected ha rves t ra te fo r example) might prove to be more a p p r o p r i a t e . The best means of t e s t i n g the s u i t a b i l i t y of the i n d i r e c t cos t approach suggested i s to employ the techn ique to fo rmula te t imber management s t r a t e g i e s fo r more r e a l i s t i c examples . The ease of a s s i g n i n g i n d i r e c t c o s t s to v a r i o u s management o p t i o n s and the i n f l u e n c e of d i f f e r e n t l e v e l s of i n d i r e c t cos t on the s o l u t i o n w i l l p rov ide a good i n d i c a t i o n of whether the work r e q u i r e d to implement the suggested approach i s wor thwh i l e . The model fo rmula ted f o r the example assumed a cons tan t b e n e f i t / c o s t d i f f e r e n c e . T h i s r e s u l t e d in an i n d i r e c t c o s t which was l i n e a r l y r e l a t e d to the a c t i v i t y l e v e l . As i n d i c a t e d in the p r ev i ous s e c t i o n , t h i s may not be r e f l e c t i v e of the a t t i t u d e of the d e c i s i o n maker. I t would be p o s s i b l e to fo rmu la te a problem 183 in such a way tha t n o n l i n e a r i n d i r e c t c o s t s are i n c o r p o r a t e d i n t o the o b j e c t i v e f u n c t i o n , but t h i s would g r e a t l y comp l i c a t e the s o l u t i o n p rocedu re . S o l u t i o n s fo r a number of examples c o u l d be compared us ing both n o n l i n e a r c o s t f u n c t i o n s and l i n e a r a p p r o x i m a t i o n s . I t i s r easonab le to expect that the use of a n o n l i n e a r cos t f u n c t i o n c o u l d on l y i n f l u e n c e the s o l u t i o n s i g n i f i c a n t l y i f the a c t i v i t i e s in the f i r s t few p e r i o d s are s e n s i t i v e to the l e v e l of r i s k a v e r s i o n . In such cases i t would l i k e l y be p o s s i b l e to approximate the use of a n o n l i n e a r f u n c t i o n wi thout r e s o r t i n g to some formal n o n l i n e a r programming t e c h n i q u e . 10.2 .2 Development of G u i d e l i n e s fo r De te rm ina t i on of  A p p r o p r i a t e B e n e f i t / C o s t L e v e l s Adopt ion of a p a r t i c u l a r r i s k averse p o s i t i o n i s of l i t t l e importance in s i t u a t i o n s where the management a c t i o n s s e l e c t e d fo r the f i r s t few p e r i o d s are s t a b l e fo r f a i r l y l a r g e d i f f e r e n c e s between b e n e f i t s and c o s t s . However, i f the compos i t i on of the management s t r a t e g y fo r the f i r s t few p e r i o d s i s s e n s i t i v e to sma l l v a r i a t i o n s in the d i f f e r e n c e between b e n e f i t s and c o s t s , the d e c i s i o n maker must dec ide ( i m p l i c i t l y or e x p l i c t i l y ) what l e v e l of d i f f e r e n c e i s a p p r o p r i a t e p r i o r to choos ing a s t r a t e g y . The c a u s a l r e l a t i o n s h i p between r i s k a v e r s i o n and the p e r c e i v e d d i f f e r e n c e between va lues a s s o c i a t e d w i th p o s i t i v e and nega t i ve d e v i a t i o n s from expected v a l u e s remains u n c l e a r . Is the degree of r i s k a v e r s i o n an i nhe ren t c h a r a c t e r i s t i c of the d e c i s i o n maker which determines h i s p e r c e p t i o n of b e n e f i t s and 184 c o s t s of d e v i a t i o n s or does the d e c i s i o n maker ' s p e r c e p t i o n of b e n e f i t s and c o s t s determine h i s r i s k a v e r s i o n ? The. d i s t i n c t i o n i s perhaps a moot po in t in t h i s a n a l y s i s . P e r c ep t i ons of b e n e f i t s and c o s t s of d e v i a t i o n s appear to be a means of approx imat ing the degree of r i s k a v e r s i o n . However, the q u e s t i o n of how b e n e f i t s and c o s t s of d e v i a t i o n s from e x p e c t e d . v a l u e s can be measured and the monetary va lue to p l a c e on such d e v i a t i o n s remains . The b e n e f i t s and c o s t s of d e v i a t i o n s shou ld depend on l o c a l c o n d i t i o n s to some e x t e n t . F a c t o r s such as the l o c a l s t r u c t u r e of the economy, p o s s i b i l i t i e s fo r a l t e r n a t i v e f o r e s t u se s , et  c e t e r a , w i l l a l l i n f l u e n c e the p e r c e i v e d impacts of d e v i a t i o n s . Reg iona l and g l o b a l c o n s i d e r a t i o n s are a l s o n e c e s s a r y , e s p e c i a l l y in s i t u a t i o n s i n v o l v i n g more than one g e o g r a p h i c a l l y separa te management un i t under the same ownersh ip . I t i s important tha t some l i n k a g e be ma in ta ined between b e n e f i t / c o s t de t e rm ina t i ons fo r the d i f f e r e n t management u n i t s , both g e o g r a p h i c a l l y and t e m p o r a l l y . T h i s would r e q u i r e the development of a system of g u i d e l i n e s gove rn ing the assignment of b e n e f i t s and c o s t s to p o t e n t i a l d e v i a t i o n s . I d e a l l y the g u i d e l i n e s shou ld be f i r m enough to remove some of the ad hoc nature of determing the extent of r i s k a v e r s i o n whi le r e t a i n i n g enough f l e x i b i l i t y to a l l ow l o c a l c o n d i t i o n s to be r e f l e c t e d . T h i s ba lance may not be easy to a c h i e v e . 10 .2 .3 Development of Computer Rout ines The a c t i v i t y mat r ix r e q u i r e d by the l i n e a r programming s o l u t i o n a l g o r i t h m was genera ted by hand f o r t h i s example. Whi le 185 manual gene ra t i on i s f e a s i b l e fo r sma l l p rob lems , the s i z e of the mat r ix necessary fo r r e a l i s t i c a l l y s i z e d problems would make manual g e n e r a t i o n i m p r a c t i c a l . If an approach s i m i l a r to that suggested i s to be implemented on an o p e r a t i o n a l b a s i s , some matr ix g e n e r a t i n g r o u t i n e would have to be employed. A mat r ix genera tor c o u l d be c o n s t r u c t e d from f i r s t p r i n c i p l e s or by adap t ing an e x i s t i n g mat r ix g e n e r a t i n g r o u t i n e to c r e a t e a range of a c t i v i t i e s of i n t e r e s t to the d e c i s i o n maker. Gene ra t i on of a complete range of p o s s i b l e a c t i v i t i e s would q u i c k l y produce a mat r ix which i s beyond the c a p a b i l i t y of even the most power fu l s o l u t i o n a l g o r i t h m s . Some r i g i d r u l e s must be employed to keep the number of a c t i v i t i e s genera ted to a workable s i z e . On the o ther hand, i t i s important tha t the d e c i s i o n maker r e t a i n some f l e x i b i l i t y in the gene r a t i on of a c t i v i t i e s . The advantage of b u i l d i n g an o r i g i n a l matr ix gene r a t i ng r o u t i n e i s tha t i t c o u l d be des igned to s u i t a p a r t i c u l a r ownership and p o l i c y s t r u c t u r e . I t c o u l d r e t a i n f l e x i b i l i t y in c e r t a i n a spec t s of a c t i v i t y g e n e r a t i o n thought to be of major i n t e r e s t and app ly r i g i d r u l e s e lsewhere to c o n s t r a i n problem s i z e . The d i sadvantage of d e s i g n i n g an o r i g i n a l r o u t i n e would be the t ime and expense i n v o l v e d . Adapt ing an e x i s t i n g r o u t i n e would l i k e l y be q u i c k e r and l e s s e x p e n s i v e . F i g u r e 8 p rov i des an i l l u s t r a t i o n of a component s t r u c t u r e which c o u l d prove u s e f u l f o r gene ra t i ng a Type I input matr ix fo r some l i n e a r programming s o l u t i o n a l g o r i t h m and summarize the r e s u l t s . A b r i e f d i s c u s s i o n of the v a r i o u s components f o l l o w s . No attempt i s made to specu l a t e on the a c t u a l s t r u c t u r e of the 186 i n d i v i d u a l components. The methodology p resen ted . r e q u i r e s the c r e a t i o n of a weighted aggregate y i e l d curve fo r each type group in the e x i s t i n g t imber and fo r a l l of the management o p t i o n s a p p l i c a b l e to each type group f o l l o w i n g h a r v e s t i n g . E s s e n t i a l l y t h i s would i n v o l v e g e n e r a t i n g a f i n i t e number of p o t e n t i a l outcomes fo r the c i r cums tances a s s o c i a t e d wi th each r e q u i r e d weighted y i e l d c u r v e . Every p o t e n t i a l outcome would be a s s i gned a y i e l d curve and a s u b j e c t i v e p r o b a b i l i t y l e v e l a s s o c i a t e d w i th the c o n f i d e n c e tha t the d e c i s i o n maker has in the outcome a c t u a l l y o c c u r r i n g . Subsequent development of weighted y i e l d cu rves would be a matter of s imple a r i t h m e t i c . T h i s whole p rocess would l i k e l y be hand led most e f f i c i e n t l y by deve lop ing an i n t e r a c t i v e r o u t i n e which would prompt the user fo r t imber t ype , management o p t i o n , p o t e n t i a l outcome and s u b j e c t i v e p r o b a b i l i t y i n f o r m a t i o n . Such a r o u t i n e shou ld a l low subsequent r e v i s i o n by the user p r i o r to gene r a t i ng f i n a l weighted y i e l d c u r v e s . Each p o t e n t i a l management o p t i o n would be compr ised of a s e r i e s of d i r e c t c o s t s spaced over t ime . Present va lue of the d i r e c t c o s t s can be c a l c u l a t e d by a p p l y i n g some d i s c o u n t r a te to f u t u r e c o s t s and summing fo r each management o p t i o n . D i r e c t c o s t fo r each of the management a c t i v i t i e s can be c a l c u l a t e d by a d j u s t i n g the present va lue of the d i r e c t cos t f o r the management a c t i o n a s s o c i a t e d w i th the a c t i v i t y to r e f l e c t the t im ing of the a c t i v i t y . 187 gure 8: I l l u s t r a t i o n of the Components of a Computa t iona l Approach to a Timber Management S t r a t egy Fo rmu la t i on P rob lem. •EXISTING TIMBER CLASSES ^MANAGEMENT OPTIONS POTENTIAL OUTCOMES (YIELDS) SUBJECTIVE PROBABILITIES ACTIVITY GENERATOR EXPECTED YIELD GENERATOR I POTENTIAL ACTIVITIES T DISCOUNT RATE I BENEFIT/COST VALUES DISCOUNT RATE I DIRECT COSTS EXPECTED YIELD CURVES i INDIRECT COST GENERATOR i INDIRECT COSTS FOR ACTIVITIES 1 DIRECT COST GENERATOR DIRECT COSTS FOR ACTIVITIES OTHER RESTRICTIONS LINEAR PROGRAMMING MATRIX GENERATOR AREAS BY AGE CLASS AND TIMBER TYPE MBER HARVEST PATTERN LINEAR PROGRAMMING MATRIX 1 SOLUTION ALGORITHM I SOLUTION REPORT WRITER 188 I n d i r e c t c o s t s fo r each management op t i on can be c a l c u l a t e d based on the sum of p o t e n t i a l d e v i a t i o n s from the expected y i e l d curve (or the a s s o c i a t e d growth curve) weighted by the s u b j e c t i v e p r o b a b i l i t y and the b e n e f i t or cos t a s s o c i a t e d w i th the d e v i a t i o n . As wi th d i r e c t c o s t s , i n d i r e c t c o s t s must be determined as a present va lue and ad ju s t ed fo r the t im ing of the v a r i o u s a c t i v i t i e s us ing some d i s c o u n t r a t e . P o t e n t i a l management a c t i v i t i e s can be genera ted fo r e x i s t i n g t imber types by knowledge of the management o p t i o n s a v a i l a b l e and the t im ing r e s t r i c t i o n s on the h a r v e s t i n g of e x i s t i n g and regenera ted t imbe r . For a Type I l i n e a r programming f o r m u l a t i o n , each a c t i v i t y would c o n s i s t of h a r v e s t i n g a p a r t i c u l a r age c l a s s of some t imber type d u r i n g a c e r t a i n time p e r i o d and subsequent l y managing the l and a c c o r d i n g to one of the management o p t i o n s . Output from the aggregate y i e l d r o u t i n e , d i r e c t and i n d i r e c t cos t r o u t i n e s and the a c t i v i t y genera to r r o u t i n e would p r o v i d e the input fo r the mat r ix g e n e r a t o r . D e s i r e d t imber ha r ves t p a t t e r n , a reas in each age c l a s s f o r the d i f f e r e n t t imber types and other r e s t r i c t i o n s would be input i n t o t h i s r o u t i n e to a l l ow development of s u i t a b l e c o n s t r a i n t s . The mat r ix genera to r would assemble t h i s i n f o rma t i on i n t o a format s u i t a b l e fo r input i n t o the l i n e a r programming s o l u t i o n a l g o r i t h m employed. A r epo r t w r i t e r c o u l d be deve loped to summarize the s o l u t i o n f o r each s c e n a r i o examined. The r epo r t w r i t e r would e x t r a c t the r e l e v a n t i n f o r m a t i o n from the s o l u t i o n and combine t h i s w i t h , i n f o r m a t i o n from the aggregate y i e l d , a c t i v i t y 189 gene ra to r , d i r e c t and i n d i r e c t cos t r o u t i n e s to produce summary t ab l e s fo r any p a r t i c u l a r computer r un . T h i s would p rov ide a b a s i s f o r r e a d i l y comparing the r e s u l t s of s e v e r a l runs to a i d in the s e l e c t i o n of a management s t r a t e g y to f o l l ow u n t i l the s t r a t e g i c p l an fo r managing the t imber r esource on a p a r t i c u l a r management u n i t i s r e v i s e d . 190 CHAPTER XI  CONCLUSIONS 11.1 Genera l Summary Fo res t management d e c i s i o n s take p l a ce in an u n c e r t a i n env i ronment . J u r i s d i c t i o n a l s e p a r a t i o n of the f o r e s t management problem i n to resource-use ca tegory subproblems and g e o g r a p h i c a l s e p a r a t i o n i n t o management u n i t s s i m p l i f i e s the d e c i s i o n environment of the subproblems, but c r e a t e s d i f f i c u l t y in s y n t h e s i s . Management of any resource component of the f o r e s t i s c en t r ed on a d d r e s s i n g two i n t r i c a t e l y l i n k e d q u e s t i o n s : (1) 'What l e v e l of r esource use to a l l ow over t ime? ' and (2) 'What management s t r a t e g y to employ to a l low that l e v e l of u s e ? ' . T h i s d i s s e r t a t i o n s p e c i f i c a l l y addressed the f o r m u l a t i o n and s e l e c t i o n of t imber management s t r a t e g i e s . A concep tua l s e p a r a t i o n of the d e c i s i o n of how much to cut over time (the t imber ha rves t pa t t e rn ) from the d e c i s i o n of how to manage the t imber r esource over t ime (the t imber management s t r a t e g y ) i s advoca ted . A l though the two d e c i s i o n s are c l o s e l y r e l a t e d , s e p a r a t i o n p r o v i d e s important advantages to both d e c i s i o n p r o c e s s e s . The p r o j e c t i o n of t imber supply w i l l p rov ide the necessary l i n k a g e between the two d e c i s i o n s . Timber supp ly m o d e l l i n g r ep re sen t s on l y one source of i n f o rma t i on a v a i l a b l e f o r t imber ha rves t p a t t e r n d e c i s i o n s . In fo rmat ion from other s o u r c e s , i n c l u d i n g p r o j e c t i o n of demand fo r t imber and other f o r e s t r e sou r ces shou ld p l a y a l a rge r o l e in de t e rm in ing how much to ha r ves t over t ime . Timber ha r ves t 191 p a t t e r n s are s p e c i f i c to a p a r t i c u l a r management u n i t to the extent that the amount c o n s i d e r e d a v a i l a b l e f o r ha rves t i s l i m i t e d by the present f o r e s t s t r u c t u r e and the gene ra l management i n t e n s i t y assumed. Timber ha rves t p a t t e r n d e c i s i o n s are l i n k e d in space and time by p o l i c y which p r o v i d e s the s t r u c t u r e fo r mode l l i ng t imber s u p p l y . P o l i c y a l s o p rov idesan i n d i c a t i o n of the d e s i r e d f u tu r e s t a t e fo r the f o r e s t . On p u b l i c l a n d , the d e c i s i o n about how much to ha rves t over t ime i s u l t i m a t e l y made at a p o l i t i c a l ' l e v e l . P o l i t i c i a n s and s en i o r p u b l i c se r van t s r e s p o n s i b l e fo r s e t t i n g t imber h a r v e s t i n g p a t t e r n s shou ld r e a l i z e the importance of a long-term p l a n n i n g h o r i z o n fo r the t imber r e s o u r c e . P lans based on long-term p l ann ing h o r i z o n p rov ide a t a r g e t towards which f o r e s t managers can aim the f o r e s t s t r u c t u r e on s p e c i f i c management u n i t s . The extent to which the d i r e c t i o n and ra te of change of the f o r e s t system can be c o n t r o l l e d d e f i n e s the boundar ies of f o r e s t management. The l eng th of t ime between s u c c e s s i v e h a r v e s t s on a g i ven u n i t of l and and the u n c e r t a i n t y of response of tha t l and area to v a r i o u s management a c t i o n s make • the c o n t r o l of the f o r e s t system a slow and r i s k y p r o c e s s . Fu r the rmore , s i n ce the d e s i r e d f u t u r e s t a t e of the f o r e s t system env i saged in the present i s not l i k e l y to be the d e s i r e d s t a t e in the f u t u r e , the manager i s e s s e n t i a l l y a iming at a s h i f t i n g t a r g e t . F o r t u n a t e l y , much of the u n c e r t a i n t y connected wi th the l e v e l of the f u tu r e ha rves t i s c e n t r e d in the more d i s t a n t f u t u r e . The heavy impact of major changes to the t imber h a r v e s t i n g r a t e on l o c a l and r e g i o n a l economies has been noted p r e v i o u s l y . Most p o l i c y systems on p u b l i c l and c o n t r o l the r a te 192 of a l l owab l e changes between management p e r i o d s . T h i s tends to make the h a r v e s t i n g ra te in the next management p e r i o d much l e s s u n c e r t a i n than the ra te p r o j e c t e d s e v e r a l p e r i o d s in the f u t u r e . P e r i o d i c r e p l a n n i n g a l l ows the mon i to r i ng of responses of the f o r e s t system to management and r e v i s i o n of the d e s i r e d h a r v e s t i n g p a t t e r n to r e f l e c t c u r r e n t and p r e d i c t e d c o n d i t i o n s . Major d e c l i n e s in the h a r v e s t i n g r a te are n e i t h e r p r e d i c t a b l e nor d e s i r a b l e . Under these c o n d i t i o n s i t i s e s s e n t i a l tha t the f o r e s t s t r u c t u r e be ma in ta ined at a l e v e l which w i l l a l l ow adjustment to sudden changes to the f o r e s t s t r u c t u r e and/or economic c o n d i t i o n s . T r a d i t i o n a l l y t h i s has been done by h a r v e s t i n g the f o r e s t in a manner which a l l ows some minimum harves t l e v e l to be a v a i l a b l e in p e r p e t u i t y from a p a r t i c u l a r l and base shou ld such a l e v e l be r e q u i r e d . ' P o t e n t i a l shor tages of a v a i l a b l e t imber r e s u l t i n g from expected responses of the c u r r e n t f o r e s t s t r u c t u r e to p resen t l e v e l s of management are p r e d i c t a b l e through a management system i n v o l v i n g f requent r ep l ann ing and mon i to r i ng of r e sponses . T h i s shou ld p r o v i d e the f o r e s t manager w i th enough l ead time to min imize the nega t i ve impacts a s s o c i a t e d wi th p r e d i c t e d shor tages of wood s u p p l y . I f t imber supp ly p r o j e c t i o n s i n d i c a t e a s i g n i f i c a n t drop in p e r i o d i c supp ly from presen t l e v e l s then the management agency ' s o p t i o n s might be c a t e g o r i z e d as f o l l o w s : 1. Ma in t a i n t imber management expend i t u r e s and a c t i o n s at the present l e v e l but decrease the expected l e v e l of t imber a v a i l a b l e in the f u tu r e to r e f l e c t c u r r e n t p r e d i c t i o n s . Take s teps to a m e l i o r a t e l o c a l impacts of p r e d i c t e d s h o r t f a l l s . 2. Change management p r a c t i c e s to i n c r ea se the y i e l d from the f o r e s t base to ' a l l o w ' the c u r r e n t h a r v e s t i n g l e v e l to be ma in ta ined i n t o the f u t u r e . 193 3. Implement some combina t ion of the above two approaches . There are unden iab le economic b e n e f i t s to keeping h a r v e s t i n g l e v e l s h igh i f the re i s a f a v o r a b l e market fo r the t imber p r o d u c t s . There a r e , however, c o s t s a s s o c i a t e d wi th m a i n t a i n i n g or enhancing p resen t ha rves t r a t e s . These c o s t s a r i s e from i n t e n s i f y i n g p resen t management a c t i v i t i e s to a l low h a r v e s t i n g r a t e s to be m a i n t a i n e d , t r a d i n g p o t e n t i a l f u tu re s h o r t f a l l s f o r p resent ga in and/or f o r ego ing o ther p o t e n t i a l f o r e s t u ses . It i s d i f f i c u l t to make such d e c i s i o n s on p u r e l y economic terms. Fu tu re u n c e r t a i n t y r e g a r d i n g requ i rements from the f o r e s t as a whole and the d i f f i c u l t y of de te rm in ing the b e n e f i t s and c o s t s of a p a r t i c u l a r t imber h a r v e s t i n g p a t t e r n c o n t r i b u t e to a complex d e c i s i o n env i ronment . F a i t h u l t i m a t e l y must p l ay a l a rge r o l e in the d e c i s i o n of how much t imber to ha rves t over t ime . Sepa ra t i on of the t imber management s t r a t e g y d e c i s i o n from the h a r v e s t i n g p a t t e r n d e c i s i o n i n the manner suggested in t h i s d i s s e r t a t i o n r e q u i r e s the assumpt ion tha t the d e s i r e d t imber ha rves t p a t t e r n w i l l not change. Whi le such an assumpt ion i s not l i k e l y to be v a l i d , i t i s e s s e n t i a l to the a n a l y s i s of the fo rmu la ted p rob lem. For t h i s r e a son , the s t r a t e g y chosen shou ld not be c o n s i d e r e d ' o p t i m a l ' , but r a the r as the ' b e s t ' s t r a t e g y of the s t r a t e g i e s c o n s i d e r e d shou ld the assumpt ions necessary fo r model f o r m u l a t i o n a l l ho ld t r u e . If r e p l a n n i n g occurs at f requent i n t e r v a l s ( i . e . every f i v e or ten y e a r s ) , the on ly p o r t i o n of the s t r a t e g y the manager shou ld be committed to implement ing i s tha t pa r t of the s t r a t e g y 194 which i s a p p l i c a b l e to tha t p e r i o d of t ime . T h i s i s a l s o the p o r t i o n of the p l ann ing h o r i z o n f o r which the h a r v e s t i n g r a te i s the most c e r t a i n . If t e c h n o l o g y , economic c o n d i t i o n s or the f o r e s t l and base are found to have changed upon r e f o r m u l a t i o n of the p rob lem, the management s t r a t e g y shou ld be changed to r e f l e c t the new c o n d i t i o n s . The need fo r ex tend ing the management s t r a t e g y over the long-term p l ann ing h o r i z o n and d e s i g n i n g a s t r a t e g y to ' a l l o w ' a n t i c i p a t e d f u t u r e h a r v e s t i n g requ i rements a r i s e s out of the d e s i r e to min imize the p o s s i b i l i t y of management a c t i o n s now caus i ng an u n a n t i c i p a t e d change in f u t u r e wood s u p p l y . In o ther words, employ ing a long-term p l a n n i n g h o r i z o n a l l ows the f o r e s t manager to exer t g rea te r c o n t r o l over the movement of the f o r e s t system than would be p o s s i b l e us ing on l y shor t- te rm p l a n n i n g . The d e s i r e of the f o r e s t manager to ma in ta in as much c o n t r o l over the f o r e s t as p o s s i b l e i s r e f l e c t e d in h i s a t t i t u d e towards r i s k . A l l e l s e e q u a l , he would l i k e the o v e r a l l response of the f o r e s t system to a t imber management s t r a t e g y to be as p r e d i c t e d . T h i s ho lds t rue even though the s t r a t e g y i s l i k e l y not based on the h a r v e s t i n g p a t t e r n which w i l l u l t i m a t e l y be f o l l o w e d . The manager 's degree of r i s k a v e r s i o n w i l l d i c t a t e how much he would be w i l l i n g to i n c r ea se the cos t of implement ing a management s t r a t e g y in o rder to i n c r e a s e the degree of c o n t r o l exe r ted over the f o r e s t by some amount. The u n c e r t a i n t y a s s o c i a t e d w i th the response of a t imber c l a s s to some management sequence i s r e f l e c t e d in the d i s t r i b u t i o n of p o t e n t i a l y i e l d cu rves p e r c e i v e d to e x i s t i n d i c a t i n g the r esponse . The p r o b a b i l i t y of an average hec ta re -195 f o l l o w i n g any g iven y i e l d e x p r e s s i o n i s d i r e c t l y r e l a t e d to the s i m i l a r i t y of i t s growing c o n d i t i o n s to the c o n d i t i o n s under which the y i e l d e x p r e s s i o n was f o r m u l a t e d . S ince c o n d i t i o n s which a f f e c t y i e l d are r e l a t e d to the b i o t i c and a b i o t i c components of the f o r e s t system, c l i m a t i c e f f e c t s , et. c e t e r a , the u n c e r t a i n t y su r round ing any response i s r e l a t e d to how we l l the f a c t o r s which i n f l u e n c e development are unders tood and how we l l t h e i r occur rence can be p r e d i c t e d . The f a c t that p r o j e c t i o n s need to be made we l l i n t o the f u t u r e makes i t imposs ib l e to a s s o c i a t e a s t r i c t l y o b j e c t i v e d i s t r i b u t i o n wi th average y i e l d . I f the d e c i s i o n maker i s o ther than r i s k n e u t r a l , he would s t i l l wish to i n c l u d e h i s p e r c e p t i o n of r i s k in the cho i c e of a management s t r a t e g y . In o rder to do t h i s e x p l i c i t l y , s u b j e c t i v e p r o b a b i l i t i e s must be employed to c a l c u l a t e both the expected y i e l d s and i n d i r e c t c o s t s a s s o c i a t e d w i th any management sequence. Such a procedure may appear ad hoc , but there are few v i a b l e a l t e r n a t i v e s to u s i ng s u b j e c t i v e p r o b a b i l i t i e s in some form or o t h e r . Fo rmu la t i ng management s t r a t e g i e s assuming average y i e l d s are c e r t a i n i s no l e s s ad hoc than assuming a number of d i s c r e t e p o t e n t i a l outcomes and i s l e s s r e a l i s t i c . S cena r i o s c o u l d be examined which fo rmu la te management s t r a t e g i e s under d i f f e r e n t assumed c o n d i t i o n s . However, the cho i ce among management s t r a t e g i e s must s t i l l be made and the manager must app ly some c r i t e r i a to a i d in h i s c h o i c e which may or may not be c o n s i s t e n t wi th h i s b e l i e f s . The use of s u b j e c t i v e p r o b a b i l i t i e s in the manner advocated w i l l at l e a s t d i r e c t a t t e n t i o n towards the range of responses 196 thought p o s s i b l e under any management sequence. T h i s w i l l enable the d e c i s i o n maker to e x p l i c i t l y s t a t e h i s b e l i e f s and address the u n c e r t a i n t y he p e r c e i v e s . Such a p rocess o f t e n p rov ides added i n s i g h t in i t s e l f . Whi le a t t e n t i o n has been d i r e c t e d p r i m a r i l y towards the t imber management s t r a t e g y d e c i s i o n , the use of s u b j e c t i v e p r o b a b i l i t i e s fo r p o t e n t i a l responses c o u l d a i d in the de t e rm ina t i on of an a p p r o p r i a t e h a r v e s t i n g r a t e f o r the f i r s t management p e r i o d . The a l l owab l e cut e f f e c t s t i p u l a t e s that i n c r e a s i n g f u tu r e y i e l d s by improv ing management at the present time shou ld r e s u l t in h igher ha r ves t r a t e s immedia te l y . I n c o r p o r a t i o n of t h i s e f f e c t in de t e rm in ing ha rves t r a te without much p r i o r knowledge of average response under the proposed management sequences may i n c r ease expected f u t u r e y i e l d and a l low a h igher p resent ha rves t r a t e , but on l y at the cos t of g r e a t l y i n c r e a s i n g the r i s k of not meet ing f u tu r e e x p e c t a t i o n s . A s s o c i a t i n g d i r e c t and i n d i r e c t c o s t s wi th each management sequence w i l l a l l ow compar ison of the cos t components of the ' b e s t ' s t r a t e g i e s fo r v a r i o u s t imber ha rves t p a t t e r n s . T h i s would p rov i de the d e c i s i o n maker w i th a d d i t i o n a l i n f o rma t i on upon which to base the ha rves t p a t t e r n d e c i s i o n . I t would a l s o be p o s s i b l e to l i m i t i n d i r e c t cos t to some v a l u e , perhaps one a s s o c i a t e d wi th the ' b e s t ' s t r a t e g y fo r the c u r r e n t ha rves t p a t t e r n . If i n c r e a s i n g the p resen t h a r v e s t i n g r a te to some h ighe r l e v e l by implement ing i n t e n s i v e management a c t i v i t i e s does not i n c r ease the i n d i r e c t c o s t s above some l i m i t i n g v a l u e , then the i n c r ease in h a r v e s t i n g r a t e would be g r a n t e d . O b v i o u s l y , the implementa t ion of such a p rocedure would 197 be con t i ngen t on b e t t e r unders tand ing of i n d i r e c t c o s t s and the development of a s u i t a b l e procedure fo r a s s o c i a t i n g i n d i r e c t c o s t s wi th p a r t i c u l a r management sequences . 11.2 E v a l u a t i o n of the Methodology It i s d i f f i c u l t to deve lop o b j e c t i v e c r i t e r i a f o r j udg ing the a p p l i c a b i l i t y of the framework deve loped fo r f o r m u l a t i n g t imber management s t r a t e g i e s in t h i s . d i s s e r t a t i o n . N e v e r t h e l e s s , some c l u e s as to the a p p l i c a b i l i t y can be gathered by examining the problem s t r u c t u r e upon which the framework i s based and the i n f o rma t i on r e q u i r e d to implement the methodology . F i v e q u e s t i o n s were posed in S e c t i on 1.3 to a i d in t h i s exam ina t i on . T h i s s e c t i o n w i l l address each of these q u e s t i o n s in t u r n . (1) Is the framework f o r t imber management s t r a t e g y d e c i s i o n s based on a p l a u s i b l e d e s c r i p t i o n of the d e c i s i o n environment? Chapters III and VII I d e s c r i b e the f o r e s t management d e c i s i o n environment and the development of the methodology r e s p e c t i v e l y . The framework deve loped i s e s s e n t i a l l y based on two p r e m i s e s : (1) The t imber management subproblem can be sepa ra ted both c o n c e p t u a l l y and j u r i s d i c t i o n a l l y from the o ther resource use components of the f o r e s t management p rob lem; and (2) The t imber management subproblem i s i t s e l f sepa rab le i n t o a t imber ha rves t p a t t e r n d e c i s i o n and a t imber management s t r a t e g y d e c i s i o n . The f i r s t premise i s a normal s t a t e of a f f a i r s in most f o r e s t management a g e n c i e s . Whi le i t would be d e s i r e a b l e to c o n s i d e r management of the f o r e s t in an h o l i s t i c manner, the 198 comp lex i t y of the f o r e s t system coup led w i th the long-term p l a n n i n g h o r i z o n s norma l l y a s s o c i a t e d wi th f o r e s t management to data have p reven ted d e t a i l e d m o d e l l i n g to a i d f o r e s t management d e c i s i o n s . As t imber i s most o f t e n the dominant f o r e s t use and i s s p a t i a l l y and/or t empora l l y i n compa t ib l e w i th some f o r e s t uses , a common procedure i s to d e f i n e a p a r t i c u l a r f o r e s t l and base w i th t imber as the dominant use and deve lop a t imber management s t r a t e g y fo r tha t l and base . For p l a n n i n g purposes , development of a framework p r e d i c a t e d on a s e p a r a t i o n of the t imber management subproblem from other r esource use i s sues i s q u i t e r e a s o n a b l e . S epa ra t i on of the t imber h a r v e s t i n g p a t t e r n d e c i s i o n from the t imber management s t r a t egy d e c i s i o n , on the o ther hand, i s not a r e f l e c t i o n of cu r r en t p r a c t i c e in most management a g e n c i e s . The c l o s e r e l a t i o n s h i p between these two d e c i s i o n p rocesses was s t r e s s e d a number of t imes throughout the d i s s e r t a t i o n . However, s e p a r a t i o n fo r a n a l y t i c purposes i s an e s s e n t i a l component of the methodology deve l oped . The exact r e l a t i o n s h i p between the t imber ha r ves t p a t t e r n and the t imber management s t r a t e g y d e c i s i o n s w i l l be a p roduct of the p l a n n i n g p rocess in e f f e c t . The key p o i n t i s that s e p a r a t i o n of the d e c i s i o n p r o c e s s e s fo r a n a l y t i c purposes does not r e q u i r e complete s p e a r a t i o n in the p l a n n i n g p r o c e s s . It was noted that the p rocess of t imber supp ly m o d e l l i n g can p l a y a key r o l e in t imber management d e c i s i o n s . There are four i n f o r m a t i o n sources necessa ry fo r t imber supp ly m o d e l l i n g : (1) c u r r e n t i n v e n t o r y , (2) d e s i r e d ha rves t l e v e l s over t ime , (3) p o l i c y s t r u c t u r e and (4) t imber management s t r a t e g y i n f o r m a t i o n . 199 Cur rent i n ven to r y i s f i x e d by d e f i n i t i o n of the management a r e a . If ha r ves t l e v e l i n f o rma t i on and p o l i c y s t r u c t u r e are f i x e d e x t e r n a l l y to the t imber supp ly model , then the t imber supply m o d e l l i n g procedure can be employed to fo rmula te a t imber management s t r a t e g y a p p r o p r i a t e to the f i x e d c o n d i t i o n s . A n a l y t i c s e p a r a t i o n of the t imber h a r v e s t i n g p a t t e r n from the t imber management s t r a t e g y d e c i s i o n e s s e n t i a l l y se rves to f i x t imber ha rves t p a t t e r n s and p o l i c y fo r a p a r t i c u l a r a n a l y s i s of t imber management s t r a t e g y . Whi le the t imber ha rves t p a t t e r n d e c i s i o n was not examined in d e t a i l , some tempora l o v e r l a p between the two d e c i s i o n p rocesses was s t a t e d to be a l i k e l y occu rence . I f such i s the c a s e , i t would be p o s s i b l e to c y c l e between the d e c i s i o n s to u l t i m a t e l y a r r i v e at a t imber ha rves t p a t t e r n and a t imber management s t r a t e g y which are compat ib le and the ' b e s t ' the d e c i s i o n maker can c r ea t e g i ven h i s p e r c e p t i o n of the l i k e l i h o o d of f u t u r e events and h i s p r e f e r e n c e s t r u c t u r e . (2) Is the i n fo rma t i on r e q u i r e d r e a d i l y a v a i l a b l e ? The i n f o r m a t i o n r e q u i r e d fo r s u c c e s s f u l a p p l i c a t i o n of the methodology can be summarized as f o l l o w s : (1) Cur ren t i n v e n t o r y ; (2) Expected response to p a r t i c u l a r management sequences ; (3) P o l i c y s t r u c t u r e ; (4) Timber ha r ves t p a t t e r n d e s i r e d ; (5) D i r e c t cos t of implement ing p a r t i c u l a r management sequences ; and 200 ( 6 ) I n d i r e c t c o s t s a s s o c i a t e d wi th the d i f f e r e n t management sequences . Inventory i n fo rma t i on i s a necessary component of any t imber management p l ann ing system, and i s u s u a l l y r e a d i l y a v a i l a b l e . A fundamental q u e s t i o n a s s o c i a t e d w i th a c q u i r i n g i nven to ry i n f o r m a t i o n i s the l e v e l of p r e c i s i o n d e s i r e d . T h i s i s not an easy q u e s t i o n to address because i nven to ry i n f o r m a t i o n i s used fo r many purposes and the i m p l i c a t i o n s of e r r o r s in i n ven to r y i n f o r m a t i o n , at l e a s t in terms of f o r e s t management p l a n n i n g , are u n c l e a r . T h i s d i f f i c u l t y , however, i s a problem wi th any p l a n n i n g methodology, and not s p e c i f i c to the framework deve loped h e r e . I n fo rmat ion on the expected response of s tands to p a r t i c u l a r management sequences and s p e c i f i c a t i o n of p o l i c y s t r u c t u r e f a l l i n t o the same ca tegory as i nven to ry i n f o r m a t i o n . Any p l a n n i n g system r e q u i r i n g i m p l i c i t or e x p l i c i t p r o j e c t i o n of t imber supp ly needs t h i s i n f o r m a t i o n . Response i n f o r m a t i o n i s necessary to choose a management s t r a t e g y and to p r e d i c t t imber supply under any p a r t i c u l a r management s t r a t e g y . Some p o l i c y s t r u c t u r e i s necessary to r e l a t e management s t r a t e g y to h a r v e s t i n g l e v e l and to ma in ta in l i n k a g e s between t imber management and management of o ther f o r e s t r e s o u r c e s . An e s t a b l i s h e d t imber ha r ves t p a t t e r n i s a p r e r e q u i s i t e to the f o r m u l a t i o n of a t imber management s t r a t e g y under the framework p r e s e n t e d . I t i s d i f f i c u l t to s e l e c t an a p p r o p r i a t e t imber ha r ves t p a t t e r n wi thout c o n s i d e r a t i o n of t imber management s t r a t e g y . A s o l u t i o n to t h i s dilemma i s to ma in t a i n a c a p a b i l i t y f o r c y c l i n g between the t imber ha rves t p a t t e r n 201 d e c i s i o n and the t imber management s t r a t e g y d e c i s i o n in the p l ann ing p r o c e s s . Under such a system i t would on ly be necessa ry to s t a r t the procedure with some h a r v e s t i n g p a t t e r n and a l l ow the f o r m u l a t i o n of the t imber management s t r a t e g y and f i n a l c h o i c e of t imber h a r v e s t i n g p a t t e r n to deve lop from that p o i n t . Whi le the c o s t of implement ing v a r i o u s management sequences may not be a c r i t e r i o n which i s e x p l i c i t l y c o n s i d e r e d in s e l e c t i o n of a l l management s t r a t e g i e s , such i n f o rma t i on shou ld not be d i f f i c u l t to o b t a i n . There may be some u n c e r t a i n t y wi th r espec t to the c o n d i t i o n s under which the cos t f i g u r e s ho ld and the p o t e n t i a l changes to such c o s t s in the f u t u r e , but such u n c e r t a i n t y p a l e s bes ide the u n c e r t a i n t y a s s o c i a t e d wi th the o ther i n f o r m a t i o n requ i rements of t imber supp ly m o d e l l i n g . The use of a p p r o p r i a t e d i s c o u n t r a tes to express management c o s t s as a p resent va lue fo r the v a r i ous management regimes tends to favour sequences w i th sma l l e r i n i t i a l e x p e n d i t u r e s . T h i s appears to be a r easonab le approach p r o v i d i n g h a r v e s t i n g p a t t e r n c o n s t r a i n t s are met and the money necessa ry fo r the implementat ion of the management sequences i s a v a i l a b l e when r e q u i r e d . It would be a s imple matter to r e s t r i c t d i r e c t c o s t expend i tu res f o r any one p e r i o d or group of p e r i o d s in the model to a range thought to be r e a sonab l e . The i n d i r e c t cos t a s s o c i a t e d w i th the v a r i o u s management sequences depends on the a t t i t u d e towards r i s k taken by the manager. Chapter X c o n t a i n s some d i s c u s s i o n of the d i f f i c u l t y of e s t a b l i s h i n g an a p p r o p r i a t e a t t i t u d e towards r i s k . S e n s i t i v i t y ana l y ses on the impact of s p e c i f i c b e n e f i t / c o s t va lues f o r d e v i a t i o n s from the expected response w i l l i n d i c a t e the 202 s e n s i t i v i t y of the management s t r a t e g y compos i t i on to changes in the manager 's a t t i t u d e towards r i s k , but w i l l not suggest an a p p r o p r i a t e p o s i t i o n . Whi le i t would be b e n e f i c i a l f o r p u b l i c f o r e s t management agenc ies to e s t a b l i s h a documented s tance towards p o t e n t i a l d e v i a t i o n s from expected responses under d i f f e r e n t management sequences , i t i s not a necessa ry requi rement f o r the use of the methodology. E x p l o r a t i o n of the r a m i f i c a t i o n s of changing a t t i t u d e s towards r i s k on the compos i t i on of management s t r a t e g i e s w i l l p ro v i de the d e c i s i o n maker w i th v a l u a b l e i n f o r m a t i o n , but the d e c i s i o n maker i s l e f t to make the f i n a l c h o i c e . (3) Do c r i t e r i a employed by the m o d e l l i n g procedure in f o r m u l a t i n g the t imber management s t r a t e g y r e f l e c t c o n s i d e r a t i o n s important to the model user when making the a c t u a l d e c i s i o n ? Two c r i t e r i a are employed by the model to a i d in f o r m u l a t i o n of t imber management s t r a t e g i e s : d i r e c t c o s t of implement ing p o t e n t i a l management sequences and the r i s k p e r c e i v e d f o r each sequence (the i n d i r e c t c o s t ) . An argument s u p p o r t i n g the re l evance of these c r i t e r i a was p resen ted in Chapter V I I I . Only the s a l i e n t p o i n t s w i l l be p r e sen ted below. In a s i t u a t i o n where the d e s i r e d t imber ha r ves t p a t t e r n and responses to p a r t i c u l a r management sequences a re known, the d e c i s i o n maker would wish to ma in t a i n a f o r e s t s t r u c t u r e which would ' a l l o w ' the d e s i r e d t imber ha rves t p a t t e r n to be a c h i e v e d . Given a c h o i c e among management s t r a t e g i e s which would ma in ta in such a f o r e s t s t r u c t u r e , he would wish to choose the s t r a t e g y w i th the lowest cos t of imp lemen ta t i on . Models deve loped to a i d 203 the f o r m u l a t i o n of 'optimum' t imber management s t r a t e g i e s under such c o n d i t i o n s shou ld choose among cand ida te management sequences on the b a s i s of t h e i r implementat ion cos t and t h e i r c o n t r i b u t i o n towards p roduc ing the d e s i r e d t imber h a r v e s t i n g p a t t e r n . I f the s i t u a t i o n i s such tha t the d e s i r e d h a r v e s t i n g p a t t e r n i s assumed known but u n c e r t a i n t y i s r e cogn i zed in p r e d i c t i n g responses to p a r t i c u l a r management sequences , then the d e c i s i o n maker ' s a t t i t u d e towards r i s k comes i n t o p l a y . A r i s k averse d e c i s i o n maker would be w i l l i n g to pay some premium in terms of c o s t of implementat ion i f i t w i l l reduce h i s p e r c e p t i o n of the r i s k of the f o r e s t not m a i n t a i n i n g the d e s i r e d ha rves t p a t t e r n . In choos ing among management s t r a t e g i e s the d e c i s i o n maker would c o n s i d e r both the cos t of implement ing the s t r a t e g y and the r i s k that the s t r a t e g y may not p rov ide a f o r e s t s t r u c t u r e s u i t a b l e fo r the t imber ha rves t p a t t e r n d e s i r e d . Models employed to a i d in the f o r m u l a t i o n of t imber management s t r a t e g i e s under t h i s set of assumpt ions shou ld choose among cand ida te management sequences on the b a s i s of t h e i r implementat ion c o s t , c o n t r i b u t i o n to o v e r a l l r i s k and t h e i r c o n t r i b u t i o n towards the d e s i r e d t imber h a r v e s t i n g p a t t e r n . The a n a l y t i c a l p rocedure deve loped in t h i s d i s s e r t a t i o n takes t h i s approach . A r e a l i s t i c d e c i s i o n environment i n v o l v e s a t imber h a r v e s t i n g p a t t e r n which i s sub jec t to f u tu re changes and responses to t imber management sequences which are u n c e r t a i n . No e x p l i c i t c o n s i d e r a t i o n of the t imber ha rves t p a t t e r n and i t s a s s o c i a t e d r i s k i s p resent in the a n a l y t i c procedure deve loped 204 f o r f o r m u l a t i n g t imber management s t r a t e g i e s . Hence, the p rocedu re , c o n s i d e r e d in i s o l a t i o n of the p l a n n i n g p r o c e s s , i s not r e f l e c t i v e of whatever i n f l u e n c e the r i s k a s s o c i a t e d w i th t imber ha rves t p a t t e r n d e c i s i o n s w i l l have on the cho i ce of the t imber management s t r a t e g i e s . Such c r i t i c i s m s l o se much of t h e i r weight when the procedure i s c o n s i d e r e d as one component of a p l a n n i n g p rocess which would employ such p a s s i v e d e c i s i o n s t r a t e g i e s as f requent r e p l a n n i n g and maintenance of o p t i o n s . U n c e r t a i n t y w i th r e spec t to f u tu r e t imber ha rves t p a t t e r n s would tend to de l ay s i g n i f i c a n t management expend i t u r e s as long as p o s s i b l e . The use of a d i s c o u n t r a te fo r f u tu r e expend i tu res in the e s t i m a t i o n of d i r e c t c o s t s fo r c and ida te management sequences serves the same purpose . Management sequences w i th de l ayed expend i t u r e s under such a system tend to have lower d i r e c t c o s t s and be s e l e c t e d fo r a p p l i c a t i o n e a r l i e r in the p l a n n i n g h o r i z o n . T h i s was i l l u s t r a t e d in the example p resen ted in Chapter I X where the n a t u r a l r egene ra t i on o p t i o n was s e l e c t e d to compr ise the e a r l i e s t p e r i o d s of the t imber management s t r a t e g i e s fo rmu la ted under a l l s c e n a r i o s except those that were devoted to m i n i m i z i n g r i s k w i th no c o n s i d e r a t i o n of d i r e c t c o s t . Hence, the absence of any e x p l i c i t c o n s i d e r a t i o n of the r i s k a s s o c i a t e d w i th the t imber h a r v e s t i n g p a t t e r n in f o r m u l a t i n g t imber management s t r a t e g i e s does not appear to c r ea t e any s e r i o u s consequences . (4) Can the framework be implemented o p e r a t i o n a l l y ? T h i s q u e s t i o n was addressed in some d e t a i l in the l a s t c h a p t e r . Implementat ion on an o p e r a t i o n a l b a s i s would r e q u i r e 205 the development of a new mat r ix g e n e r a t i n g r o u t i n e or s u b s t a n t i a l r e v i s i o n s of e x i s t i n g r o u t i n e s . P e r i p h e r a l r o u t i n e s to deve lop and t e s t d e v i a t i o n s from expected y i e l d and to c o n s t r u c t p e n a l t y c o s t s would a l s o be r e q u i r e d . Such developments would r e q u i r e a few man-years to implement and t e s t , but the necessa ry programs would be r e l a t i v e l y s t r a i g h t fo rward . (5) Does the framework demonstrate an improvement over e x i s t i n g p rocedures ? The u l t i m a t e c r i t e r i o n fo r the acceptance of any methodology i s whether i t demonstrates an improvement over e x i s t i n g t e c h n i q u e s . In the case of the methodology deve loped in t h i s d i s s e r t a t i o n , the l a ck of q u a n t i t a t i v e data and the nature of the problem n e c e s s i t a t e h e u r i s t i c arguments. The s i t u a t i o n i s f u r t h e r c o m p l i c a t e d by the l a ck of u n i f o r m i t y in e x i s t i n g a n a l y t i c and p l a n n i n g p rocedures between d i f f e r e n t management a g e n c i e s . Timber supp ly m o d e l l i n g at a l e v e l beyond tha t of s imple y i e l d r e g u l a t i o n p rocedures i s not w ide ly employed by management agenc ies a c r o s s Canada at the p resen t t ime . The t r end in the past decade has been towards the acceptence of formal t imber supp ly m o d e l l i n g p rocedures because they g r e a t l y f a c i l i t a t e ana l y ses of the i m p l i c a t i o n s of p a r t i c u l a r management a c t i o n s on t imber s u p p l y . The advantage of employ ing such ana l y ses to a i d in the d e c i s i o n p rocess have been w ide ly r e c o g n i z e d . T h i s i s ev idenced by the f a c t tha t p a r t i c u l a r m o d e l l i n g approaches are r e q u i r e d when p roduc ing management p l ans f o r N a t i o n a l Fo res t 206 lands in the Un i t ed S t a t e s . T r a d i t i o n a l t imber supply models do not r e cogn ize u n c e r t a i n t y in the i n fo rma t i on s u p p l i e d to the model . F a i l u r e to i n c o r p o r a t e u n c e r t a i n t y r ep resen t s a l o s s of i n f o rma t i on to the d e c i s i o n maker who w i l l use r e s u l t s from the model to guide h i s d e c i s i o n s . Another p e r s p e c t i v e on t h i s d i f f i c u l t y i s to r e cogn i ze tha t the models are f o r m u l a t i n g t imber management s t r a t e g i e s u s i ng c r i t e r i a d i f f e r e n t than those the d e c i s i o n maker would wish to use i f he were s e l e c t i n g a management s t r a t e g y from among a cand ida te set of management s t r a t e g i e s . S t o c h a s t i c programming approaches , wh i le t h e o r e t i c a l l y sound, to date have proven to be not a c c e p t a b l e o p e r a t i o n a l l y because of problems wi th d i m e n s i o n a l i t y . Attempts at approx imat ing s t o c h a s t i c programming approaches by combining v a r i o u s o p t i m i z a t i o n techn iques c o n t i n u e , but no f u l l y a c c e p t a b l e p rocedure has been produced f o r t imber supply m o d e l l i n g p rob lems . L i n e a r programming techn iques reduce d i m e n s i o n a l i t y p rob lems . L i n e a r p rocedures can p r o v i d e an a c c e p t a b l e approx imat ion in many i n s t ances ( H i l l i e r and Lieberman 1980). The s t r u c t u r e of the a n a l y t i c p rocedure deve loped in t h i s d i s s e r t a t i o n a l l ows the use of l i n e a r programming techn iques and some c o n s i d e r a t i o n of u n c e r t a i n t y . The procedure may not produce a t imber management s t r a t e g y which i s 'opt imum' in the same sense as a s t r a t e g y produced by a more ma themat i ca l l y e l egant p rocedu re . I t i s , however, an improvement over the f o r m u l a t i o n of t imber management s t r a t e g i e s wi thout c o n s i d e r a t i o n of r i s k . Fu r the rmore , l a ck of mathemat ica l e l egance may not be a s e r i o u s 207 flaw g i ven the u n c e r t a i n t y which e x i s t s o u t s i d e of the t r a d i t i o n a l bounds of t imber supply models . 11.3 Fu ture D i r e c t i o n s The key to b e t t e r f o r e s t management i s Improved unders tand ing of the f o r e s t system and the d e c i s i o n env i ronment . T h i s d i s s e r t a t i o n has addressed a number of broad i s s u e s . A l though c o n s i d e r a b l y more q u e s t i o n s have been r a i s e d than have been answered, i t r ep r e sen t s an attempt to o rder p e r c e p t i o n s of the f o r e s t management d e c i s i o n environment i n t o a more unders tandab le form. How a d e c i s i o n maker p e r c e i v e s a d e c i s i o n environment can not change the r e a l i t y of the s i t u a t i o n , but i t can i n f l u e n c e how he manages the f o r e s t . The p r e v i ous s e c t i o n i n d i c a t e d some of the d i f f i c u l t i e s a s s o c i a t e d wi th a t t empt ing to eva lua te a methodology which i s not yet o p e r a t i o n a l . A l o g i c a l fo l l ow-up to t h i s d i s s e r t a t i o n would be the development of the computer r o u t i n e s necessa ry to a l l ow the a p p l i c a t i o n of the methodology to r e a l i s t i c t imber supp ly m o d e l l i n g s i t u a t i o n s . T h i s would enable more o b j e c t i v e e v a l u a t i o n of model pe r fo rmance . T h i s d i s s e r t a t i o n c o n c e n t r a t e d on a n a l y s i s of t imber management s t r a t e g y d e c i s i o n s . A s i m i l a r type of a n a l y s i s needs to be a p p l i e d to t imber ha rves t p a t t e r n d e c i s i o n s . Only when a c cep t ab l e c r i t e r i a f o r j udg ing t imber ha rves t p a t t e r n d e c i s i o n s are e s t a b l i s h e d can a t r u e l y i n t e g r a t e d p l a n n i n g system fo r t imber management be e s t a b l i s h e d . A n a l y s i s of the t imber harves t p a t t e r n d e c i s i o n must address e lements of both p o l i c y a n a l y s i s and f u tu r e u n c e r t a i n t y w i th r e spec t to the d e s i r e d f u tu r e s t a t e 208 of the t imber r e s o u r c e . Such an a n a l y s i s can not be adequate l y completed in i s o l a t i o n of o ther f o r e s t r e s o u r c e s . A n a l y t i c p rocedures such as tha t p resen ted in t h i s d i s s e r t a t i o n tend to dea l s p e c i f i c a l l y on l y w i th p a r t i c u l a r components of the f o r e s t management p rob lem. P l ann ing p rocesses are r e q u i r e d which can i n t e g r a t e ana l y ses of p a r t i c u l a r f o r e s t components i n t o a s u i t a b l e management scheme fo r the f o r e s t as a whole. Such a p l ann ing p rocess would need to be based on a b e t t e r unders tand ing of the l i n k a g e s between the d i f f e r e n t r esource uses which compr ise the o v e r a l l r e t u r n from the f o r e s t . Attempts to q u a n t i f y the u n c e r t a i n t y f aced by the f o r e s t manager need to be made. Any s t u d i e s in t h i s a rea w i l l r e q u i r e the a c t i v e involvement of the d e c i s i o n makers themselves s i n ce u n c e r t a i n t y i s a product of the d e c i s i o n maker ' s p e r c e p t i o n of the l i k e l i h o o d of f u tu r e e ven t s , not of the events themse lves . Only through an examinat ion of the d e c i s i o n environment can the d e c i s i o n maker a r t i c u l a t e the u n c e r t a i n t y he p e r c e i v e s . The more complex the d e c i s i o n env i ronment , the g r ea t e r the n e c e s s i t y f o r a d e t a i l e d a n a l y s i s . In order fo r the d e c i s i o n maker to make r a t i o n a l c h o i c e s w i t h i n a complex environment he must unders tand the environment to the extent p o s s i b l e p r i o r to s i m p l i f y i n g the environment to a l l ow a n a l y t i c a l s o l u t i o n s to p a r t i c u l a r p rob lems . E s t ab l i shment of a proper d e c i s i o n con tex t i s an i n i t i a l s t ep towards improv ing f o r e s t management. A f o r e s t manager working w i t h i n such a con tex t shou ld be ab l e to app l y the r e s u l t s of a wide range of r e sea r ch t o p i c s to a i d in managing the f o r e s t . S t ud i e s rang ing from f o r e s t dynamics to p rocedures f o r m in im iz i ng l o s s 209 of t imber to damaging agents can c o n t r i b u t e to improved a p p r e c i a t i o n of the dynamics of the f o r e s t system and i n c r ease knowledge of the range of op t i ons a v a i l a b l e fo r d i r e c t i n g f u tu r e f o r e s t deve lopment . Fo res t management p l ann ing always dea l s wi th an u n c e r t a i n f u t u r e . It i s on l y by a d d r e s s i n g t h i s u n c e r t a i n t y , s e t t i n g r e a l i s t i c goa l s and a s s e s s i n g r i s k s , tha t a d e c i s i o n maker can cha r t a course which appears to be best at the p resen t t ime . 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O c t . 29, 1981. 18 pp . 224 APPENDIX I A SUMMARY OF THE ACTIVITIES AVAILABLE AND CORRESPONDING YIELDS Management Opt ion A - P l a n t i n g 'No rma l ' Stock PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS A1 : 1 2 836.27 668.8 A1 : 1 1 826.31 668.8 A1 : 10 807.90 668.8 A1 : 9 779.27 668.8 A1 : 8 735.20 668.8 A1 7 668 .81 668.8 A1 : 6 572.51 668.8 A2: 12 845.57 668 . 8 A2: 1 1 836.27 668.8 A2: 1 0 826.31 668.8 A2 9 807.90 668.8 A2 8 779.27 668.8 A2: 7 735.20 668.8 A2: 6 668 .81 668.8 A2< 5 572.51 668.8 A3' 1 2 850.57 668.8 A3 1 1 845.57 668.8 A3 10 836.27 668.8 A3: 9 826.31 668.8 A3: 8 807.90 668 . 8 A3 7 779.27 668.8 A3< 6 735.20 668.8 A3 5 668 .81 668.8 A3 4 572.51 668.8 A4: 1 2 853.41 668 . 8 A4. 1 1 850.57 668.8 A4 10 845.57 668.8 A4 9 836.27 668.8 A4 8 826.31 668.8 A4 7 807.90 668.8 A4' 6 779.27 668 . 8 A4 5 735.20 668.8 A4 4 668 .81 668.8 A4 3 572.51 668 . 8 A5 1 1 853.41 668 . 8 A5 10 850.57 668.8 A5: 9 845.57 668.8 A5. 8 836.27 668 . 8 A5 7 826.31 668 . 8 A5 ,6 807.90 668 . 8 A5 5 779.27 668 . 8 PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST ;  1 ST HARVEST SUBSEQUENT HARVESTS A5: 4 735.20 668.81 A5:3 668.81 668.81 A5: 2 572.51 668.81 A6:10 853.41 668.81 A6:9 850.57 668.81 A6:8 845.57 668.81 A6:7 836.27 668.81 A6:6 826.31 668.81 A6: 5 807.90 668.81 A6:4 779.27 668.81 A6:3 735.20 668.81 A6:2 668.81 668.81 A6: 1 572.51 668.81 A7:9 853.41 668.81 A7:8 850.36 668.81 A7:7 845.57 668.81 A7:6 836.27 668.81 A7:5 826.31 668.81 A7:4 807.90 668.81 A7:3 779.27 668.81 A7:2 735.20 668.81 A7: 1 668.81 668.81 A8:8 853.41 668.81 A8:7 850.36 668.81 A8:6 845.57 668.81 A8:5 836.27 668.81 A8:4 826.31 668.81 A8:3 807.90 668.81 A8:2 779.27 668.81 A8: 1 735.20 668.81 A9:7 853.41 668.81 A9:6 850.36 668.81 A9:5 845.57 668.81 A9: 4 836.27 668.81 A9:3 826.31 668.81 A9:2 807.90 668.81 A9 : 1 779.27 668.81 A1 0:6 853.41 668.81 A1 0:5 850.36 668.81 Al 0:4 845.57 668.81 A10:3 836.27 668.81 A1 0:2 826.31 668.81 A1 0: 1 807.90 668.81 A1 1 :5 853.41 668.81 A1 1 :4 850.36 668.81 A1 1 :3 845.57 668.81 A1 1 :2 836.27 668.61 A1 1 :1 826.31 668.81 A1 2:4 853.41 668.81 A1 2:3 850.36 668.81 A12:2 845.57 668.81 PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS 12 A12:1 836.27 668.81 1"3' A13:3 853.41 668.81 A13:2 850.36 668.81 A l3 :1 845.57 668.81 14 A14:2 853.41 668.81 A14 : 1 850.36 668.81 15 A15:1 853.41 668.81 Opt ion B - P l a n t i n g ' Improved ' Stock PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS B1 1 2 836.27 715.37 B1 1 1 826.31 715.37 B1 10 807.90 715.37 B1 9 779.27 715.37 B1 •8 735.20 715.37 B1 7 668.81 715.37 B1 6 572.51 715.37 B2 1 2 845.57 715.37 B2 1 1 836.27 715.37 B2 • 1 0 826.31 715.37 B2 9 807.90 715.37 B2 :8 779.27 715.37 B2 7 735.20 715.37 B2 6 668 .81 715.37 B2 5 572.51 715.37 B3 : 1 2 850.57 715.37 B3 . 1 1 845.57 715.37 B3 : 10 836.27 715.37 B3 :9 826.31 715.37 B3 8 807.90 715.37 B3 7 779.27 715.37 B3 6 735.20 715.37 B3 :5 668.81 715.37 B3 •4 572.51 715.37 B4 12 853.41 715.37 B4 • 1 1 850.57 715.37 B4 10 845.57 715.37 B4 9 836.27 715.37 B4 8 826.31 715.37 B4 7 807.90 715.37 B4 .6 779.27 715.37 B4 :5 735.20 715.37 B4 •4 668.81 715.37 B4 .3 572.51 715.37 PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS B5 1 1 853.41 715.37 B5 10 850.57 715.37 B5 9 845.57 715.37 B5 8 836.27 715.37 B5 7 826.31 715.37 B5 6 807.90 715.37 B5 5 779.27 715.37 B5 4 735.20 715.37 B5 3 668.81 715.37 B5 2 572.51 715.37 B6 10 853.41 715.37 B6 •9 850.57 715.37 B6 •8 845.57 715.37 B6 7 836.27 715.37 B6 6 826.31 715.37 B6 5 807.90 715.37 B6 :4 779.27 715.37 B6 :3 735.20 715.37 B6 :2 668.81 715.37 B6 1 572.51 715.37 B7 9 853.41 715.37 B7 •8 850.36 715.37 B7 :7 845.57 715.37 B7 :6 836.27 715.37 B7 :5 826.31 715.37 B7 4 807.90 715.37 B7 3 779.27 715.37 B7 •2 735.20 715.37 B7 : 1 668.81 715.37 B8 :8 853.41 715.37 B8 il 850.36 715.37 B8 :6 845.57 715.37 B8 .5 836.27 715.37 B8 ;4 826.31 715.37 B8 :3 807.90 715.37 B8 :2 779.27 715.37 B8 : 1 735.20 715.37 B9 :7 853.41 715.37 B9 6 850.36 715.37 B9 .5 845.57 715.37 B9 4 836.27 715.37 B9 :3 826.31 715.37 B9 :2 807.90 715.37 B9 • 1 779.27 715.37 B1 0 6 853.41 715.37 B1 0 5 • 850.36 715.37 B1 0 4 845.57 715.37 B1 0 .3 836.27 715.37 B1 0 :2 826.31 715.37 B10 : 1 807.90 715.37 BI 1 •5 853.41 715.37 228 PERIOD OF ACTIVITY 1ST HARVEST 11 B1 1 4 •BI 1 3 B1 1 2 B1 1 1 1 2 B1 2: 4 BI 2' 3 B1 2 2 1 2 B1 2 1 1 3 B1 3 3 B1 3 .2 B1 3 : 1 1 4 BI 4 :2 B1 4 : 1 1 5 B1 5 1 YIELDS (M**3/HA) ST HARVEST SUBSEQUENT HARVESTS 850.36 715.37 845.57 715.37 836.27 715.37 826.31 715.37 853.41 715.37 850.36 715.37 845.57 715.37 836.27 715.37 853.41 715.37 850.36 715.37 845.57 715.37 853.41 715.37 850.36 715.37 853.41 715.37 Opt ion C - N a t u r a l Regenera t ion PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS CI . 1 2 836.27 587.88 C1 1 1 826.31 587.88 C1 10 807.90 587.88 CI 9 779.27 587.88 C1 :8 735.20 587.88 CI :7 668.81 587.88 CI :6 572.51 587.88 C2 12 845.57 587.88 C2 . 1 1 836.27 587.88 C2 •10 826.31 587.88 C2 •9 807.90 587.88 C2 .8 779.27 587.88 C2 .7 735.20 587.88 C2 :6 668.81 587.88 C2 .5 572.51 587.88 C3 : 1 2 850.57 587.88 C3 1 1 845.57 587.88 C3 10 836.27 587.88 C3 9 826.31 587.88 C3 8 807.90 587.88 C3 7 779.27 587.88 C3 6 735.20 587.88 C3 :5 668.81 587.88 C3 :4 572.51 587.88 C4 : 1 2 853.41 587.88 C4 1 1 850.57 587.88 C4 •10 845.57 587.88 PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS C4:9 836.27 587.88 C4:8 826.31 587.88 C4:7 807.90 587.88 C4:6 779.27 587.88 C4:5 735.20 587.88 C4:4 668.81 587.88 C4:3 572.51 587.88 C5:11 853.41 587.88 C5:1 0 850.57 587.88 C5:9 845.57 587.88 C5:8 836.27 587.88 C5:7 826.31 587.88 C5:6 807.90 587.88 C5:5 779.27 587.88 C5:4 735.20 587.88 C5:3 668.81 587.88 C5:2 572.51 587.88 C6: 10 853.41 587.88 C6:9 850.57 587.88 C6:8 845.57 587.88 C6:7 836.27 587.88 C6:6 826.31 587.88 C6:5 807.90 587.88 C6:4 779.27 587.88 C6:3 735.20 587.88 C6:2 668.81 587.88 C6: 1 572.51 587.88 C7:9 853.41 587.88 C7:8 850.36 587.88 C7:7 845.57 587.88 C7:6 836.27 587.88 C7:5 826.31 587.88 C7:4 807.90 587.88 C7:3 779.27 587.88 C7:2 735.20 587.88 C7 : 1 668.81 587.88 C8:8 853.41 587.88 C8:7 850.36 587.88 C8:6 845.57 587.88 C8:5 836.27 587.88 C8:4 826.31 587.88 C8:3 807.90 587.88 C8:2 779.27 587.88 C8:1 735.20 587.88 C9:7 853.41 587.88 C9:6 850.36 587.88 C9:5 845.57 587.88 C9:4 836.27 587.88 C9:3 826.31 587.88 C9:2 807.90 587.88 C9:1 779.27 587.88 PERIOD OF ACTIVITY YIELDS (M**3/HA) 1ST HARVEST 1ST HARVEST SUBSEQUENT HARVESTS 10 Cl 0:6 853.41 587.88 C10:5 850.36 587.88 C10:4 845.57 587.88 C1 0:3 836.27 587.88 C10:2 826.31 587.88 C1 0:1 807.90 587.88 11 Cl 1 s 5 853.41 587.88 Cl 1 :4 850.36 587.88 C1 1 :3 845.57 587.88 C1 1 : 2 836.27 587.88 C1 1 :1 826.31 587.88 1 2 C12:4 853.41 587.88 C12:3 850.36 587.88 Cl 2:2 845.57 587.88 1 2 Cl 2: 1 836.27 587.88 1 3 C13:3 853.41 587.88 C13:2 850.36 587.88 Cl 3:1 845.57 587.88 1 4 Cl 4:2 853.41 587.88 Cl 4: 1 850.36 587.88 15 C1 5: 1 853.41 587.88 231 APPENDIX II YIELDS AND SUBJECTIVE PROBABILITIES ASSOCIATED WITH THE VARIOUS OUTCOMES CONSIDERED FOR EACH MANAGEMENT OPTION Note : A l l y i e l d s are from the MOF (1982b) v a r i a b l e d e n s i t y y i e l d t a b l e s fo r C o a s t a l D o u g l a s - f i r and assume a SI of 30 m and a d iameter l i m i t of 17.5 cm. MANAGEMENT OPTION A - P l a n t i n g 'No rma l ' Stock YIELDS FOR POTENTIAL OUTCOMES AGE. - CONDITION 60% CC 75% CC 90% CC PROB=.10 PROB=.50 PROB=.40 10 • .72 .89 1 .07 20 22.46 27.77 32.90 30 100.39" 123.69 1 45.66 40 219.60 270.36 317.62 50 340.99 420.37 493.91 60 440.51 544.37 640.69 70 512.68 635.37 749.65 80 561.32 697.72 825.51 90 592.64 738.77 876.55 100 612.17 765.14 910.29 AGGREGATE * (EXPECTED) YIELD TABLE AGE VOLUME PER HA MAI (M**3) (M** 3/HA/YEAR) 10 .94 .09 20 29.29 1 .46 30 130.15 4. 34 40 284.19 7.10 50 441.85 8.84 60 572.51 9.54 70 668.81 9.55 80 735.20 9.19 90 779.27 8.66 100 807.90 8.08 * NOTE: Expected y i e l d f o l l o w i n g t h i s o p t i o n i s the same as the y i e l d assumed fo r the s t a n d i n g t i m b e r . 232 MANAGEMENT OPTION B - P l a n t i n g ' Improved ' Stock YIELDS FOR POTENTIAL OUTCOMES AGE CONDITION 75% CC 90% CC PROB=.30 PROB=.70 10 .89 1 .07 20 27.77 32.90 30 123.69 145.66 40 270.36 317.62 50 420.37 493.91 60 544.37 640.69 70 635.37 749.65 80 697.72 825.51 90 738.77 876.55 100 765.14 910.29 AGGREGATE (EXPECTED) YIELD TABLE AGE VOLUME PER HA MAI (M**3) (M* * 3/HA/YEAR) 1 0 1 .02 .10 20 - 31.36 1 .57 30 139.07 4.64 40 303.44 7.59 50 471.85 9.44 60 611.79 10.20 70 715.37 10.22 80 787.17 9.84 90 835.22 9.28 100 866.74 8.67 233 MANAGEMENT OPTION C - N a t u r a l Regenera t ion YIELDS FOR POTENTIAL OUTCOMES AGE CONDITION 60% CC 75% CC 90% CC NO 10 YR NO 10 YR NO 10 YR DELAY DELAY DELAY DELAY DELAY DELAY P=.125 P=.125 P=.250 P=.250 P=. 125 P=.125 10 . .72 .89 1 .07 20 22.46 .72 27.77 .89 32.90 1 .07 30 100.39 22.46 123.69 27.77 145.66 32.90 40 219.60 100.39 270.36 123.69 317.62 1 45.66 50 340.99 219.60 420.37 270.36 493.91 317.62 60 440.51 340.99 544.37 420.37 640.69 493.91 70 512.68 440.51 635.37 544.37 749.65 640.69 80 561.32 512.68 697.72 635.37 825.51 749.65 90 592.64 561.32 738.77 697.72 876.55 825.51 1 00 612.17 592.64 765.14 738.77 910.29 876.55 AGGREGATE (EXPECTED) YIELD TABLE AGE VOLUME PER HA MAI (M**3) (M**3/HA/YEAR) 10 .45 .04 20 14.31 .72 30 75.54 2.52 40 196.42 4.91 50 344.20 6.88 60 480.70 8 .01 . 70 587.88 8.40 80 664.42 8.31 90 716.12 7.96 100 749.93 7.50 234 APPENDIX III INDIRECT COSTS FOR THE DIFFERENT MANAGEMENT OPTIONS BY PERIOD OF INITIAL HARVEST A) Cost of a 1 m**3/ha/year d e v i a t i o n from expec ted average growth ra te = $10.00 Bene f i t of a 1 m**3/ha/year d e v i a t i o n from expected average growth ra te = $5.00 Cor respond ing S e r i e s Cos ts (Present va lue to time of i n i t i a l h a r v e s t ) : PNS: $77.45 PIS: $56.85 NR: $92.42 PERIOD OF INITIAL HARVEST PNS 1 66.07 2 49. 1 6 3 36.58 4 27.22 5 20.25 6 15.07 7 11.21 8 8.34 9 6.21 1 0 4.62 1 1 3 . 44 12 2.56 1 3 1 .90 1 4 1 .42 1 5 1 .05 INDIRECT COSTS (DOLLARS) PIS NR 48.49 78.84 36.08 58.66 26.85 43.65 1 9.98 32.48 1 4.87 24.17 1 1 .06 17.98 8.23 13.38 6.12 9.96 4.56 7.41 3.39 5.51 2.52 4.10 1 .88 3.05 1 .40 2.27 1 . 04 1 .69 .77 1 .26 235 B) Cost of a 1 m**3/ha/year d e v i a t i o n from expected average ; growth ra te = $20.00 B e n e f i t of a 1 m**3/ha/year d e v i a t i o n from expected average growth ra te = $5.00 Cor respond ing S e r i e s Cos ts (Present va lue to t ime of i n i t i a l h a r v e s t ) : PNS: $231.37 PIS: $170.20 NR: $276.58 PERIOD OF INITIAL HARVEST PNS 1 198.21 2 147.48 3 109.74 4 81 .66 5 60.75 6 45.21 7 33.63 8 25.02 9 18.63 1 0 13.86 1 1 10.32 12 7.68 13 5.70 1 4 4.26 1 5 3.15 INDIRECT COSTS (DOLLARS) PIS NR 145.47 236.52 108.24 175.98 80.55 130.95 59.94 97.44 44.61' 72.51 33. 18 53.94 24.69 40.41 18.36 29.88 1 3.68 22.23 10.17 16.53 7.56 1 2.30 5.64 9.15 4.20 6.81 3.12 5.07 2.31 3.78 APPENDIX IV A LISTING OF THE TOTAL COSTS ASSOCIATED WITH THE VARIOUS  MANAGEMENT OPTIONS BY PERIOD OF INITIAL HARVEST FOR THE DIFFERENT COST SCENARIOS A) TOTAL COSTS FOR SCENARIOS (1) AND (4) PERIOD OF TOTAL COSTS INITIAL HARVEST (DOLLARS) PNS PIS NR 1 1242.31 1461.54 0.00 2 924.90 1087.53 0.00 3 687.84 809.23 0.00 4 511.82 602.14 0.00 5 384.84 448.05 0.00 6 283.38 339.39 0.00 7 207.92 244.61 0.00 8 154.71 182.01 0.00 9 115.12 135.44 0.00 10 85.66 100.78 0.00 11 63.74 74.99 0.00 12 47.43 55.80 0.00 13 35.29 41.52 0.00 14 23.32 27.43 0.00 15 17.35 20.41 0.00 B) TOTAL COSTS FOR SCENARIOS (2) AND (5) PERIOD OF TOTAL COSTS INITIAL HARVEST (DOLLARS) PNS PIS NR 1 1308.38 1510.03 78.84 2 974.06 1123.61 58.66 3 724.42 835.68 43.65 4 539.04 622.12 32.48 5 405.09 462.92 24. 17 6 298.45 350.45 17.98 7 219.13 252.84 13.38 8 163.05 188.13 9.96 9 121.33 140.00 7.41 10 90.28 104.17 5.51 1 1 67. 18 77.51 4.10 12 49.99 57.68 3.05 13 37. 19 42.92 2.27 1 4 24.74 28.47 1 .69 15 18.40 21.18 1 .26 C) TOTAL COSTS FOR SCENARIOS (3) AND (7) PERIOD OF TOTAL COSTS INITIAL HARVEST (DOLLARS) PNS PIS NR 1 66.07 48.49 78.84 2 49. 1 6 36.08 58.66 3 36.58 26.45 43.65 4 27.22 19.98 32.48 5 20.25 14.87 24. 17 6 1 5.07 1 1 .06 17.98 7 11.21 8.23 13.38 8 8.34 6.12 9.96 9 6.21 4.56 7.41 10 4.62 3.39 5.51 1 1 3.44 2.52 4.10 1 2 2.56 1 .88 3.05 13 1 .90 1 .40 2.27 14 1 .42 1 .04 1 .69 1 5 1 .05 .77 1 .26 D) TOTAL COSTS FOR SCENARIO (6) PERIOD OF TOTAL COSTS INITIAL HARVEST (DOLLARS) PNS PIS NR 1 1440.52 1607.01 236.52 2 1072.38 1195.80 1 75.98 3 797.58 888.68 130.95 4 . 593.48 662.08 97.44 5 445.59 492.66 72.51 6 328.59 372.57 53.94 7 241.55 269.30 40.41 8 179.73 200.37 29.88 9 133.75 149.12 22.23 10 99.52 110.95 16.53 1 1 74.06 82.55 . 12.30 12 55. 1 1 61.44 9.15 1 3 40.99 45.72 6.81 14 27.58 30.55 5.07 1 5 20.50 22.72 3.78 

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