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An application of linear programming to log allocation in the forest industry of British Columbia Sydneysmith, Sam 1964

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AN A P P L I C A T I O N OF LINEAR PROGRAMMING TO LOG ALLOCATION IN THE FOREST INDUSTRY OF B R I T I S H COLUMBIA by Sam S y d n e y s m i t h B.A.Sc,  The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1956  A THESIS SUBMITTED I N PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF Master of Arts i n t h e Department of Economics  We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e required  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA April,  1964  OF  In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of • B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study*  I further agree that per-  mission f o r extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives.  I t i s understood that, copying or p u b l i -  cation of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission^.  S. Sydneysmith. Department of  ranpftMIC-fi  The University of B r i t i s h Columbia, Vancouver 8, Canada D a  *  e  A p r i l 24th. 1964.  —  ii  ABSTRACT T h i s t h e s i s p r e s e n t s an a p p l i c a t i o n o f l i n e a r programming t o t h e q u e s t i o n of e f f i c i e n t l o g a l l o c a t i o n i n t h e f o r e s t i n d u s t r y o f B r i t i s h Columbia.  Current procedures f o r  a l l o c a t i n g l o g s among a l t e r n a t i v e u t i l i z a t i o n p r o c e s s e s a r e d i s c u s s e d and i t i s suggested  t h a t a more e f f i c i e n t  allocation  m i g h t be o b t a i n e d through a s y s t e m a t i c approach t o t h e p r o blem.  The economic n e c e s s i t y o f i m p r o v i n g  net returns t o  the l o g s u p p l y i s emphasized. A l i n e a r programme l o g - a l l o c a t i o n model i s p r e s e n t e d , based on an i n t e g r a t e d - i n d u s t r y i n t h e c o a s t a l r e g i o n o f B r i t i s h Columbia.. The model encompasses t h r e e main c a t e g o r i e s o f l o g - u s e , namely s a w m i l l i n g , plywood p r o d u c t i o n and p u l p p r o d u c t i o n , and demonstrates how a g i v e n s u p p l y o f l o g s may be o p t i m a l l y d i s t r i b u t e d among these s t r u c t u r a l l y ferent log-conversion  dif-  processes.  Emphasis throughout t h i s s t u d y i s on the s t r u c t u r e of the l i n e a r programme model, a l t h o u g h c o n s i d e r a b l e e f f o r t was d i r e c t e d to obtaining r e a l i s t i c data.  S o l u t i o n s of the  model, o b t a i n e d t h r o u g h t h e s e r v i c e s o f t h e Computing Cent r e a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , a r e d i s c u s s e d , and a s u p e r f i c i a l comparison i s made w i t h a c t u a l l o g a l l o c a t i o n i n the i n d u s t r y .  M o d i f i c a t i o n s o f t h e model t o s u i t  the l o g - a l l o c a t i o n problem f a c e d by an i n d i v i d u a l f i r m i n the s h o r t - r u n a r e d i s c u s s e d and normal c o m p a r a t i v e - s t a t i c s a p p l i c a t i o n s are considered.  iii It tions  i s p o i n t e d o u t t h a t many o f t h e s i m p l i f y i n g  i n t h e m o d e l may  be r e l a x e d .  However, the main  l i m i t a t i o n t o i t s p r a c t i c a l a p p l i c a t i o n by i n d u s t r y government l i e s  i n t h e q u a l i t y and t y p e o f d a t a  I n t h i s respect i t i s suggested t h a t model of t h i s t h e s i s duction data required the  forest  industry.  assump-  and  available.  t h e l i n e a r programme  provides a v a l u a b l e guide t o the prot o improve economic e f f i c i e n c y i n  iv  ACKNOWLEDGEMENTS  The encouragement and a d v i c e o f Dr. P.H.Pearse, as d i r e c t o r o f t h i s s t u d y , and Dr. G.Rosenbluth, as m e t h o d o l o g i c a l c o n s u l t a n t , i s g r a t e f u l l y acknowledged. I n a d d i t i o n , t h e a u t h o r wishes t o thank a l l o f those p e r s o n s who s u p p l i e d d a t a and t e c h n i c a l  knowledge  on t h e v a r i o u s phases o f t h e f o r e s t i n d u s t r y i n B r i t i s h Columbia.  V  TABLE OF CONTENTS Page L i s t o f Tables  .  v i i  L i s t of Figures CHAPTER I :  viii INTRODUCTION  1  I.  L o g - A l l o c a t i o n i n the Forest Industry  2  Scope o f t h e S t u d y  6  II. CHAPTER I I :  THE CASE FOR IMPROVED LOG ALLOCATION . . .  12  I.  12  II. III. IV.  The Nature o f t h e F o r e s t I n d u s t r y  . .  Problems o f t h e I n d u s t r y  16  I n d u s t r y Trends  21  Conclusions  26  CHAPTER I I I :  EXPOSITION OF THE LOG-ALLOCATION PROBLEM .  CHAPTER  CONSTRUCTION OF A LOG-ALLOCATION LINEAR  IV:  PROGRAMME MODEL I. II. III. CHAPTER V:  28  3^  B a s i c O u t l i n e o f t h e Model  34-  S t r u c t u r e o f t h e Model  36  Assumptions o f t h e Model  4-4-  DATA AND SOLUTION OF THE MODEL  4-9  r.  4-9  II. 111.  Activity Coefficients U n i t - L e v e l R e t u r n s o f the A c t i v i t i e s  60  Restraints  66  vi Page IV. V.  CHAPTER V I :  S o l u t i o n s of t h e L i n e a r Programme  . .  72  Appendix t o Chapter F i v e  74  RESULTS AND DISCUSSION  38  I. II.  CHAPTER V I I :  67  Method o f S o l u t i o n  Results  88  A p p l i c a t i o n s o f the Model  95  Appendix t o Chapter S i x  104  SUMMARY AND CONCLUSION  109  vii  LIST OF TABLES  gage The Value of F o r e s t P r o d u c t i o n i n B r i t i s h Columbia by I n d u s t r i a l C a t e g o r i e s i n S e l e c t e d Years  14  The Log Supply i n the C o a s t a l Region of Columbia, 1962 .  74  British  Log Sawing A c t i v i t y T e c h n o l o g i c a l C o e f f i c i e n t s  . . .  75  Log P e e l i n g A c t i v i t y T e c h n o l o g i c a l C o e f f i c i e n t s . . .  76  Plywood P r o d u c t i o n A c t i v i t y C o e f f i c i e n t s  77  Pulp P r o d u c t i o n A c t i v i t y C o e f f i c i e n t s  ',78  Plywood Manufacturing Costs as Percent of S a l e s Price  79  Plywood P r o d u c t i o n A c t i v i t y U n i t - L e v e l Returns  . . .  80  Pulp P r o d u c t i o n A c t i v i t y U n i t - L e v e l Returns  81  Log S e l l i n g A c t i v i t y U n i t - L e v e l Returns .  82  Lumber S e l l i n g A c t i v i t y U n i t - L e v e l R e t i r n s  . . . .  .83  Veneer S e l l i n g A c t i v i t y U n i t - L e v e l Returns  84  Pulp Chip S e l l i n g A c t i v i t y U n i t - L e v e l Returns . . . .  85  M o d i f i e d C o e f f i c i e n t s of A c t i v i t y No. 9 ; f o r Case II  86  Volume of Log Supply by S p e c i e s and Grade . . . . . . 87 T o t a l Net R e t u r n s , i n Lumber, Plywood, and Pulp Production 104 Optimum Log A l l o c a t i o n  105  Lumber S a l e s by Species and Grade . . . . . . . . . Plywood and Veneer S a l e s Pulp S a l e s  . ,  .106 107 108  viii  L I S T OF FIGURES  Figure I  Schematic P r e s e n t a t i o n  o f Log A l l o c a t i o n  L i n e a r Programme M o d e l . (attached inside rear  cover)  CHAPTER I INTRODUCTION The  f o r e s t resource  of B r i t i s h Columbia i s pre-  dominately owned by the Crown, but  exploited entirely  private enterprise.  ' e f f i c i e n c y of  A question  of  a l l o c a t i o n ' a r i s e s t h e r e f o r e at two  levels:  by  resource  at the f o r e s t  management l e v e l which i s i n the hands of the P r o v i n c i a l Government, and  at the e n t r e p r e n e u r i a l or p r i v a t e l e v e l  f i r m s consuming timber as a raw f o r optimal  resource  material.  The  conditions  a l l o c a t i o n at each l e v e l d i f f e r ,  give r i s e to d i f f e r e n t maximizing  and  criteria.  As owner of most of the f o r e s t resource  the  Pro-  v i n c i a l Government c o n t r o l s the a l l o c a t i o n of timber to f o r e s t industry.' ' 1  To e f f i c i e n t l y d i s c h a r g e  i t must be guided by the  of  this  the  function  s o c i a l aspects of resource  ex-  p l o i t a t i o n as w e l l as by the demands of the p r i v a t e f o r e s t i n d u s t r y , f o r the u l t i m a t e  o b j e c t i v e of resource  ment i s to maximize the value The  of the resource  to society.  e f f i c i e n t owner i s concerned t h e r e f o r e w i t h  i n g f u t u r e b e n e f i t s and resource,  and  manage-  estimat-  c o s t s a s s o c i a t e d w i t h the f o r e s t  with e s t a b l i s h i n g time r a t e s of preference  be a p p l i e d i n d i s c o u n t i n g  these f u t u r e b e n e f i t s t o  to  present  1 The term ' f o r e s t i n d u s t r y ' as used i n t h i s t h e s i s r e f e r s c o l l e c t i v e l y to the p r i v a t e f i r m s engaged i n e x t r a c t i o n and p r o c e s s i n g of l o g s . Government a d m i n i s t r a t i o n of the f o r e s t s i s t h e r e f o r e not considered a p a r t of the f o r e s t i n d u s t r y .  2  values.  On the s t r e n g t h of these e v a l u a t i o n s the owner i s  a b l e t o develop s u i t a b l e forest-management p o l i c i e s t o guide p r i v a t e i n d u s t r y i n i t s e x p l o i t a t i o n o f t h e r e s o u r c e . At t h e i n d u s t r y l e v e l e f f i c i e n t r e s o u r c e  allocation  r e s u l t s from t h e p r o f i t - m a x i m i z i n g b e h a v i o u r o f each p r i vate f i r m .  The s u p p l y o f t i m b e r  t o each f i r m i s one o f  s e v e r a l i n p u t f a c t o r s w h i c h i t seeks t o a l l o c a t e i n a manner t h a t y i e l d s i t a maximum o v e r - a l l n e t r e t u r n . a l l o c a t i o n of timber  Efficient  i n the f o r e s t i n d u s t r y as a whole  t h e r e f o r e depends upon t h e aggregate p r o f i t - m a x i m i z i n g behaviour  o f a l l f i r m s i n t h e i n d u s t r y , each one o p t i m i z i n g  i t s own p r o d u c t i o n f u n c t i o n .  The problem i s removed from  any w e l f a r e i m p l i c a t i o n s o t h e r t h a n those imposed by the government. T h i s t h e s i s c o n s i d e r s the e f f i c i e n c y of l o g a l l o c a t i o n a t t h e second o f these two l e v e l s , namely, a t the l e v e l o f i n d u s t r i a l u s e . The main o b j e c t i v e i s t o p r e s e n t a systematic mal  approach t o t h e problem of a t t a i n i n g an o p t i -  a l l o c a t i o n o f l o g s among v a r i o u s u t i l i z a t i o n  processes,  such t h a t t h e r e t u r n t o a g i v e n s u p p l y o f l o g s i s maximized. I t w i l l be u s e f u l t h e r e f o r e t o e l a b o r a t e upon c u r r e n t l o g a l l o c a t i o n p r o c e d u r e s i n the i n d u s t r y , b e f o r e c o n s i d e r i n g the l o g - a l l o c a t i o n problem f a c e d by i n d i v i d u a l f i r m s . 1.  LOG ALLOCATION IN THE FOREST INDUSTRY  Two forms o f l o g a l l o c a t i o n i n the f o r e s t i n d u s t r y may be d i s t i n g u i s h e d . competitive  firms.  F i r s t , a l l o c a t i o n o f l o g s among  Second, a l l o c a t i o n o f l o g s w i t h i n each  3 f i r m , between i t s v a r i o u s Log  A l l o c a t i o n Among  alternative utilization  processes.  Firms.  This problem i s solved  ( t h e o r e t i c a l l y ) through the  open market f o r l o g s , where p r i c e s a r e e s t a b l i s h e d by t h e usual  forces  of supply  a n d demand a n d t h e p r i c e s y s t e m r a -  t i o n s the a v a i l a b l e supply market.  to competitive  firms  i n the  Not a l l o f the timber i n the c o a s t a l r e g i o n  through t h e open-log market, but p r i c e s e s t a b l i s h e d are used as a basis transactions.  f o r c o m p l e t i n g most " c l o s e d "  I n theory  t h e p r i c e system should  goes there  market result i n  maximum e c o n o m i c e f f i c i e n c y i n l o g a l l o c a t i o n f o r t h e e c o n omy a s a w h o l e , p r o v i d i n g t h a t p e r f e c t c o m p e t i t i o n  exists  t h r o u g h o u t (many b u y e r s , many s e l l e r s , homogeneous p r o d u c t , f r e e e x i t and e n t r y  of firms, etc.).  In practice i ti s questionable  whether the market i s  2 a c t u a l l y "open and c o m p e t i t i v e " .  F o r example, i n the  c a s e o f i n t e g r a t e d f i r m s w h i c h h a v e t h e i r own l o g g i n g a t i o n s i t m i g h t be a r g u e d t h a t " i n t e r n a l "  oper-  l o g transactions  o c c u r r i n g w i t h i n t h e f i r m a r e n o t a p a r t o f t h e o p e n market.  I n a d d i t i o n there  i s an element o f d i r e c t p r i c e  dis-  t o r t i o n a r i s i n g from an i n t e r p l a y between t h e open-log market and t h e market f o r c h i p s  and small-wood  residues.  2 "The c o n d i t i o n a n d o p e r a t i o n o f t h e o p e n - l o g m a r k e t and c h i p a n d s m a l l - w o o d m a r k e t i n g i n t h e "Vancouver F o r e s t D i s t r i c t " , R e p o r t t o t h e S e l e c t S t a n d i n g Committee o f F o r e s t r y o f the L e g i s l a t i v e Assembly of B r i t i s h Columbia. B. C. F o r e s t S e r v i c e , V i c t o r i a , ( J a n . 1962) - s u p p l i e d i n confidence t o the author.  1+  At  the p r e s e n t time the  p a i d under c o n t r a c t  i n d u s t r y a c c e p t s t h a t the  f o r wood c h i p s  t o t h e p r i c e e s t a b l i s h e d on  c a n he  price  related  directly  the Vancouver l o g market f o r 3  number t h r e e  g r a d e h e m l o c k , and  vice versa.  Any  firm in  a p o s i t i o n to c o n t r o l p r i c e s i n e i t h e r of these markets therefore other  could  given  short run, with given u t i l i z a t i o n  l o g s u p p l i e s f o r each f i r m , the  w i t h the  optimal  a l l o c a t i o n p l a n f o r the  Such m i s a l l o c a t i o n r e f l e c t s imperfections  capacities  aggregate a l l o c a t i o n  o f l o g s t o d i f f e r e n t u t i l i z a t i o n p r o c e s s e s may  cation  the  market. I n the  and  quite f e a s i b l y manipulate p r i c e s i n  not  coincide  i n d u s t r y as a w h o l e . i n the  log-allo-  system.  k Log  Allocation Within The  Integrated  integrated forest products f i r m i s usually  fronted with a given  o r known l o g s u p p l y  a l l o c a t e among i t s v a r i o u s t h a t maximizes t o t a l net  seeking  an  conversion  r e t u r n to the  m a x i m i z i n g b e h a v i o u r of the volves  Firms. con-  which i t seeks  to  p r o c e s s e s i n a manner enterprise.  Profit-  integrated firm therefore i n -  optimum a l l o c a t i o n o f i t s l o g s u p p l y .  The  3 "The c o n d i t i o n and o p e r a t i o n o f t h e o p e n - l o g m a r k e t and c h i p and s m a l l - w o o d m a r k e t i n g i n t h e V a n c o u v e r F o r e s t D i s t r i c t " , R e p o r t t o the S e l e c t S t a n d i n g Committee of F o r e s t r y o f t h e L e g i s l a t i v e A s s e m b l y o f B r i t i s h C o l u m b i a . B. C. F o r e s t S e r v i c e , V i c t o r i a , ( J a n . 1962) - supplied i n confidence t o the a u t h o r . k I n t h i s t h e s i s a l l r e f e r e n c e s t o t h e f i r m w i l l assume an i n t e g r a t e d f o r e s t - p r o d u c t s e n t e r p r i s e . Most of the d i s c u s s i o n however i s e q u a l l y a p p l i c a b l e t o s m a l l e r f i r m s s p e c i a l i z i n g i n a s i n g l e u t i l i z a t i o n p r o c e s s , such as sawmilling.  5 given  l o g supply  holdings by  i s u s u a l l y d e t e r m i n e d by t h e f i r m ' s  of timber-cutting  trading or purchasing  Current  own  r i g h t s , b u t i t may be augmented  l o g s on t h e open m a r k e t .  Procedures. The  a l l o c a t i o n o f l o g s among v a r i o u s  conversion  pro-  cesses i n an i n t e g r a t e d f o r e s t products e n t e r p r i s e i s p r e s e n t l y a haphazard p r o c e d u r e c o n d u c t e d m o s t l y by " r u l e s o f thumb".  Each i n t e g r a t e d f i r m g e n e r a l l y has a c e n t r a l -  ized co-ordinator  responsible  on a b a s i s o f e x p e r i e n c e , for  assessing  t h i s respect  s p e c i a l k n o w l e d g e , and a t a l e n t  t h e l o g demand s u b m i t t e d b y e a c h m i l l . the c e n t r a l l o g supply  a co-ordination is difficult  forcontrolling log allocation  t o c o n c e i v e o f any h i g h degree o f economic e f -  and  r e q u i r i n g d e c i s i o n s based on e x p e r i e n c e  i n d i v i d u a l 'judgement.  systematic  approach.  i s t r u e t h a t m a r k e t s i t u a t i o n s may c h a n g e r a p i d -  l y and u n p r e d i c t a b l y , and  performs  r a t h e r t h a n a n a l l o c a t i o n f u n c t i o n , and i t  f i c i e n c y r e s u l t i n g from the former It  control office  In  and r i g o r o u s  Nevertheless,  the lack of a  a n a l y s i s o f normal l o g requirements,  t h e absence o f a t e c h n i q u e f o r q u i c k l y determining  most e f f i c i e n t  (profit-maximizing)  the  a l l o c a t i o n of logs, a l -  most c e r t a i n l y r e s u l t s i n a h i g h , a n d u n n e c e s s a r y , d e g r e e of  inefficiency. Some i m p o r t a n t o b s t a c l e s  t o developing  an e f f e c t i v e  l o g - a l l o c a t i o n procedure are the l a c k of s u f f i c i e n t cific  d a t a o n l o g y i e l d s and p r o d u c t i o n  complexity  of the c a l c u l a t i o n s involved  spe-  c o s t s , and t h e e v e n when t h e  6  required data are a v a i l a b l e . It may be argued that the industry has hitherto lacked an incentive to develop e f f i c i e n t l o g - a l l o c a t i o n procedures, f o r p r o f i t s have been high and exploitation characterized by an "extensive" use of a r e l a t i v e l y cheap and ubiquitous resource.  I t w i l l be pointed out below though that these  conditions are changing r a p i d l y and that trends i n the value of the resource are already such that e f f i c i e n c y i n a l l o cating timber among alternate uses demands a more systema t i c and rigorous approach.  The development of such an  approach comprises the subject of this study. II.  SCOPE OF THE STUDY  This study examines the problem of e f f i c i e n t a l l o cation of logs i n the forest industry.  S p e c i f i c a l l y , the  purpose i s to develop a solution technique f o r a r r i v i n g at the optimal a l l o c a t i o n plan for a given supply of logs. The form of the problem therefore i s similar to that faced by an integrated forest products enterprise i n a l l o c a t i n g i t s logs among alternative u t i l i z a t i o n plants. The l o g - a l l o c a t i o n problem lends i t s e l f to mathemati c a l solution by linear programming techniques.  Thus we  s h a l l discuss the elements of "choice", "optimization", and " r e s t r a i n t " , and t h e i r mathematical analogues i n a l i n e a r programme model of the a l l o c a t i o n problem, before proceeding to a solution and discussion of p r a c t i c a l applications. The emphasis throughout i s on the structure of the model.  Although considerable e f f o r t has been devoted to  7 seeking poses of  out  of  the  the  most  analysis,  statistical  insufficient  ysis.  In these  broad  a useful  lines to  made  (as  noted  of the  the  for  the  i n a form poorly  have been made.  insight  available  Frequently  instances  and a s s u m p t i o n s the  or  data  no c l a i m i s  accuracy.  been  that  accurate  for  a high  data  for  efficiency  achieved of  the  degree  the  has  anal-  extrapolations  Nevertheless,  results  pur-  available  suited  below),  the  it  is  will  hoped  provide  log-allocation  process. Thus, rigorous ate  while  the  primary objective  methodological  empirical data  are  approach  on the  numerical results.  nature  of  technical  for  the  and economic  programming i s  planning  a complex  of  possible  (optimal)  fashion."  the  depends e n t i r e l y  present  a  p r o b l e m , more much r e l i a n c e  study data  points  that  solution  are  accurcan  out  be  the  required  developed.  concerned  interdependent The  upon the  w i t h the  activities  v a l i d i t y of  quality  of  data  problem  of  i n the  best  results  how-  supplied  to  problem. Three  task  the  to  Analysis.  "Linear  ever  The  p r a c t i c a l a p p l i c a t i o n of  Framework of  the  required before  placed  the  to  is  of  different  assembling  data  approaches for  the  were  considered  proposed model;  to  these  the were  5 A . C h a r n e s , W. W. C o o p e r a n d A . H e n d e r s o n , A n I n t r o d u c t i o n to L i n e a r Programming, W i l e y & Sons I n c . , N . Y . , c h .  1.  8  to base the model on either, (i)  imaginary data,  (ii)  case-study data,  (iii)  industry-average data.  The f i r s t alternative was discarded on grounds that i t would convey l i t t l e of the p r a c t i c a l significance of a l i n e a r programme approach to log a l l o c a t i o n , and would be of limited interest to those concerned with industry problems. data.  Nor would i t specify the shortcomings of existing I t would be l i t t l e more than an exercise  i n linear  programming. The second alternative was discarded for two reasons. F i r s t l y , i t was considered u n l i k e l y that any firm would be prepared to supply s u f f i c i e n t l y detailed data, much of which would probably be regarded as c o n f i d e n t i a l .  Secondly, a  case study would inevitably r e f l e c t special c h a r a c t e r i s t i c s of the case-study firm. The t h i r d alternative was  selected  since i t would  avoid most of the above objections and would be of p r a c t i cal  interest to both government and industry.  Although the  purpose of t h i s study i s mainly to demonstrate the a p p l i cation of l i n e a r programming to log a l l o c a t i o n i t was considered  important to keep the demonstration as r e a l i s t i c and  as general as possible.  I t w i l l be shown l a t e r how both  government and industry might modify the "industry-wide" model to analyze t h e i r own special problems.  9 I n c o n j u n c t i o n w i t h the d e c i s i o n t o use average data  i t was  decided  t o b a s e t h e m o d e l on t h e  o f an " i n t e g r a t e d - i n d u s t r y " . t r e a t a l l the t i m b e r - u s i n g  industry-  The  concept  g e n e r a l a p p r o a c h was  industries i n a given  log-market  a r e a , d r a w i n g on a g i v e n s u p p l y o f l o g s , a s a s i n g l e p l e t e l y - i n t e g r a t e d e n t i t y w i t h i n which timber about without  cost to i t s place of highest  Having decided an  moved  value-in-use.  t o b a s e t h e l i n e a r programme m o d e l  mained t o s e l e c t an area  The  com-  c o u l d be  "integrated-industry" using industry-average  effectively  to  data  i n which these proposals  on  i t re-  could  be  implemented. a r e a c h o s e n was  t h a t p a r t of the B r i t i s h  f o r e s t i n d u s t r y w h i c h draws i t s s u p p l y o f l o g s f r o m C o l u m b i a F o r e s t S e r v i c e I n v e n t o r y Zone 1 and t o r y Zone 2.  I n v e n t o r y Zone 1 c o v e r s  l a n d and V a n c o u v e r I s l a n d , and  Columbia British  p a r t of  the lower  Inven-  c o a s t a l main-  the r e l e v a n t p a r t of  Inventory  Zone 2 c o m p r i s e s t h e c o a s t a l s e c t o r o f t h e P r i n c e R u p e r t Forest D i s t r i c t .  This area w i l l  c o l l e c t i v e l y as t h e G u t h r i e and cal "isolation"  h e n c e f o r t h be  referred to  "coastal region." Armstrong have u n d e r l i n e d t h e  geographi-  o f t h e c o a s t a l r e g i o n , b o u n d e d on t h e  east  by t h e C o a s t R a n g e , on t h e w e s t by t h e P a c i f i c O c e a n and  to  7 t h e n o r t h and  s o u t h by f r o n t i e r s w i t h t h e U n i t e d  States.  6 C o n t i n u o u s F o r e s t I n v e n t o r y o f B r i t i s h C o l u m b i a . B.C. D e p t . o f L a n d s & F o r e s t s , V i c t o r i a , B.C., (1958), T a b l e s A - I . 7  J . A. G u t h r i e , G. R. A r m s t r o n g , W e s t e r n F o r e s t I n d u s t r y An E c o n o m i c O u t l o o k , The J o h n H o p k i n s P r e s s , B a l t i m o r e ,  (1961), c h . l .  -  1 0  Rankin has pointed  out the low  c o s t of water t r a n s p o r t a t i o n o  f o r f o r e s t products w i t h i n the We  region.  can summarize the p r i n c i p a l reasons f o r s e l e c t -  i n g the c o a s t a l r e g i o n as our  study area t h e r e f o r e , as  fol-  lows: (i)  An i s o l a t e d economic u n i t . " i s o l a t i o n " and  The  geographic  h i g h m o b i l i t y of l o g s w i t h i n  the c o a s t a l r e g i o n make i t f r e e from any t e r n a l complications movements i n t o and The  such as s i g n i f i c a n t l o g  out of the  i n the r e g i o n i s concentrated  facilities  i n the G u l f  of  a r e a , i n t o which most of the c o a s t a l  l o g supply flows at low t i o n s of a completely are thus not (ii)  region.  major p o r t i o n of c o n v e r s i o n  Georgia  ex-  cost.  The  assump-  "integrated-industry"  unrealistic,  A c o n s i s t e n t l o g supply.  The  commercial tim-  ber of the c o a s t a l r e g i o n i s r e l a t i v e l y u n i form w i t h r e s p e c t t o s p e c i e s , s i z e and There are d e f i n i t e b i o l o g i c a l trends  grades.  within  the r e g i o n , such as a higher percentage of spruce i n the northern  s e c t o r , but these are  s u b s t a n t i a l l y o f f s e t by cheap t r a n s p o r t a t i o n 8 A. G. Rankin, " C o s t - P r i c e R e l a t i o n s h i p s i n the F o r e s t I n d u s t r y " , The F o r e s t r y C h r o n i c l e , v. 3 9 , (Mar. 1 9 6 3 PP.  6  9  -  7  9  .  )  ,  11 and Gulf (iii)  by t h e a c t i v e open market f o r l o g s i n t h e of Georgia,  A s i n g l e administrative area. the  timber resource i n t h i s  the  sole  Forest sult  jurisdiction  Service.  Management o f  region  i s under  of the B r i t i s h  This  Columbia  has the d e s i r a b l e r e -  ( f o r our p u r p o s e s ) o f u n i f o r m and  consistent data reporting. single authority reports B r i t i s h Columbia only, fluences  In addition  this  t o t h e government o f  so t h a t p o l i t i c a l i n -  o n management o f t h e f o r e s t s a r e  u n i f o r m and c o n s i s t e n t , (iv)  A s u b s t a n t i a l p o r t i o n of the industry. official  Latest  f i g u r e s f o r B r i t i s h C o l u m b i a show  t h a t i n 1962  approximately 5 8 percent of the  t o t a l l o g - s c a l e f o r B r i t i s h C o l u m b i a was r e corded i n the c o a s t a l r e g i o n . the  9  c o a s t a l region comprises a  Thus a l t h o u g h relatively  small p o r t i o n of the t o t a l area of B r i t i s h Columbia, i t accounts f o r a very p o r t i o n of the current  log-scale.  significant This  permits  t h e m o d e l t o b e e m p l o y e d w i t h more c o n f i d e n c e i n d e m o n s t r a t i n g t h e i m p l i c a t i o n s o f a change i n f o r e s t management p o l i c y on t h e f o r e s t industry's profits  and consumption  9 A n n u a l R e p o r t , B. C. F o r e s t (19627:  pattern.  Service, Victoria,  B.C.,  12  CHAPTER I I THE The  CASE FOR  IMPROVED LOG  main reasons f o r i n e f f i c i e n c y i n l o g a l l o c a t i o n  have a l r e a d y  been r e f e r r e d t o ; i n t h i s c h a p t e r the  improved l o g a l l o c a t i o n i n the It w i l l one  ALLOCATION  be  shown t h a t  industry w i l l  be  examined.  improvement i n l o g - a l l o c a t i o n o f f e r s  o f the most p r o m i s i n g avenues toward g r e a t e r  e f f i c i e n c y i n the We dustry  i n d u s t r y as a  coastal region.  The  by  the  most l i k e l y f u t u r e research  will  be  I.  THE  the  forest i n -  trends i n i n d u s t r i a l  h a v i o u r a i m e d a t o v e r c o m i n g some o f t h e c u l t i e s faced  economic  whole.  s h a l l b e g i n by b r i e f l y r e v i e w i n g  i n the  case f o r  industry w i l l  be  increasing  be-  diffi-  i n d i c a t e d , and  the  courses of t e c h n o l o g i c a l development  and  outlined. NATURE OF  THE  FOREST INDUSTRY  Size. The on  f o r e s t i n d u s t r y i n the  saw-timber p r o d u c t i o n ,  derived  from the  c o a s t a l r e g i o n was  which enjoyed a unique  coast.  and  e x p a n d i n g m a r k e t s i n C a n a d a and  ing  r a t e s of e x p l o i t a t i o n of the of the  advantage  p a r t i c u l a r l y large high-quality trees  grew i n a b u n d a n c e a l o n g t h e  s i v e use  founded  logs harvested.  e s t resource i n the  Technological  progress  abroad l e d to  increas-  f o r e s t s , and  t o a more i n t e n -  A t p r e s e n t most o f t h e  coastal region,  that  and  indeed  for-  throughout  B r i t i s h C o l u m b i a , i s u n d e r some f o r m o f f o r e s t management.  1 3  The i n d u s t r i e s w h i c h consume l o g s d i r e c t l y as a raw material are usually divided mills, and  i n t o three  p l y w o o d m i l l s , and p u l p m i l l s .  categories;  saw-  The r e l a t i v e  size  growth r a t e f o r each of these i n d u s t r i e s , f o r s e l e c t e d  y e a r s f r o m 1 9 5 4 t o 1 9 6 2 , i s shown i n T a b l e 2 . 1 on t h e f o l lowing  page.  I t i s apparent t h a t lumber p r o d u c t i o n  major i n d u s t r y i n terms of t o t a l value  of  i s the  production.  The s l o w p e r c a p i t a g r o w t h r a t e i n t h e l u m b e r t r y has b e e n d i s c u s s e d low  ly its  b y many w r i t e r s ' " ' " ' ' " ^ who n o t e t h e 1 1  l e v e l of research  industry.  indus-  2  1  and development e x p e n d i t u r e i n t h i s  I n a d d i t i o n , s u b s t i t u t e p r o d u c t s have u n d o u b t e d -  influenced  t h e demand f o r l u m b e r a d v e r s e l y ,  r a t e of growth.  and r e d u c e d  3 y c o n t r a s t , t h e p l y w o o d and p u l p  t r i e s have e x p e r i e n c e d  indus-  s u b s t a n t i a l growth over the past t e n  years. Much o f t h e g r o w t h i n p l y w o o d demand c a n be t r a c e d t o a more g e n e r a l materials ska as  trend  t o w a r d t h e u s e o f c o m p o n e n t s and s h e e t  t o reduce o n - s i t e labour  has s t r e s s e d  i n construction.  Zinuv-  the importance of c o n s t r u c t i o n labour  an e x t e r n a l i n f l u e n c e on plywood  demand.  costs  -I h.  1 1 J . A. Z i n u v s k a , "The F o r e s t P r o d u c t s M i x i n a C h a n g i n g Economy," P r o c e e d i n g s , S o c . o f A m e r i c a n F o r e s t e r s , ( I 9 6 0 ) , PP.  5  9  -  6  3  .  1 2 J o s e p h Z a r e m b a , E c o n o m i c s o f A m e r i c a n Lumber I n d u s t r y , R o b e r t S p e l l e r P u b l i s h e r s , New Y o r k , ( 1 9 6 3 ) , c h . 5 . 1 3 J. Industry more, ( 1 14 J .  A. G u t h r i e and G. R. A r m s t r o n g , W e s t e r n F o r e s t - An E c o n o m i c O u t l o o k , The J o h n H o p k i n s P r e s s , B a l t i 9 6 1 ) , c h . 2 and 3 . ik. Z i n u v s k a , o p . c i t .  TABLE  2.1  THE VALUE OF FOREST PRODUCTION  IN BRITISH  COLUMBIA  BY INDUSTRIAL CATEGORIES I N SELECTED YEARS (millions  Lumber  Pulp &  1954  1957  1959  1961  1962  270.1  275.4  323.9  359.0  388.3  71.8  75.5  79.8  89.6  177.4  23^.5  258.4  53.0  Plywood  156.2  Paper  Source:  of dollars)*  Annual Report, B r i t i s h Columbia V i c t o r i a , B. C., (1962).  *  Values include the P r o v i n c e .  loading  Forest  Service,  and f r e i g h t c h a r g e s  within  292.0  15 It  s h o u l d be n o t e d h o w e v e r t h a t t h i s  growth i n plywood  sumption has o c c u r r e d l a r g e l y a t t h e expense sumption i n t r a d i t i o n a l lumber Growth strong,  con-  o f lumber  con-  markets.  i n the p u l p i n d u s t r y has been c o n s i s t e n t l y  f o l l o w i n g the steady increase  i n paper and paper-  p r o d u c t s c o n s u m p t i o n , a n d a u g m e n t e d by a n i n c r e a s i n g u s e o f h i g h - g r a d e p u l p o r c e l l u l o s e as a raw m a t e r i a l  f o r t h e chem-  ical industries. Organization The ber  of the  lumber  Industry.  industry i s characterized  of individual enterprises  raw m a t e r i a l w i t h  research  available  Some w r i t e r s h a v e s u g g e s t e d  s t r u c t u r e o f the lumber  largely responsible ket  a widely  num-  r e l a t i v e l y l o w - c a p i t a l r e q u i r e m e n t s and  r e l a t i v e l y easy entry. t h i s fragmented  consuming  by a l a r g e  that  i n d u s t r y has been  f o r i t s l a c k o f t e c h n o l o g i c a l a n d mar-  and t h u s i t s s l u g g i s h r a t e  quote Z i n u v s k a , " . . . t h i s  i s an industry  of growth. structure  To which  m i g h t warm t h e h e a r t o f Adam S m i t h , b u t i t w o u l d b r e a k t h e 15 h e a r t o f any i n d u s t r i a l r e s e a r c h while  there  i s a l a r g e number o f s m a l l  P a c i f i c Coast there ducing  director."  Nevertheless,  sawmills  on t h e  a r e a l s o s e v e r a l v e r y l a r g e lumber  pro-  plants. In contrast,  pulp production  t h e number o f i n d i v i d u a l p l y w o o d a n d  plants  i n the c o a s t a l region  i s relatively  small. L a t e s t f i g u r e s i n d i c a t e t h e r e were s i x t e e n plywood r? J . A. Z i n u v s k a , "The F u t u r e f o r Wood i n a C o m p e t i t i v e Market," paper f o r p r e s e n t a t i o n a t j o i n t meeting Puget Sound and C o l u m b i a R i v e r s e c t i o n s , S o c i e t y o f A m e r i c a n F o r e s t e r , L o n g v i e w , Wash., May 4, 1963.  16 mills  16 and t h i r t e e n p u l p m i l l s 17 i n o p e r a t i o n i n t h e c o a -  s t a l r e g i o n d u r i n g 1961.  C o n c e n t r a t i o n i n t h e p l y w o o d and  pulp industries i s c l o s e l y associated with large o f s c a l e , and t h e h i g h l e v e l o f t e c h n o l o g i c a l n e c e s s a r y t o expand II.  economies  innovation  i n t o world markets. PROBLEMS OF THE INDUSTRY  C o s t c o n t r o l i n t h e f o r e s t i n d u s t r y seems t o v a r y i n v e r s e l y w i t h t h e age o f t h e i n d u s t r y .  Thus t h e r e i s l e s s  k n o w l e d g e o f u n i t - c o s t s i n t h e l o g g i n g and l u m b e r t h a n t h e r e i s i n t h e y o u n g e r p l y w o o d and p u l p  industries  industries.  Inadequate c o s t c o n t r o l here r e f e r s t o an i n s u f f i c i e n t  know-  ledge of u n i t - c o s t s f o r each stage of the p r o d u c t i o n process. The p r o b l e m may e x i s t f o r two r e a s o n s : (a)  insufficient  data or (b)  r i s k and u n c e r t a i n t y .  An i n s u f f i c i e n c y o f d a t a may a r i s e m e r e l y b e c a u s e the r e q u i r e d data i s d i f f i c u l t t o c o l l e c t .  F o r example,  the l o g g i n g i n d u s t r y i s faced w i t h a heterogeneous  supply  o f raw m a t e r i a l ( t r e e s ) f r o m w h i c h i t p r o d u c e s an e q u a l l y heterogeneous product ( l o g s ) .  Great d i f f i c u l t y  i s experi-  enced t h e r e f o r e i n d e t e r m i n i n g t h e c o s t o f p r o d u c t i o n  16 V e n e e r and P l y w o o d M i l l s . D o m i n i o n B u r e a u o f S t a t i s t i c s , C a t a l o g u e No. 35-206, Queen's P r i n t e r s , O t t a w a , (July, 1963). 17 P u l p and P a p e r M i l l s . D o m i n i o n B u r e a u o f S t a t i s t i c s , C a t a l o g u e No. 36-204, Queen's P r i n t e r s , O t t a w a , ( O c t . 1963).  17  a t t r i b u t a b l e t o each l o g , p a r t i c u l a r l y since logs of f e r e n t g r a d e a r e t y p i c a l l y p r o d u c e d f r o m t h e same  dif-  felled  tree. A s i m i l a r problem a r i s e s i n the lumber w h e r e a v a r i e t y o f d i f f e r e n t l u m b e r g r a d e s and f r e q u e n t l y p r o d u c e d f r o m t h e same l o g . mill  operations  duction  industry s i z e s are  P l y w o o d and p u l p  a r e more a m e n a b l e t o m e a s u r e m e n t o f  d a t a and  pro-  show a r e a s o n a b l y h i g h d e g r e e o f c o s t  con-  trol. In a d d i t i o n to the d i f f i c u l t y cost data there the problem.  of c o l l e c t i n g u n i t -  h a s so f a r b e e n l i t t l e  I n the l o g g i n g  incentive to tackle  and l u m b e r i n d u s t r i e s o f t h e  p a s t t h e small-owner a p p r o a c h has p r e v a i l e d , w i t h l i t t l e no a t t e n t i o n d i r e c t e d t o u n i t - c o s t s a s l o n g s h e e t showed a p r o f i t . of l a r g e i n t e g r a t e d  f i r m s and a g r o w i n g a w a r e n e s s  been any a t t e m p t t o measure u n i t - c o s t s o f Risk  and  as the b a l a n c e  O n l y r e c e n t l y w i t h t h e emergence  i n d u s t r y of the r e a l l i m i t s to i t s resource  (b)  by t h e  b a s e , has  Uncertainty.  t o r i s k and u n c e r t a i n t y ging costs vary w i t h  logging. is  there  production,  Inadequate c o s t - c o n t r o l i n the f o r e s t i n d u s t r y  fluence  or  the f i r e  i s inevitable.  seasonal  weather  For example,  due log-  conditions which i n -  h a z a r d and t h e p h y s i c a l d i f f i c u l t i e s  Some m e a s u r e o f t h e p r e d i c t a b i l i t y o f t h e s e  of risks  p o s s i b l e b u t i t depends upon d a t a w h i c h i s l a c k i n g i n  IB most p a r t s o f t h e p r o v i n c e . The  u n c e r t a i n t y o f f u t u r e stumpage v a l u e s  a problem throughout the f o r e s t i n d u s t r y . flects  Stumpage r e -  t h e t r u e r e s i d u a l o f market p r i c e l e s s estimated  of production.  remains i n t h e hands o f t h e Crown,  s i n c e t h e g o v e r n m e n t changes stumpage w i t h  these  cost  Since ownership o f the f o r e s t resource i n  most p a r t s o f t h e p r o v i n c e and  presents  harvest,  costs to the forest industry are highly unpredictable.  1  I n summary, t h e l o g g i n g a n d l o g - c o n v e r s i o n i n d u s t r i e s s u f f e r varying degrees o f inadequate The  lack of unit-costs curtails  production-cost  control.  t h e measurement o f c o n v e r -  s i o n e f f i c i e n c y and p r o d u c t i v i t y w h i c h i n t u r n d i r e c t l y a f fects earnings. The  l a c k o f c o n t r o l over  supply costs i s r e f l e c t e d  i n the i n d u s t r y ' s c u r r e n t haphazard a l l o c a t i o n o f logs among v a r i o u s c o n v e r s i o n p r o c e s s e s . must o v e r c o m e t h e s e  C l e a r l y the industry  cost-control deficiencies i f i t i s to  e x p a n d a n d meet t h e i n c r e a s i n g c o m p e t i t i o n f o r i t s m a r k e t s . Market Problems. The  lumber i n d u s t r y o f B r i t i s h Columbia f a c e s  competition from s u b s t i t u t e products,  notably  p l a s t i c s , c o n c r e t e , a l u m i n i u m , and s t e e l . c o m p e t i t i o n has occurred  plywood,  Most o f t h i s  i n t h e t r a d i t i o n a l markets f o r lum-  b e r where t h e i n d u s t r y h a s b e e n f o r c e d t o e i t h e r c o s t s , reduce p r o f i t s ,  strong  or concede t h e market.  reduce  The p l y w o o d  18 A. M i l t o n M o o r e , F o r e s t r y T e n u r e s a n d T a x e s i n C a n a d a , C a n a d i a n T a x F o u n d a t i o n , T o r o n t o , (1957), c h . 2.  19 and  p u l p i n d u s t r i e s , u n l i k e l u m b e r , h a v e n o t f a c e d t h e same  degree of c o m p e t i t i o n from  substitutes.  I n f a c t , they  have  made i n r o a d s i n t o a r e a s p r e v i o u s l y d o m i n a t e d b y l u m b e r , 19 cotton, jute,e t c . The sell  lumber and p u l p i n d u s t r i e s o f B r i t i s h  a major p o r t i o n o f t h e i r output  Columbia  i nforeign  markets;  20 a p p r o x i m a t e l y 77 p e r c e n t  o f the lumber output  a n d 89 p e r -  cent o f the pulp output from t h e c o a s t a l r e g i o n i s export21 ed.  Since c o a s t a l B r i t i s h Columbia accounts  f r a c t i o n of the t o t a l world  f o ra small  supply of these products  this  r e g i o n must, e s s e n t i a l l y , take w o r l d market p r i c e s f o r t h e s e products as g i v e n . The ically  coast m i l l s , which a r e o f t e n constructed  t o serve f o r e i g n markets,  ship a higher  specif-  percentage  of  t h e i r output t o w o r l d markets t h a n does t h e average  in  the province.  mill  However, i t i s g e n e r a l l y agreed  that the  f o r e s t i n d u s t r y of the i n t e r i o r region of B r i t i s h  Columbia  will  forest  account  f o r an i n c r e a s i n g  share o f the t o t a l  i n d u s t r y i n t h e p r o v i n c e , as s t o c k s o f l a r g e - d i a m e t e r mature t i m b e r o n t h e c o a s t a r e d e p l e t e d , and i m p r o v e d  technology  makes p o s s i b l e t h e h a r v e s t i n g o f p r e v i o u s l y n o n - c o m m e r c i a l 22 s t a n d s o f s m a l l d i a m e t e r s p r u c e , b a l s a m , p i n e s and f i r . 19  J . A. G u t h r i e and G. R. A r m s t r o n g ,  o p . c i t . c h . 6.  20 P r o d u c t i o n , Lumber M i l l s , D o m i n i o n B u r e a u o f S t a t i s t i c s , C a t a l o g u e No. 35-003, Queen's P r i n t e r s , O t t a w a , ( a c c u m u l a t e d m o n t h l y i s s u e s 1963). 21 L. R e a d , E c o n o m i s t & S t a t i s t i c i a n , C o u n c i l o f F o r e s t I n d u s t r i e s , V a n c o u v e r , B.C. (1964) - u n o f f i c i a l e s t i m a t e , s i n c e primary source not a v a i l a b l e . 22 J . A. G u t h r i e and G. R. A r m s t r o n g , o p . c i t . c h . 5.  20 As t h e l u m b e r i n d u s t r y i s f o r c e d i n t o t i m b e r o f d e clining  s i z e and q u a l i t y i t s p o s i t i o n i n w o r l d  w i l l become w e a k e r .  The i n d u s t r y w i l l be f o r c e d t o compete  i n a market f o r p r o d u c t s produced growth  from predominantly  f o r e s t s , not u n l i k e those found  the w o r l d , and w i l l age  advant-  lumber.  Supply.  A p e r v a s i v e problem  f a c i n g the f o r e s t i n d u s t r y i s  the d e c l i n i n g q u a l i t y of timber. l u m b e r and p l y w o o d ficient  second-  i n other parts of  thereby lose i t s former n a t u r a l  i n large-dimension clear  Raw M a t e r i a l  markets  The p r o b l e m  affects the  i n d u s t r i e s m o s t , f o r no m a t t e r how e f -  t h e l o g g i n g and l o g - c o n v e r s i o n t e c h n i q u e s may b e -  come, l o g q u a l i t y u l t i m a t e l y g o v e r n s  l u m b e r and  plywood  quality. The hastened  t r a n s i t i o n t o l o w e r q u a l i t y raw m a t e r i a l i s  b y t h e f a c t t h a t l u m b e r and p l y w o o d  tors f o r the l i m i t e d  are competi-  stock of high q u a l i t y logs.  The p l y -  wood i n d u s t r y i n p a r t i c u l a r p r e f e r s l a r g e - d i a m e t e r l o g s , c o n t a i n i n g a high percentage  o f c l e a r wood.  these has r i s e n , i n t h e f a c e o f l i m i t e d p o i n t where l o g c o s t s now a c c o u n t t o t a l plywood  costs.  The p r i c e o f  supply, t o the  f o r up t o 60 p e r c e n t o f  2~\ 2k ' J  23 W. E. Mayhew, "A New M e t h o d o f A l l o c a t i n g C o s t s t o V e n e e r by G r a d e s , " F o r . P r o d . J o u r n . , v . 8, ( A u g . 1958), pp. 27A-30A. 2k A. G. R a n k i n , " C o s t - P r i c e R e l a t i o n s h i p s i n t h e F o r e s t I n d u s t r y , " The F o r e s t r y C h r o n i c l e , v . 39, ( M a r . 1963), PP. 69-79.  21 While timber quality i s declining the annual har25 vest i s increasing s t e a d i l y ,  7  and the logging industry  i s being forced to log In more inaccessible areas and at progressively higher elevations.  These trends are being  accompanied however by technological advances i n logging methods, and by more intensive u t i l i z a t i o n of the raw material on the part of the log-conversion i n d u s t r i e s . III.  INDUSTRY TRENDS  The forest industry i s f u l l y aware of i t s production and market problems, and has taken steps to overcome them.  ' '  Research and development i n technology and mar-  keting have been strongly supported i n recent years.  The  plywood and pulp industry have always been strong i n r e search and development, but only i n recent years have the logging and lumber industries made important advances i n these f i e l d s .  S t r u c t u r a l changes i n the industry have also  been s i g n i f i c a n t .  These trends are discussed i n the f o l -  lowing sections. Research and Development. (a)  Technological Research and Development. Recent technological advances i n a l l phases of the  forest industry have been directed towards lowering u n i t production costs, r a i s i n g o v e r - a l l u t i l i z a t i o n of the raw  25 "Progress to September, 1962 and Future Prospects of the B r i t i s h Columbia Sustained Y i e l d Forestry Program." B.C. F.S., submitted to T a r i f f Commission of the United States of America, Washington, D.C. October, 1962. 26 27  J . A. Zinuvska, op. c i t . A. G. Rankin, op. c i t .  22  m a t e r i a l , a n d d e v e l o p i n g new p r o d u c t s . advances occur effort  concurrently.  Frequently  these  A great deal of the research  i s c a r r i e d o u t by government a g e n c i e s  and t h e u n i -  v e r s i t i e s , a s i d e from i n d u s t r i a l r e s e a r c h performed by t h e larger private enterprises. (i)  Reduction  i nunit-costs.  T h e s e g a i n s a r e made  through  an improvement i n p r o c e s s i n g e f f i c i e n c y , e i t h e r by  raising  output  cost per unit  per d o l l a r of operating cost or reducing of throughput.  Some e x a m p l e s a r e p o r t a b l e -  s p a r l o g g i n g , band saws a n d a u t o m a t e d g r e e n - c h a i n s mills,  t h i n n e r veneers  i n saw-  i n plywood p r o d u c t i o n , and c o n t i n u o u s  digesters i n pulping. (ii)  Increased u t i l i z a t i o n .  g a i n s aimed a t r a i s i n g where h i g h e r p r o d u c t  These a r e b a s i c a l l y p h y s i c a l  over-all conversion  y i e l d s p e r u n i t of raw m a t e r i a l l e a d  to higher net returns.  T y p i c a l examples a r e c h i p p i n g o f  s a w m i l l waste, p a t c h i n g veneer sheets and  recovering chemicals  pulp-mill (iii) be  efficiency  to raise their  (such as l i g n o s u l p h o n a t e s )  grade, from  effluents.  New p r o d u c t s .  The d e v e l o p m e n t o f new p r o d u c t s  s t i m u l a t e d by r e s e a r c h d i s c o v e r i e s o r b y changing  k e t demands, o r some c o m b i n a t i o n  of these f o r c e s .  d u c t s may r e s u l t f r o m t h e i m p r o v e m e n t o f e x i s t i n g  may mar-  New p r o processes  o r t h e y may r e q u i r e a n e n t i r e l y new p r o d u c t i o n  facility.  Some e x a m p l e s a r e g l u e d - l a m i n a t e d  beams,  structural  mixed s p e c i e plywoods, s p e c i a l t y p u l p s l u l o s e ) and w o o d - e x t r a c t  adhesives.  (high alpha  cel-  23 (b)  M a r k e t R e s e a r c h and D e v e l o p m e n t . B o t h i n d i v i d u a l f i r m s and i n d u s t r y  h a v e made e f f o r t s  organizations  i n r e c e n t y e a r s t o improve  t h e market  a c c e p t a n c e o f wood p r o d u c t s , t h r o u g h h i g h e r s t a n d a r d s o f market  s e r v i c e and by m a i n t a i n i n g c o m p e t i t i v e p r i c e s a n d  quality.  I n a d d i t i o n , t h e i n d u s t r y h a s s o u g h t new mar-  kets either  through product d i f f e r e n t i a t i o n or through  d i r e c t p r o m o t i o n o f new u s e s f o r wood. (i)  Improved  market  ber customers  acceptance.  B e t t e r s e r v i c e t o lum-  has been a c h i e v e d through b u n d l i n g o f lumber,  where e a c h b u n d l e c l a s s has a f i x e d p r o p o r t i o n o f s p e c i fied  grades o f lumber  customer's  needs.  selected  Improved  t o conform w i t h a t y p i c a l  service through the e s t a b l i s h -  ment o f a u t h o r i z e d l u m b e r d e a l e r s h a s a l s o p r o m o t e d  better  acceptance. (ii)  New M a r k e t s .  ularly active  I n d u s t r y a s s o c i a t i o n s have been p a r t i c -  i n p r o m o t i n g new u s e s f o r wood p r o d u c t s  t h r o u g h p u b l i c a t i o n s and a d v e r t i s e m e n t s .  F o r example,  d r a w i n g s and p l a n s f o r h o u s e s , b o a t s , t r a i l e r s , offered at subsidized  ( o f t e n zero) p r i c e s as an i n d u c e -  ment t o u s e wood p r o d u c t s . has been a t t e m p t e d f o r e i g n markets  e t c . , are  Promotion of overseas  markets  through organized trade missions to  by prominent  B r i t i s h Columbia  wood-product  manufacturers. Structural  Adjustments.  There  i s a marked t e n d e n c y  B r i t i s h Columbia  towards  i n the f o r e s t industry of  i n t e g r a t i o n , b o t h v e r t i c a l and  2k horizontal.  I t w i l l he w o r t h w h i l e  p l i c a t i o n s o f these (a)  t o consider here the im-  two forms o f s t r u c t u r a l  adjustment.  Horizontal Integration. We h a v e n o t e d  and  the c o m p e t i t i o n between t h e lumber  plywood i n d u s t r i e s f o r h i g h - q u a l i t y l o g s .  In addition,  the lumber i n d u s t r y f a c e s c o m p e t i t i o n from t h e pulp try at  f o r poorer-grade  logs.  l e a s t i n p a r t , through  T h i s c o n f l i c t c a n be r e s o l v e d ,  horizontal integration.  the l a r g e f i r m w i t h s u b s t a n t i a l timber achieve  maximum u t i l i z a t i o n  indus-  holdings  of i t s timber  seeks t o  by i n t e g r a t i n g  the  lumber, plywood and p u l p p r o d u c t i o n p r o c e s s e s  its  own p l a n t .  The h i g h - g r a d e  Thus  within  p e e l e r l o g s a r e used as p l y -  wood s t o c k ; t h e b u l k o f t h e b e t t e r g r a d e l o g s g o e s t o t h e s a w m i l l s ; and t h e r e m a i n i n g and  plywood-mill  facilitates use.  l o g s p l u s waste from lumber  o p e r a t i o n s go t o t h e p u l p m i l l .  t h e a l l o c a t i o n o f l o g s t o t h e i r most  However, i n t e g r a t i o n o f t h i s  This profitable  sort i s practical  only  w i t h i n t h e l a r g e r companies. Some m e a s u r e o f p a r t i a l the  i n t e g r a t i o n i s secured  by  exchange o f l o g s between f i r m s o r by t h e s a l e o f p u l p  chips.  F o r e x a m p l e , a p u l p m i l l may e x c h a n g e D o u g l a s f i r  p e e l e r l o g s f r o m i t s own h o l d i n g s , f o r h e m l o c k o r s m a l l l o g s t h a t a plywood m i l l wishes t o d i s p o s e m i l l may s e l l i t s c h i p s t o a n e a r b y p u l p (b)  o f , o r a saw-  mill.  Vertical Integration. The  development o f t h e f o r e s t i n d u s t r y concurs  S c o t t ' s stage  11 i n a l l a s p e c t s , w i t h t h e p o s s i b l e  with  exception pointed  of i n d u s t r i a l organization.  As Z i n u v s k a h a s  o u t however, t h e inducement t o i n v e s t i n t h e f o r e s t  industry derives  from manufacturing p r o f i t s  i n consuming  t i m b e r ( o r wood) a s a r a w m a t e r i a l r a t h e r t h a n f r o m t h e r e -  2Q turns  t o growing timber.  t o merge w i t h  ( i n v e s t i n ) more h i g h l y r e f i n e d  f a c t u r i n g processes. trend  ' Thus f o r e s t i n d u s t r y f i r m s  This  i s substantiated  wood-manu-  by the r e c e n t  t o v e r t i c a l i n t e g r a t i o n f o r w a r d s b y many o f t h e l a r g e r  f o r e s t product  enterprises.  Vertical vides  integration f o r large integrated firms  pro-  a d e g r e e o f s t a b i l i z a t i o n i n p r o d u c t p r i c e s and s a l e s  volumes, through the mutual a s s o c i a t i o n of a given c a p a c i t y w i t h a known and c a p t i v e m a r k e t .  Also,  productive  vertical  i n t e g r a t i o n f r e q u e n t l y r e s u l t s i n a broader f i n a n c i a l for  tend  the integrated u n i t , enabling  economies o f s c a l e  base through  i n v e s t m e n t i n l a r g e - c a p a c i t y p l a n t s , which i n t u r n a r e supported (c)  by t h e g u a r a n t e e d s u p p l i e s and m a r k e t s ,  Summary. S t r u c t u r a l adjustments i n the f o r e s t i n d u s t r y i n  recent  y e a r s have r e s u l t e d i n t h e f o r m a t i o n  grated  forest-product  enterprises.  of large  A l t h o u g h some  inte-  social  b e n e f i t s f r o m more c o m p l e t e u t i l i z a t i o n o f t h e r a w m a t e r i a l may r e s u l t ,  this  need n o t n e c e s s a r i l y c o i n c i d e w i t h  greater  28 A. D. S c o t t , "The D e v e l o p m e n t o f t h e E x t r a c t i v e I n d u s t r i e s , " The C a n . J o u r . E c o n . a n d P o l . S c i e n c e , v. 28,  ( F e b . 1962), p p . 70-87. 29  J . A. Z i n u v s k a ,  op. c i t .  26 economic e f f i c i e n c y .  A discussion of the ramifications  of government forest p o l i c y on s t r u c t u r a l adjustments withi n the forest industry, however, i s outside the scope of t h i s thesis.  Nevertheless i t i s apparent that the form-  ation of large integrated firms creates a managerial problem for each, i n finding the optimal d i s t r i b u t i o n of i t s available log supply among the various u t i l i z a t i o n processes.  This was discussed i n the previous chapter. IV.  CONCLUSIONS  To quote Zinuvska again, "...the challenge of competition i n the forest industry today i s the challenge 30  of technology and markets." ~* The problem i s b a s i c a l l y a question of achieving maximum economic e f f i c i e n c y i n the use of the forest resource.  With strong competition  i n world markets and i n many cases from substitute products, the forest industry as a whole i s impelled to lower i t s 31 32 unit-costs.  In addition, as several writers suggest,  '  the forest industry i s under considerable pressure to achieve f u l l e r u t i l i z a t i o n of the raw material, which may not always coincide with attaining maximum economic e f ficiency.  Nevertheless, i t i s generally agreed that both  questions can be solved only through greater expenditures on research and development, i n both technology and marketing. 30. J . A. Zinuvska, op. c i t . 31. op. c i t . 32. J . A. Guthrie & G. R. Armstrong, op. c i t . ch. 6.  27 As a p r e r e q u i s i t e to r a i s i n g the economic e f f i c i e n c y of l o g - c o n v e r s i o n however,  the i n d u s t r y must ensure that  i t uses i t s raw m a t e r i a l i n an optimum manner. cally,  it  Specifi-  i s important that each l o g be a l l o c a t e d to the  process where i t  can earn i t s h i g h e s t r e t u r n .  It  is  clear  that t h i s c o n d i t i o n i s r e f l e c t e d i n the q u e s t i o n of e f f i c i ent l o g a l l o c a t i o n d i s c u s s e d i n the p r e v i o u s  chapter.  In a d d i t i o n to observing the problem of l o g a l l o c a t i o n we have now d i s c u s s e d i t s r e l a t i v e importance to the f u t u r e expansion of the f o r e s t i n d u s t r y .  As a p a r t of  the r e s e a r c h and development e f f o r t c a l l e d f o r ,  improved  l o g a l l o c a t i o n o f f e r s one of the more promising and f r u i t f u l avenues toward greater economic e f f i c i e n c y i n the i n d u s t r y as a whole.  2 8  CHAPTER I I I EXPOSITION OF THE The  problem  LOG-ALLOCATION PROBLEM  of e f f i c i e n t l y a l l o c a t i n g  l o g s among a l -  t e r n a t i v e u t i l i z a t i o n p r o c e s s e s h a s b e e n d e s c r i b e d and i t s importance emphasized.  I n t h i s chapter the elements  p r o b l e m w i l l be d i s c u s s e d , w i t h a v i e w t o w a r d  of the  synthesizing  a l i n e a r programming s o l u t i o n i n the f o l l o w i n g c h a p t e r . Three  c o n d i t i o n s u n d e r l y the problem of l o g  c a t i o n i n the f o r e s t i n d u s t r y , (1)  The  allo-  namely:  o b j e c t i v e o f p r o f i t m a x i m i z a t i o n on  the p a r t o f the owners o f  log-utilization  plants. (2)  A limited  l o g supply.  (3)  Interdependence  among t h e v a r i o u s l o g -  conversion processes. These c o n d i t i o n s w h i c h determine  the n a t u r e of the  l i n e a r programme m o d e l w a r r a n t e x a m i n a t i o n i n f u r t h e r  detail.  P r o f i t Maximization. It  i s n o t u n r e a s o n a b l e t o assume t h a t e a c h f i r m i n  t h e f o r e s t i n d u s t r y attempts t o maximize seeks t o maximize its  p r o f i t s and  the r e t u r n to a l l i t s imputs,  hence  including  log supply. I f the l o g supply i s g i v e n , a t zero c o s t , then  mum  r e t u r n , n e t o f m a n u f a c t u r i n g and  s t i t u t e s the h i g h e s t p o s s i b l e  sum  maxi-  conversion costs,  of e n t r e p r e n e u r i a l  con-  profit  29 on  l o g u t i l i z a t i o n and economic r e n t t o t h e l o g s u p p l y .  the other hand, i f l o g c o s t s a r e deducted from t o t a l t h e maximum r e t u r n r e p r e s e n t s  On  returns,  maximum e n t r e p r e n e u r i a l p r o f i t  ( o n l y ) t h a t c a n be e a r n e d i n l o g u t i l i z a t i o n . L i m i t e d Log S u p p l y . F o l l o w i n g the assumptions discussed consider  e a r l i e r , we  will  a s i n g l e i n t e g r a t e d - i n d u s t r y w i t h a t o t a l l o g con-  sumption equal  to the annual l o g scale of the c o a s t a l region.  The  i s limited  l o g supply  vest of timber from previous  i n a given year  by t h e a c t u a l  i n t h e r e g i o n , p l u s any c a r r y o v e r years.  l o g supply  f o r e s t s so t h a t  i s very heterogeneous w i t h respect  q u a l i t y and s p e c i e . other  of inventory  I n the coastal region this harvest i s  based a l m o s t e n t i r e l y on n a t u r a l " o l d - g r o w t h " the  harvest  logged,  to size,  G o v e r n m e n t r e g u l a t i o n s r e q u i r i n g , among  t h i n g s , t h e complete removal o f a l l useable  each stand  tend  timber  to increase the heterogeneity  from  of the  by f o r c i n g t h e i n c l u s i o n o f m a t e r i a l t h a t would  w i s e be l e f t  har-  other-  unharvested.  I n p r a c t i c e , each f i r m i s f r e e t o purchase o r trade l o g s o n t h e o p e n m a r k e t and t h e r e b y best  supply  of logs f o r i t s p a r t i c u l a r  Interdependent U t i l i z a t i o n It w i l l processes  be e x p e d i e n t  operations.  Processes. to categorize the u t i l i z a t i o n  under three headings:  wood p r o d u c t i o n , important  attempt t o assemble the  lumber p r o d u c t i o n ,  and p u l p p r o d u c t i o n .  s p e c i a l t y processes  ply-  We s h a l l d i s r e g a r d l e s s  which involve the production  30 of such products (a)  as s h i n g l e s , p a r t i c l e - b o a r d , e t c .  Lumber P r o d u c t i o n . I n b r o a d t e r m s we may d e s c r i b e t h i s p r o c e s s  c o n v e r s i o n o f l o g s i n t o wood p r o d u c t s  as t h e  whose s h a p e a n d d i -  m e n s i o n a r e l i m i t e d by t h e s i z e and q u a l i t y o f t h e l o g i m pute. (b)  Plywood  Production.  This process  may b e d e s c r i b e d a s t h e c o n v e r s i o n o f  l o g s i n t o wood p r o d u c t s  whose shape a n d d i m e n s i o n a r e n o t  g o v e r n e d , e n t i r e l y , by t h e i n i t i a l (c)  Pulp  l o g dimension.  Production.  Pulp p r o d u c t i o n i n v o l v e s decomposing l o g s i n t o m e n t a l wood f i b r e s , e i t h e r the  c h e m i c a l l y o r m e c h a n i c a l l y , and  subsequent r e c o n s t i t u t i o n  sheets.  of these  fibres into  pulp  I n t h e m o d e l t o f o l l o w we s h a l l n o t c o n s i d e r  c e s s i n g beyond the p u l p chemicals,  stage, i . e . , i n t o paper  pro-  products,  t e x t i l e s , e t c . P u l p c a n c o n v e n i e n t l y be  ed a s a f i n a l p r o d u c t  ele-  regard-  s i n c e i t a c t u a l l y e n t e r s the market  i n t h i s form. Process  Interdependencies. T h e r e a r e two t y p e s o f i n t e r d e p e n d e n c e  ed i n t h e l o g - a l l o c a t i o n p r o b l e m . each l o g - u t i l i z a t i o n process  t o be c o n s i d e r -  I n the f i r s t  instance  o r a c t i v i t y draws raw m a t e r i a l  d i r e c t l y f r o m t h e l o g g i n g i n d u s t r y and c o n s u m e s a p o r t i o n of the l i m i t e d l o g supply.  Therefore  c o n s u m p t i o n i n one u t i l i z a t i o n p r o c e s s duces the supply  of logs available  any n e t i n c r e a s e i n i n a given year r e -  t o the other  utilization  31  processes.  In an optimizing problem this relationship per  se i s t r i v i a l , f o r logs would be allocated s o l e l y to the process which yields the maximum return per log.  Neverthe-  l e s s , this interdependence i s important and of p r a c t i c a l significance to the industry, f o r optimal log a l l o c a t i o n i n t h i s instance depends on the r e l a t i v e prices of the f i n a l products. A second type of interdependence arises through the physical or technological relationships between u t i l i z a t i o n processes.  For example, the pulp industry has become i n -  creasingly dependent upon sawmill residues f o r i t s raw 33 material (chip) supply.  S i m i l a r l y , the cores remaining  a f t e r a log has been peeled f o r veneer are often sawn into lumber, and waste from t h i s operation converted into chips for pulping.  Technological interdependencies arise through 34  the production of "composite-products".  Typical examples  are plywood doors (a combination of plywood and lumber) and laminated beams (a combination of d i f f e r e n t types of lumber). It should be observed i n p a r t i c u l a r that plywood and pulp are also composite-products, of veneer and chips, respectively.  I t i s clear that a change i n the production l e v e l of a  composite-product w i l l influence the production l e v e l s of 33 J . A. Guthrie & G. R. Armstrong, Western Forest Industry - An Economic Outlook, The John Hopkins Press, Baltimore, (1961), ch. 3 . 34 We s h a l l define composite-products as products which involve combining two or more wood products produced e a r l i e r i n the u t i l i z a t i o n system to form a new product.  32  i t s components, and the p r o d u c t i o n l e v e l s of other compos i t e - p r o d u c t s u s i n g any of the same components. T e c h n o l o g i c a l or p h y s i c a l interdependence  - that i s  where the a c t u a l l e v e l of one process depends on the a c t u a l l e v e l o f some other p r o c e s s ( e s ) - i s the key t o a l i n e a r programme f o r m u l a t i o n of the l o g - a l l o c a t i o n problem. o b j e c t i v e i s t o f i n d t h a t optimum combination  The  o f processes  and process l e v e l s which w i l l y i e l d a maximum r e t u r n t o the l o g supply as a whole. Summary. A l o g - a l l o c a t i o n problem a r i s e s out o f three charact e r i s t i c s o f the f o r e s t i n d u s t r y : l i m i t e d l o g supply,and  p r o f i t maximization, a  t e c h n o l o g i c a l interdependence  d i f f e r e n t u t i l i z a t i o n processes.  among  T h i s i s not t o suggest  t h a t these a r e the o n l y r e l e v a n t c o n s i d e r a t i o n s , f o r we have overlooked q u e s t i o n s o f l i m i t e d process c a p a c i t y , imm o b i l i t y of f a c t o r s of p r o d u c t i o n , homogeneity of production functions, etc. discussed  Some of these c o n s i d e r a t i o n s w i l l be  later.  I t should be noted t h a t each u t i l i z a t i o n  category,  lumber, plywood and p u l p , p r e s e n t s i t s own programming problem r e s u l t i n g from a l i m i t e d  supply of raw m a t e r i a l w i t h  t e c h n o l o g i c a l l y interdependent a c t i v i t i e s and a p r o f i t -  33 "if.  OcT  maximizing objective.  '  '  "i<"J  '  In addition, however,  plywood and pulp production involve a recombination  of i n -  termediate products ( i . e . , veneer and chips) to form f i n a l products ( i . e . , plywood and pulp), whereas sawmilling r e s u l t s d i r e c t l y i n a f i n a l product plus some intermediate products (e.g. chips) f o r use i n other technologically interdependent  activities.  The contribution of this thesis  l i e s i n the construction of a l i n e a r programme model which combines these s t r u c t u r a l l y d i f f e r e n t a c t i v i t i e s  within  the confines of a single problem or model.  35 F. H. C u r t i s , "Linear Programming the Management of a Forest Property," Journal of Forestry, v. 60, (Sept. 1962), pp. 611-616. 36 N. D. Jackson and G. W. Swinton, "Linear Programming i n Lumber Production," For. Prod. Journ. v. XI, (June,  1 9 6 1 ) , pp.  272-274.  37 E. Koenigsberg, "Linear Programming Applied to the Plywood Industry," For. Prod. Journ. v. XI, (Sept. i 9 6 0 ) , pp. 481-486. 38 A. E. P a u l l , "Linear Programming - A Key to Optimum Newsprint Production," Pulp & Paper Mag, of Can., v. 57, (1956),  pp.  145-151.  34  CHAPTER IV CONSTRUCTION OF A LOG-ALLOCATION LINEAR PROGRAMME MODEL The p r e v i o u s c h a p t e r d e a l t w i t h the n a t u r e o f t h e l o g - a l l o c a t i o n problem.  I n t h i s c h a p t e r we s h a l l proceed  t o a more d e t a i l e d d i s c u s s i o n o f i t s main c h a r a c t e r i s t i c s and c o n s i d e r t h e i r m a t h e m a t i c a l i n t e r p r e t a t i o n i n a l o g a l l o c a t i o n l i n e a r programme model.  A large part of the d i s -  c u s s i o n w i l l r e l a t e t o t h e assumptions made c o n c e r n i n g t h e r e a l w o r l d and i t s m a t h e m a t i c a l analogue.  We s h a l l p o s t -  pone t o a l a t e r c h a p t e r a l l d i s c u s s i o n o f t h e i m p l i c a t i o n s of r e l a x i n g these assumptions. I.  BASIC OUTLINE OF THE MODEL  L i n e a r programming problems have t h r e e b a s i c components : (1)  An o b j e c t i v e .  (2)  Input r e s t r a i n t s .  (3)  A l t e r n a t e interdependent a c t i v i t i e s .  I t has been shown t h a t t h e l o g - a l l o c a t i o n problem under  con-  s i d e r a t i o n here c o n t a i n s each o f t h e s e t h r e e elements.  Thus  t h e o b j e c t i v e i s t o maximize  t o t a l n e t r e t u r n t o an i n t e -  g r a t e d i n d u s t r y which consumes, i n a s p e c i f i c p e r i o d , a g i v e n s u p p l y o f l o g s i n the p r o d u c t i o n o f lumber, and p u l p .  plywood  The a v a i l a b l e s u p p l y o f l o g s c o m p r i s e s t h e i n p u t  r e s t r a i n t s , and t h e v a r i o u s wood-conversion p r o c e s s e s , sawm i l l s , plywood m i l l s , and p u l p m i l l s , c o r r e s p o n d t o  35 alternate  interdependent a c t i v i t i e s .  G i v e n t h e s e t h r e e b a s i c c o m p o n e n t s we may a l i n e a r programme a s Let  describe  follows:  a ^  =  t h e amount o f i n p u t i per u n i t of output from ity j .  p.  =  the r e t u r n per u n i t - l e v e l of a c t i v i t y j  b.  =  the a v a i l a b l e input i  X. 3  =  the l e v e l of a c t i v i t y j , e x p r e s s e d as a m u l t i p l e o f i t s unit-level.  J  Then, i n a maximizing problem  required activ39  supply of  the o b j e c t i v e i s t o :  n \  Maximize  X. .  p.  J = 1 m  Subject to:  (1)  2  X  j •  a  i j <  b  i  5  J = 1»2,  ....n  i = 1 (2)  X  >  0  J  Figure I (inside tation  back cover) i s a schematic  of the l o g - a l l o c a t i o n  presen-  l i n e a r programme m o d e l  39 The u n i t - l e v e l o f e a c h a c t i v i t y may be a r b i t r a r i l y d e f i n e d to s u i t the problem. F o r example, the u n i t - l e v e l o f t h e l o g - c o n v e r s i o n a c t i v i t i e s i n the model i s d e f i n e d as 100 c u b i c o f l o g consumed. I n c h a p t e r f i v e we s h a l l s y s t e m a t i c a l l y d e f i n e the u n i t - l e v e l s of a l l a c t i v i t i e s i n the model.  36 described sisting sents  i n this thesis.  of a l i s t  of a c t i v i t y c o e f f i c i e n t s  an a c t i v i t y  manufacturing  or p r o c e s s  a number f r o m one hand s i d e l i s t s  supply put  The  considered. t o 93.  the  The  repre-  sawing a l o g  or  The  Each a c t i v i t y final  twelve  assigned  c o l u m n on t h e  f i g u r e s correspond  the  rightthe  t o the  log-  the remainder r e f e r t o i n t e r m e d i a t e i n -  r e s t r a i n t s , w h i c h we  s h a l l d e s c r i b e l a t e r on  T h e r e a r e a t o t a l o f 37  b o t t o m two  is  i n p u t s or s u p p l y r e s t r a i n t s t o  first  restraints;  chapter.  such as  (a-jj),  a plywood; the column headings d e s c r i b e  various a c t i v i t i e s  model ( b ^ ) .  Each column i n the f i g u r e con-  rows o f the  r e t u r n s f o r each a c t i v i t y  in this  r e s t r a i n t s i n the  f i g u r e c o n t a i n the ( p . ) , and  the  model.  unit-level  corresponding  activity levels (Xj). II. Allocation The  STRUCTURE OF  o b j e c t i v e f u n c t i o n , or m a t h e m a t i c a l t o t a l net r e t u r n t o the  m a t i o n of the  of f i n d i n g  a set of non-negative values  to  supply  should  be  s u i t the problem.  t i v i t y must be  i n c l u d e d i n the  A s o l u t i o n t o the problem con-  a c t i v i t y l e v e l s which w i l l s u b j e c t to the  expression  e n t e r p r i s e , i s a sum-  returns from a l l a c t i v i t i e s  l o g - a l l o c a t i o n problem.  It  MODEL  Objective.  representing  sists  THE  f o r the  Xj  s a t i s f y the o b j e c t i v e f u n c t i o n ,  restraints.  n o t e d t h a t any The  a c t i v i t y may  be  defined  o n l y r e q u i r e m e n t i s t h a t an  interdependent  w i t h a t l e a s t one  other  ac-  37 activity  i n the model.  o f a n a c t i v i t y may  I n o t h e r words, the  final  level  not  be  a r b i t r a r i l y determined at  the  are  i n t e r e s t e d i n maximizing t o t a l  start. Normally  we  r e t u r n , as d e s c r i b e d level  i n the p r e v i o u s  r e t u r n of each a c t i v i t y  chapter.  tivity total  r e t u r n s i n the net  thesis  he  negative  and  cost a c t i v i t i e s , respectively. i n the  a total later,  returns, corresponding  t o revenue The  a  in  this  net r e t u r n f i g u r e .  This w i l l  activities  summation o f  o b j e c t i v e f u n c t i o n however w i l l  i n chapter  yield  ac-  to consider p o s i t i v e r e t u r n s  and  these  summation of  I n the model p r e s e n t e d  necessary  unit-  expressed  objective function w i l l  return figure.  i t will  I f the  i n the model i s  as a n e t - r e t u r n f i g u r e , t h e n c l e a r l y the  net  be  still  yield  demonstrated  five.  Activities. Compilation  of the p e r t i n e n t a c t i v i t i e s  portant  step i n the c o n s t r u c t i o n of a l i n e a r  model.  In this  l o g - a l l o c a t i o n p r o b l e m we  l u m b e r , p l y w o o d and  pulp-production  components o f the model, but down more t h o r o u g h l y . i n t o lumber, peeled and  c h i p s may  For  activities  i t i s necessary  e x a m p l e , l o g s may  sold directly  im-  programme  have  f o r veneer, or chipped,  i n t u r n be  i s an  recognized as t h e  basic  to break  these  be and  e i t h e r sawn the  or recombined  veneer into  plywood or p u l p , r e s p e c t i v e l y . Technological was  interdependence between  noted i n the p r e v i o u s  chapter  as one  activities  of the main  sources  38 of  the a l l o c a t i o n "problem".  of  this  Furthermore, a large  i n t e r d e p e n d e n c e came f r o m t h e e x i s t e n c e o f  measure inter-  m e d i a t e p r o d u c t s s u c h a s v e n e e r and c h i p s , w h i c h c o u l d be combined i n t o composite p r o d u c t s such as plywood It  i s logical  therefore that a successful  model should i n c l u d e s e p a r a t e a c t i v i t i e s of  and p u l p .  log-allocation f o r e a c h method  p r o d u c t i o n and c o n s u m p t i o n o f t h e s e i n t e r m e d i a t e p r o -  ducts. The  activities  producing intermediate products are  r e f e r r e d t o as " i n t e r m e d i a t e - a c t i v i t i e s " , as opposed t o " f i n a l - a c t i v i t i e s " w h i c h p r o d u c e a f i n a l p r o d u c t consumed o u t s i d e t h e model.  A t an optimum s o l u t i o n t h e " i n t e r -  m e d i a t e - a c t i v i t y " l e v e l s would log  i n d i c a t e how t h e g i v e n t o t a l  s u p p l y s h o u l d be d i s t r i b u t e d  among t h e v a r i o u s l o g -  c o n v e r s i o n p r o c e s s e s ( s a w i n g , p e e l i n g and c h i p p i n g ) ; the  " f i n a l - a c t i v i t y " l e v e l s would  products  while  show how t h e i n t e r m e d i a t e  ( l u m b e r , v e n e e r a n d c h i p s ) s h o u l d be d i s p o s e d o f  either directly,  w i t h o u t f u r t h e r m a n u f a c t u r i n g , o r i n com-  b i n a t i o n as p a r t o f a f i n a l p r o d u c t such as plywood o r pulp. Intermediate  Activities.  These a c t i v i t i e s to  d e s c r i b e the consumption o f logs  p r o d u c e p r o d u c t s s u c h a s l u m b e r , v e n e e r and c h i p s .  m i g h t t h e r e f o r e be t e r m e d  cutting activities.  I n t h e model  these are segregated i n t o three n a t u r a l c a t e g o r i e s , p e e l i n g , and c h i p p i n g . activity  They  sawing,  A d e t a i l e d d i s c u s s i o n of the  c o e f f i c i e n t s i n each a c t i v i t y  i s g i v e n i n the next  39  chapter, ties  but  i t should  are the  Primary  only a c t i v i t i e s with c o e f f i c i e n t s  Input  rows o f t h e m o d e l , i n d i c a t i n g  the o n l y a c t i v i t i e s Figure  w h i c h consume l o g s a s  i n the  that they  input,  and  (i.e.,  signs are  see  g i v e n t o the  activity  s a w i n g , p e e l i n g and nature  the problem, discussed  activity,  c h i p p i n g ) , see F i g u r e  of the  intermediate  in a later  s e c t i o n of  note t h a t  activities  produce i n p u t s f o r other a c t i v i t i e s outputs  cur negative Final  i n the  from the model)  model, and  from  r e t u r n f i g u r e ( i . e . , they i n -  returns).  Activities. The  final activities  of intermediate (b)  a net  to  intermediate  i n c u r c o s t s o f p r o d u c t i o n w h i c h must be d e d u c t e d revenue t o y i e l d  This  this  A t t h i s p o i n t we  they produce negative  may  I.  restraints  chapter.  (i.e.,  coeffici-  u n i t - l e v e l r e t u r n s of each intermediate  f o l l o w s from the  gross  are  I. Negative  ents  be n o t e d h e r e t h a t c u t t i n g a c t i v i -  direct  products  selling  include:  (a)  i n t o f i n a l products  of intermediate  recombination for sale,  i n p u t s , and  and  primary  inputs. (a)  Recombination  Activities.  These a c t i v i t i e s m e d i a t e i n p u t s i n t o new  kO  See  Page No.  k  l.  describe  the recombination  products.  Each a c t i v i t y  of  inter-  represents  40 a unique combination activity  of intermediate products  and t h e  coefficients describe the r e l a t i v e proportions of  intermediate i n p u t s taken i n each case.  Recombination ac-  tivities  described i n the  r e s u l t i n "composite-products",  previous chapter.  Thus, composite p r o d u c t s  wood and p u l p a r e p r o d u c e d b y r e c o m b i n i n g cutting (b)  activities  Selling  (veneer  such as p l y -  outputs  from  peeling, chip chipping),  Activities.  These a c t i v i t i e s  arise  from an imbalance o c c u r r i n g  b e t w e e n p r o d u c t i o n and c o n s u m p t i o n o f i n t e r m e d i a t e ducts.  pro-  F o r example, t h e p r o p o r t i o n s i n which veneers o f  different  grade a r e r e q u i r e d i n t h e manufacture o f p l y -  wood a r e u n l i k e l y  t o correspond  closely  to the proportions  i n w h i c h t h e v e n e e r s a r e p r o d u c e d f r o m t h e l o g , so t h a t t h e r e w i l l be some e x c e s s  v e n e e r o f some g r a d e s .  c o u n t f o r t h i s s u r p l u s we must i n c l u d e a c t i v i t i e s ing  or d i s p o s i n g o f veneer d i r e c t l y ,  without  To a c of s e l l -  further  manufacture. A similar  situation exists  where we m i g h t e x p e c t determining  f o r mixed s p e c i e  that the technical  chip  species of  from the p r o p o r t i o n s i n  which the various species are a v a i l a b l e . selling  requirements  the proportions i n which d i f f e r e n t  c h i p s must be m i x e d w i l l d i f f e r  pulps,  Therefore,  a c t i v i t i e s w i l l be r e q u i r e d t o d i s p o s e  chip-  of any  surpluses. F i n a l l y there i s the p o s s i b i l i t y  t h a t t h e optimum  p a t t e r n o f a l l o c a t i o n f o r t h e g i v e n l o g s u p p l y may n o t c a l l  kl for  'utilization'  vides  of a l l logs.  for direct selling  Hence t h e m o d e l a l s o  o f whole  These s e l l i n g a c t i v i t i e s , all  logs w i l l  logs. i n e f f e c t , guarantee  that  be " d i s p o s e d o f " i n one way o r a n o t h e r and  t h a t a l l wood p r o d u c t s o r u n c u t l o g s w i l l be s o l d . selling activities ferred  pro-  These  correspond t o " d i s p o s a l " a c t i v i t i e s r e -  t o i n t h e g e n e r a l l i t e r a t u r e on l i n e a r program-  kl ming, in  and a r e e s s e n t i a l t o g e n e r a t i n g e q u a l i t y r e s t r a i n t s  t h e model so t h a t a u n i q u e m a t h e m a t i c a l s o l u t i o n i s  possible. Restraints. The me f a l l  r e s t r a i n t s t o t h e l o g - a l l o c a t i o n l i n e a r program-  i n t o two c a t e g o r i e s :  intermediate  input  primary input  restraints.  We  r e s t r a i n t s and  s h a l l consider  these  separately. Primary Input The  Restraints.  primary input  r e s t r a i n t s correspond t o the  ' a v a i l a b l e l o g supply', which i s 'given' m a x i m i z i n g p r o b l e m and c o n s i s t s ferent  species  objective  i n t h i s revenue-  o f a known m i x t u r e o f d i f -  and d i f f e r e n t g r a d e s o f l o g s .  function  Since the  i s t o maximize net r e t u r n , these r e -  s t r a i n t s take the form that  no more t h a n t h e g i v e n  supply  o f l o g s may be consumed. Intermediate Input The  Restraints.  intermediate  a c t i v i t i e s produce  intermediate  kl R. D o r f m a n , P. A. S a m u e l s o n and R. M. S o l o w , L i n e a r P r o g r a m m i n g a n d E c o n o m i c A n a l y s i s , McGraw H i l l , New Y o r k ,  (1958), c h . 3.  \2  products selling  w h i c h may  be  consumed i n b o t h  final activities.  mediate input r e s t r a i n t s t h a t t h e r e i s t o be Subsequently, and  recombination  This feature gives r i s e i n the model.  no a c c u m u l a t i o n  We  shall  be  to  since intermediate products  are both input  the d i s t i n g u i s h i n g comment.  produced  restraints  We  inputs with zero-value  constraints  f e a t u r e o f t h i s m o d e l , and  have seen t h a t the f i r s t  stage  deserve  o f any  involves a cutting  a product  v e n e e r o r c h i p s ) t h a t becomes a n  levels  (lumber,  a selling  activity  further  a c t i v i t y which  or a p r o d u c t i o n a c t i v i t y ,  yields input or  to  both.  l i n e a r programming t h e o r y r e q u i r e s t h a t a l l a c t i v i t y be  n o n - n e g a t i v e t h e r e i s a d a n g e r t h a t "wood" may  c o u n t e d t w i c e i n any I),  are  log-  conversion process  Since  products.  zero. Intermediate  either  inter-  assume  of intermediate  consumed i n t h e m o d e l t h e i n t e r m e d i a t e  will  and  given r e s t r a i n t  o n c e i n an i n t e r m e d i a t e a c t i v i t y  equation and  (row  be  i n Figure  again i n a  final  activity. This d i f f i c u l t y values  to the t e c h n i c a l  activity. the  i s overcome by a s s i g n i n g coefficients  These n e g a t i v e  technical  o u t t u r n of i n t e r m e d i a t e products  final  activities  the a c t i v i t y  (recombination  coefficients  Thus, n e g a t i v e  are  activity  of each  negative  intermediate  coefficients  describe  w h i c h a r e consumed i n  or d i r e c t  selling)  where  positive. coefficients  are  associated  w i t h the p r o d u c t i o n of i n t e r m e d i a t e p r o d u c t s ,  and  activity  consumption  coefficients  are a s s o c i a t e d w i t h the  positive  43 of intermediate products.  The c o n d i t i o n o f "no a c c u m u l a -  t i o n " means t h a t e a c h r e s t r a i n t e x p r e s s i o n must sum t o zero. I,  M a t h e m a t i c a l l y , f o r t h e model r e p r e s e n t e d  t h i s c o n d i t i o n may be e x p r e s s e d  i n Figure  as f o l l o w s :  37  . a.  Xj  ±  =  0  ;  j =  • 93 .  1,2,  i = 13  Double-counting  could occur a l s o i n the o b j e c t i v e  f u n c t i o n , but i t i s avoided negative values are assigned  i n t h e same way a s a b o v e .  to the u n i t - l e v e l returns of  e a c h i n t e r m e d i a t e a c t i v i t y , and p o s i t i v e l e v e l ^ r e t u r n s o f each f i n a l activity. be  Negative  regarded  total  values to the u n i t -  (recombination or s e l l i n g )  returns i n the o b j e c t i v e f u n c t i o n can  as c o s t s ( n e g a t i v e p r i c e s ) w h i c h s u b t r a c t from  gross revenues t o give T o t a l Net Return. The  d i s t i n c t i o n between p r i m a r y  p u t s demands e m p h a s i s . model.  Thus,  Primary  and i n t e r m e d i a t e i n -  inputs are 'given' t o the  T o t a l n e t r e t u r n i s t o be m a x i m i z e d w i t h r e s p e c t t o  these primary  i n p u t s and t h e p r i m a r y  input  c o n d i t i o n s take the form of i n e q u a l i t i e s .  restraint On t h e o t h e r  hand, i n t e r m e d i a t e i n p u t s a r e v a r i a b l e s w i t h i n the o p t i m i z ing  problem.  They a r e t h e l i n k i n t h e model between  i n p u t and f i n a l p r o d u c t al  p a r t of the problem.  primary  b u t t h e y a r e i n no way a c o n d i t i o n -  kk I t may h e l p t o r e a l i z e t h a t t h e i n t e r m e d i a t e o r c u t t i n g a c t i v i t i e s t a k e p r i m a r y i n p u t s ( l o g s ) as i n p u t s and produce i n t e r m e d i a t e p r o d u c t s (lumber, veneer, c h i p s ) as o u t p u t s , whereas t h e f i n a l a c t i v i t i e s , b o t h r e c o m b i n a t i o n and s e l l i n g ( e x c e p t i n g l o g s e l l i n g ) , take i n t e r m e d i a t e p r o d u c t s (lumber, veneer, c h i p s ) as i n p u t s and produce  final  p r o d u c t s (plywood, p u l p , and lumber; veneer and c h i p s ) as o u t puts . III.  ASSUMPTIONS OF THE MODEL  Two t y p e s o f assumption may be d i s t i n g u i s h e d i n the model.  F i r s t l y , Fundamental  assumptions a s s o c i a t e d w i t h t h e  m a t h e m a t i c a l p r o c e d u r e s o f l i n e a r programming.  Secondly,  C o r r e l a t i o n assumptions r e q u i r e d t o reduce t h e a c t u a l l o g a l l o c a t i o n problem under c o n s i d e r a t i o n t o a form amenable t o l i n e a r programming. Fundamental  Assumptions.  These assumptions a r e u n a v o i d a b l e as l o n g as we a r e c o n s i d e r i n g a l i n e a r programme model. c a n t i n t e r p r e t a t i o n s from an economic  They have  signifi-  v i e w p o i n t , as we s h a l l  d i s c u s s below. (1)  The term ' l i n e a r programming' r e f e r s t o t h e a p p l i -  c a t i o n o f a p a r t i c u l a r m a t h e m a t i c a l p r o c e d u r e , based on ' l i n e a r r e l a t i o n s h i p s ' and ' l i n e a r i n e q u a l i t i e s ' , t o p r o blems i n v o l v i n g c h o i c e .  M a t h e m a t i c a l l y , t h e term l i n e a r  r e f e r s t o t h e e x i s t e n c e o f a l l v a r i a b l e s i n the e x p r e s s i o n s as homogeneous and o f degree one. That i s t h e r e can be no  45 2  squared  o r higher-power terms (such as X  3  or  X ) n o r any  l o g a r i t h m i c o r r o o t terms (such as l o g X o r X ) .  To t h e  2  economist t h i s  i n d i c a t e s constant  r e t u r n s t o s c a l e i n each  production process or a c t i v i t y . (ii) The o b j e c t i v e f u n c t i o n was shown p r e v i o u s l y t o be e q u a l t o t h e summation o f t h e r e t u r n s from each m viz:  \  Z  X , j  activity;  p j  The X - v a r i a b l e i n t h i s f u n c t i o n must be homogeneous and to and  o f degree one.  Therefore, f o r the o b j e c t i v e f u n c t i o n  r e p r e s e n t a l i n e a r r e l a t i o n s h i p , p.. must be a c o n s t a n t ; constant  finite  v a l u e s o f p. i n t h i s model i m p l y b o t h i n -  elasticities  o f demand f o r t h e f i n a l - p r o d u c t  a c t i v i t y o u t p u t s , and c o n s t a n t c o s t s f o r t h e i n t e r m e d i a t e activity (iii)  outputs.  Finally,  the l i n e a r r e l a t i o n s h i p s c o n d i t i o n a l upon  t h e m o d e l mean t h a t , f o r a g i v e n a c t i v i t y , taken to  each i n p u t i s  i n a f i x e d r e l a t i v e p r o p o r t i o n t o the other  the a c t i v i t y .  proportions.  inputs  I n e c o n o m i c t e r m s t h i s means f i x e d  factor  The a c t u a l r e l a t i v e p r o p o r t i o n s t a k e n a r e  g i v e n by t h e t e c h n i c a l c o e f f i c i e n t s o f each  activity.  These c o e f f i c i e n t s a r e c o n s t a n t s determined  at the outset,  w h i c h t o g e t h e r make up t h e i n t e r n a l s t r u c t u r e o f t h e v a r i o u s activities  and f o r m t h e s k e l e t o n o f t h e m o d e l .  c i s i o n of the a c t i v i t y c o e f f i c i e n t s r e l i a b i l i t y and a c c u r a c y  The p r e -  i s c r i t i c a l to the  o f a l i n e a r programme  solution.  k6 Correlation  Assumptions,  T h e s e a s s u m p t i o n s a r e m a i n l y t o keep t h e m o d e l a s simple as p o s s i b l e . of  an i n t e g r a t e d  is  based.  (i)  i n d u s t r y , on w h i c h t h e model i n t h i s  We s h a l l  assumptions  We have a l r e a d y d i s c u s s e d t h e c o n c e p t  c o n s i d e r some a d d i t i o n a l  thesis  simplifying  below.  We s h a l l assume z e r o t r a n s p o r t a t i o n c o s t s b e t w e e n  p r o c e s s e s so t h a t , f o r example,  c h i p s produced from  waste  are identical  i n v a l u e w i t h those produced  waste  o r from whole  logs chipped a t the p u l p m i l l .  sawmill  from  veneer  The l o w -  c o s t water t r a n s p o r t a t i o n between u t i l i z a t i o n s i t e s  on t h e  c o a s t , and t h e t r e n d toward i n t e g r a t e d u t i l i z a t i o n p l a n t s , (where  s a w m i l l i n g , p e e l i n g and p u l p i n g f a c i l i t i e s  together at a central  site)  make t h i s  assumption  are located quite  plausible. (ii)  We s h a l l assume l o n g - r u n c o n d i t i o n s w h e r e i n t h e r e i s  sufficient  time f o r p l a n t c a p a c i t y t o a l t e r  t o accommodate  w h a t e v e r p a t t e r n o f l o g u t i l i z a t i o n emerges f r o m t h e optimum allocation  plan.  Given a fixed  l o g s u p p l y , and i n f i n i t e  p r i c e e l a s t i c i t y o f demand, t h e l i n e a r would  specify the l e v e l  programme  a t which each a c t i v i t y  solution  s h o u l d be  o p e r a t e d t o a c h i e v e maximum t o t a l n e t r e t u r n . (iii)  We s h a l l assume t h a t t h e s a w i n g and p e e l i n g  included  f o r each type o f l o g i n t h e model y i e l d  activities t h e maximum  amount o f h i g h - g r a d e p r o d u c t p o s s i b l e .  This assumption r e -  quires  narrow l i m i t s  of  some e x p l a n a t i o n .  t h e product produced  Within fairly  t h e grade  c a n be r a i s e d b y e x p e n d i n g more i n t h e  p r o d u c t i o n p r o c e s s ( e . g . , p a t c h i n g v e n e e r s t o remove k n o t s , o r  47  m e t i c u l o u s l y c a r v i n g out the h i g h e s t p r i c e d p i e c e s of lumber obtainable  from a l o g ) .  The  such t e c h n i c a l p e r f e c t i o n .  assumption here does not  R a t h e r , i t presumes t h a t m i l l s  are c u r r e n t l y o p t i m i z i n g t h e i r economic r e t u r n s t o i n g each type of l o g and  involve  process-  that to e x t r a c t h i g h e r - q u a l i t y  m a t e r i a l would i n v o l v e c o s t s ( b o t h o p p o r t u n i t y  and  operating  c o s t s ) i n excess of the r e t u r n s t h a t would be g a i n e d . T h i s assumption i s r e q u i r e d i n order to avoid i n c l u d i n g a l l techn i c a l l y conceivable  methods of c u t t i n g each l o g - a  t h a t would g r e a t l y c o m p l i c a t e  situation  the model w h i l e a d d i n g  little  to i t s u s e f u l n e s s . (iv)  We  s h a l l assume t h a t the i n t e g r a t e d i n d u s t r y on which  t h i s model i s based i s comprised of average u t i l i z a t i o n f o r the c o a s t a l r e g i o n , r a t h e r t h a n one t h i s manner the i n d u s t r y - a v e r a g e  s i n g l e complex.  conclusions  In  d a t a employed i n the model  b e a r s some measure of r e a l i s m t o the a c t u a l w o r l d . manipulation  plants  of t h i s i n d u s t r y - a v e r a g e  d a t a and  any  The imputed  from i t are of course s u b j e c t t o the assumptions  b u i l t i n t o the model. Summary. These assumptions are n e c e s s a r i l y r e s t r i c t i v e i n the l i g h t of c o n s t r u c t i n g a model of such a complex e n t i t y the f o r e s t i n d u s t r y .  as  Some of the assumptions are d i c t a t e d  by the n a t u r e of l i n e a r programming t e c h n i q u e s ;  some are  s i m p l i f i c a t i o n s t o make the d e m o n s t r a t i o n as c l e a r as possible.  The  assumptions d i s c u s s e d  above are c o n s i d e r e d  more i m p o r t a n t q u a l i f i c a t i o n s of the model.  Other  the  48 assumptions such as those i m p l i c i t i n the p r o d u c t i o n of the model ( i . e . , m o b i l i t y and homogeneity s h o u l d not be o v e r l o o k e d In chapter  functions  of f a c t o r inputs)  i n a s s e s s i n g the model's u s e f u l n e s s .  s i x we s h a l l c o n s i d e r the i m p l i c a t i o n s of  r e l a x i n g some of the C o r r e l a t i o n assumptions by a l t e r i n g the s t r u c t u r e o f the model, but the Fundamental remain.  assumptions  will  49 CHAPTER V DATA AND The  SOLUTION OF THE MODEL  p r i n c i p a l o b j e c t i v e i n t h i s study i s t o demon-  s t r a t e an a p p l i c a t i o n of l i n e a r programming t o the l o g a l l o c a t i o n problem.  An i n t e g r a t e d i n d u s t r y has been assum-  ed, a l o n g w i t h o t h e r a s s u m p t i o n s , t o keep the model ably simple.  Nevertheless,  reason-  t o r e n d e r the r e s u l t s as  realis-  t i c as p o s s i b l e c o n s i d e r a b l e e f f o r t has been made t o o b t a i n accurate  and r e p r e s e n t a t i v e  data.  Data used are from p u b l i s h e d possible. estimates  r e s e a r c h s t u d i e s wherever  Where u s a b l e p u b l i s h e d data were not a v a i l a b l e were o b t a i n e d  from e x p e r t s  i n the i n d u s t r y .  d i s c u s s i o n of the q u a l i t y of the data f o l l o w s i n  A  chapter  six. The  data f a l l s i n t o t h r e e c a t e g o r i e s ; a c t i v i t y  e f f i c i e n t s , a c t i v i t y u n i t - l e v e l r e t u r n s , and restraints.  input  co-  (supply)  T a b l e s o f data r e f e r r e d t o i n t h i s c h a p t e r  c o l l e c t e d together  i n an appendix a t the end I.  of t h i s  chapter.  ACTIVITY COEFFICIENTS  A d i s c u s s i o n of the a c t i v i t y c o e f f i c i e n t s and c o m p i l a t i o n f o r the l o g - a l l o c a t i o n model f a l l s i n t o parts.  The  their two  f i r s t d e a l s w i t h the p r i m a r y - i n p u t / l o g - a l l o -  c a t i o n s e c t o r or l o g - a l l o c a t i o n c o e f f i c i e n t s , the p a r t covers  second  the i n t e r m e d i a t e - i n p u t / f i n a l - p r o d u c t s e c t o r or  t e c h n o l o g i c a l c o e f f i c i e n t s , see F i g u r e I ( i n s i d e back cover).  are  50  1.  Log-Allocation Coefficients. The  deals  primary-input  l o g - a l l o c a t i o n s e c t o r of the  only with a l l o c a t i n g  a given  ious intermediate  activities.  processing  of the  log involved.  efficients  are  types  o f l o g may  ping  (i.e.,  cal  be  activity  combination  products  activities  intermediate  products  selling  twelve  The  An  supply  of  each  or a combination  intermediate The  the  chip-  of  these.  produced.  techni-  I n the  the p r o p o r t i o n s  of  there  activities unit-level  the  the p r o p o r t i o n s  i s no  activity  inter-  I n the f i n a l  rei n which  products.  transformation of  the  c o e f f i c i e n t s are u n i t y .  Technological C o e f f i c i e n t s - Intermediate  one  different  are recombined to form f i n a l  activities  of l o g s .  log-  sawing, p e e l i n g or  they describe  i t e m so t h a t a l l s e l l i n g  chipping  co-  activity.  i n each a c t i v i t y .  they describe  several intermediate  The  i s o n l y one  technological coefficients describe  mediate a c t i v i t i e s  or  Coefficients.  relationships implicit  In the  intermediate  a l l o c a t e d t o any  consumption  log-allocation  there  have c o n s i d e r e d  intermediate)  Technological The  A l l the  shown i n T a b l e 5 . 1 .  o f l o g , as  type  2.  m o d e l we  o f l o g s among v a r -  T h e r e i s no  t h e r e f o r e u n i t y , and  a l l o c a t i o n c o e f f i c i e n t per In this  supply  model  are  Activities.  sawing, p e e l i n g  of each i s d e f i n e d  h u n d r e d c u b i c f e e t o f l o g s consumed i n t h e e x p l a n a t i o n of the data used i n c o m p i l i n g  and  as  activity. these  51 activity (a)  coefficients  Log-sawing  follows,  Activities.  There are twelve log-sawing a c t i v i t i e s corresponding  to the twelve d i f f e r e n t  the  problem.  sawn, t h i s  W h i l e t h e i m p l i c a t i o n i s t h a t a n y l o g c a n be  may n o t i n f a c t be t r u e due t o t e c h n i c a l  t a t i o n s o f s i z e and s h a p e . t e c h n o l o g i c a l l y unsawable of  technically  c a n be b y p a s s e d i n t h e s e l e c t i o n I t was assumed h e r e t h a t a n y  s a w a b l e l o g w o u l d be d i r e c t e d t o a n a p p r o p r i a t e  log-sawing a c t i v i t y ,  and t h a t e c o n o m i c a l l y s a w a b l e  be d e t e r m i n e d f r o m t h e s e b y t h e l i n e a r  model, i n the l i g h t sawing-cost  limi-  However, any l o g s w h i c h a r e  log-sawing a c t i v i t i e s .  would  l o g categories considered i n  logs  programming  o f l u m b e r y i e l d s , l u m b e r p r i c e s and  data.  The l u m b e r y i e l d  f r o m any l o g i s d i v i d e d i n t o  four  c a t e g o r i e s , b a s e d on l u m b e r g r a d e s a p p r o v e d by t h e B r i t i s h C o l u m b i a Lumber M a n u f a c t u r e r s ' A s s o c i a t i o n , viz.  1.  Clear.  2. S e l e c t / M e r c h a n t a b l e . 3. C o n s t r u c t i o n / S t a n d a r d . 4. In activity,  Utility/Economy.  a d d i t i o n t o the lumber y i e l d  from each log-sawing  a c c o u n t was t a k e n o f t h e p r o d u c t i o n o f w a s t e -  wood s u i t a b l e f o r c h i p p i n g , a n d o f h o g - f u e l  (including  saw-  dust) s u i t a b l e only f o r burning.  42 S t a n d a r d G r a d i n g and D r e s s i n g R u l e s No. 59. British C o l u m b i a Lumber M a n u f a c t u r e r s ' A s s o c i a t i o n , V a n c o u v e r ,  (Feb.  1961).  52 The  y i e l d s o f intermediate product (lumber, chips  and hog f u e l ) r e s u l t i n g f r o m e a c h l o g - s a w i n g a c t i v i t y  are  shown i n T a b l e 5.2, e x p r e s s e d a s a p e r c e n t a g e o f t h e volume o f l o g consumed ( s a w n ) . f r o m numerous d i f f e r e n t activity  T h i s d a t a was c o m p i l e d a s a v e r a g e s s o u r c e s , d i s c u s s e d below.  c o e f f i c i e n t s o f each l o g - s a w i n g a c t i v i t y  The i n Figure  I a r e b a s e d o n t h e d a t a i n T a b l e 5.2, b u t e x p r e s s e d a s decimals.  T h i s i s so t h a t the c o e f f i c i e n t s w i l l  be r e a d i l y  a p p l i c a b l e t o a n y u n i t - v o l u m e o f l o g s consumed; a n d t h e u n i t - v o l u m e may be c o n v e n i e n t l y d e f i n e d t o s u i t any ular  partic-  s c a l e o f p r o b l e m and d a t a . Douglas  fir  lumber y i e l d s were o b t a i n e d p r i n c i p a l l y  f r o m d a t a p u b l i s h e d by the U n i t e d S t a t e s Department c u l t u r e , based on studies, conducted i n U n i t e d S t a t e s m i l l s west ington.  1+3 ' J  o f the Cascade  kk k^ kg k 7 » ' y  '  Mountains  of A g r i saw-  i n O r e g o n and Wash-  I t was assumed t h a t t h i s  Northwestern  3 E . E. M a t s o n , "Lumber G r a d e R e c o v e r y f r o m O r e g o n C o a s t T y p e D o u g l a s F i r , " U.S. D e p t . o f A g r i c u l t u r e , P a c . N.W. F o r e s t and Range E x p t . S t a . R e s e a r c h P a p e r No. 3, P o r t l a n d , O r e g o n , (May, 1952). L  M+ E . E . M a t s o n , "Lumber G r a d e s f r o m Y o u n g - G r o w t h D o u g l a s F i r , " U.S. D e p t . o f A g r i . , P a c . N.W. F o r e s t & Range E x p t . S t a . R e s e a r c h N o t e No. 79, P o r t l a n d , O r e g o n , ( S e p t . 1952). 5 E . E. M a t s o n , "Lumber G r a d e s f r o m D o u g l a s F i r P e e l e r L o g s , " U.S. D e p t . o f A g r i c , P a c . N.W. F o r e s t and Range E x p t . S t a . , R e s e a r c h N o t e No. 83, P o r t l a n d , O r e g o n , ( N o v . 1952). K  k6 E . E. M a t s o n , "Lumber G r a d e s f r o m O l d - G r o w t h D o u g l a s F i r S a w m i l l L o g s , " U.S. D e p t . o f A g r i c , P a c . N.W. F o r e s t and Range E x p t . S t a . , R e s e a r c h N o t e No. 125, ( J a n . 1956). 7 E. H. C l a r k e , "Lumber G r a d e R e c o v e r y f r o m O l d - G r o w t h D o u g l a s F i r a t a N o r t h w e s t e r n O r e g o n S a w m i l l , " U.S. D e p t . o f A g r i c . , P a c . N.W. F o r e s t and Range E x p t . S t a . , R e s e a r c h N o t e No. 191, P o r t l a n d , O r e g o n , ( O c t . I 9 6 0 ) . L  53 U n i t e d S t a t e s d a t a was a p p l i c a b l e t o t h e B r i t i s h  Columbia  c o a s t a l area, a f t e r appropriate adjustments f o r d i f f e r e n c e s i n t h e grade r u l e s .  Some C a n a d i a n D o u g l a s f i r  lumber  yield  d a t a was o b t a i n e d f r o m t h e F o r e s t P r o d u c t s L a b o r a t o r y , V a n c o u v e r , B. C .  k  Q  ^  Hemlock lumber y i e l d s a r e based on C a n a d i a n d a t a pub-  50 lished  by t h e F o r e s t P r o d u c t s L a b o r a t o r y i n V a n c o u v e r  and o n d i s c u s s i o n s w i t h m i l l m a n a g e r s o f l o c a l f o r e s t p r o d u c t s companies.  Spruce lumber y i e l d s a r e based s o l e l y  e s t i m a t e s s u p p l i e d b y m i l l managers i n t h e Vancouver The  upon  area.  c h i p y i e l d d a t a f o r s a w m i l l s was i n t e r p o l a t e d  from s e v e r a l sources.  I n t h e absence o f s p e c i f i c d a t a on  c h i p y i e l d s w i t h r e s p e c t t o l o g g r a d e o n t h e B. C. c o a s t , a c o r r e l a t i o n between w a s t e - c h i p p r o d u c t i o n and l o g diame t e r was a d o p t e d . ^  2  An average diameter f o r each l o g  48 C. F. M c B r i d e a n d J . M. K i n g h o r n , "Lumber D e g r a d e c a u s e d b y A m b r o s i a B e e t l e s , " B r i t i s h C o l u m b i a Lumberman, v . 44, ( J u l y , I 9 6 0 ) . 49 J . D o b i e , "A M i l l i n g S t u d y o f 150-year o l d D o u g l a s F i r , " P u b l i c a t i o n No. 1032, F o r e s t P r o d u c t s R e s e a r c h B r a n c h , C a n a d a , D e p t . o f F o r e s t r y , O t t a w a , 1962. 50  C. F. M c B r i d e , J . M. K i n g h o r n , op. c i t .  51 B. D o w d l e a n d R. B a i n , "Lumber o r C h i p s - A C o m p a r i s o n o f S m a l l - l o g U t i l i z a t i o n A l t e r n a t i v e s , " U.S. D e p t . o f A g r i c , Northeastern For. Expt. Sta., (I960). 52 M. E. H a m l i n , " E x p e r i e n c e R e p o r t - Wastewood a n d C h i p V o l u m e M e a s u r e m e n t , " Amer. P u l p w o o d A s s o c . , N o r t h e a s t T e c h . Comm. M i n u t e s , (1956).  5k  g r a d e was d e t e r m i n e d f r o m t h e l u m b e r y i e l d  d a t a and a c a l -  c u l a t i o n made o f t h e c h i p p a b l e w a s t e f r o m s a w i n g grade o f l o g .  each  The w e i g h t e d a v e r a g e d i a m e t e r s f o r e a c h l o g  grade v a r y w i t h sources o f l o g supply but t h e e s t i m a t e d c h i p - y i e l d data i s considered representative f o r the region as a whole. (b)  Log-peeling A c t i v i t i e s . Some g r a d e s o f l o g i n p u t a r e n o t e x p o s e d t o l o g -  p e e l i n g a c t i v i t i e s due t o t h e l i m i t a t i o n s o f l o g - p e e l i n g technology.  I n g e n e r a l , the l o w e s t grades o f any s p e c i e  h a v e v e r y p o o r v e n e e r y i e l d s and h i g h p e e l i n g a n d p a t c h i n g costs.  The p e e l i n g o f t h e s e l o g s i s t h e r e f o r e  t o be i n c l u d e d i n a n y p r o f i t - m a x i m i z i n g problem.  unlikely  solution to the  A c c o r d i n g l y we h a v e e x c l u d e d p e e l i n g  activities  f o r t h e No. 3 g r a d e s a w - l o g s o f e a c h s p e c i e i n t h e m o d e l . As w i t h t h e l o g - s a w i n g a c t i v i t i e s , log-peeling a c t i v i t y represent the y i e l d s  f i g u r e s i n each of veneer, chips  and h o g - f u e l , e x p r e s s e d a s a p e r c e n t a g e o f t h e volume o f l o g consumed ( p e e l e d ) .  A l l veneer y i e l d s a r e on a g r e e n -  v e n e e r b a s i s ; a p p r o x i m a t e l y e i g h t p e r c e n t volume  shrink-  age o c c u r s d u r i n g t h e v e n e e r d r y i n g s t a g e b u t t h i s accounted f o r l a t e r  loss i s  i n t h e plywood p r o d u c t i o n a c t i v i t y c o -  efficients. The  y i e l d s o f green veneer from Douglas f i r  logs,  shown i n T a b l e 5.3 were c o m p i l e d f r o m p u b l i s h e d r e s u l t s o f an e x t e n s i v e study c a r r i e d  o u t b y t h e U.S. D e p a r t m e n t o f  A g r i c u l t u r e , P a c i f i c N o r t h w e s t F o r e s t a n d Range E x p e r i m e n t a l  55 53 S t a t i o n , P o r t l a n d , Oregon,  and f r o m d i s c u s s i o n s  t h e a u t h o r and t e c h n i c a l e x p e r t s i n t h e plywood i n Vancouver.  between  industry  The p u b l i s h e d A m e r i c a n s t u d y c o v e r e d a s u r -  v e y o f 18 p l y w o o d  p l a n t s i n Oregon and W a s h i n g t o n ,  based on t h e veneer y i e l d f e e t of Douglas F i r l o g s .  a n d was  f r o m more t h a n f i v e m i l l i o n However, t h i s  board  s t u d y was c a r r i e d  o u t b e t w e e n 1950 a n d 1955 and t h e i n d u s t r y ' s t e c h n o l o g y h a s advanced  a p p r e c i a b l y i n t h e p a s t t e n y e a r s , so t h a t  s i d e r a b l e w e i g h t was g i v e n t o t h e c u r r e n t and u n o f f i c i a l )  (but estimated  data obtained from l o c a l experts.  p u b l i s h e d d a t a by McBride c o n c u r s w i t h t h e s e 54 estimates f o r the coastal region. veneer y i e l d s a r e based perts.  con-  Un-  unofficial  The h e m l o c k  and s p r u c e  s o l e l y on e s t i m a t e s by l o c a l e x -  The d a t a u s e d i n t h e m o d e l a n d shown i n T a b l e  a r e c o n s i d e r e d t o be a r e a l i s t i c  5.3  o v e r - a l l average f o r  c o a s t a l B. C. The  p r o d u c t i o n o f c h i p p a b l e waste  associated  with  log-peeling a c t i v i t i e s and A r m s t r o n g  i s based on d a t a quoted by G u t h r i e 55 f o r Western Oregon, from d a t a compiled by 56  Guernsey f o r B r i t i s h Columbia, and from i n f o r m a t i o n 53 E. H. C l a r k e a n d A. C. K n a u s s , " V e n e e r R e c o v e r y f r o m D o u g l a s F i r L o g s , " U.S. D e p t . o f A g r i c . P a c . N.W. F o r e s t a n d R a n g e E x p t . S t a . R e s e a r c h P a p e r No. 23, P o r t l a n d , O r e g o n , ( A u g . 1957). 54 C. F. M c B r i d e - u n p u b l i s h e d r e s u l t s . 55 J . A. G u t h r i e a n d G. R. A r m s t r o n g , W e s t e r n F o r e s t I n d u s t r y - A n E c o n o m i c O u t l o o k , The J o h n H o p k i n s P r e s s , B a l t i m o r e , (1961), p . 138. 56 F. W. G u e r n s e y , "Some C o n v e r s i o n F a c t o r s f o r B r i t i s h C o l u m b i a F o r e s t P r o d u c t s , " F o r e s t P r o d u c t s L a b o r a t o r y o f Cana d a p u b l i c a t i o n , V - 1027, D e p t . o f N o r t h e r n A f f a i r s a n d N a t i o n a l R e s o u r c e s , O t t a w a , (1959).  56 prepared  by t h e I n s t i t u t e  57  of F o r e s t P r o d u c t s , Washington, ' J  H o g - f u e l p r o d u c t i o n i s b a s e d on d a t a f r o m t h e same sources.  The  applicability  of a l l data to c o n d i t i o n s i n  c o a s t a l B r i t i s h C o l u m b i a was (c)  Log-chipping  c o n f i r m e d by l o c a l  Activities.  These a c t i v i t i e s  r e p r e s e n t the simple process  c o n v e r t i n g an e n t i r e l o g i n t o p u l p c h i p s . A c c o r d i n g l y , t h e r e a r e 12  chipped. to  meet t h e 12  Any  volume, as c h i p s .  In practice  this  r e p r e s e n t s an  Technological Coefficients  Activities.  We (a)  shall  selling  - Final  include both  Activities.  i n the model.  p o s s i b l e plywoods which veneers  The  grades  c o u l d be m a n u f a c t u r e d  mathematical  f o r each plywood grade.  possibilities  from  theoretically  from  these  thicknesses, panel  (number o f l a y e r s o f v e n e e r ) , and  m i x t u r e s of veneer  produced  number o f  depends upon the v a r i o u s veneer  thickness  earlier.  s e p a r a t e l y , below,  There are nine d i f f e r e n t veneer peeling activities  over  recombination  a c t i v i t i e s , as d i s c u s s e d  d i s c u s s each of these  Plywood P r o d u c t i o n  It  s c r e e n i n g the  fuel.  final activities  be  percent r e c o v e r y of the l o g  c h i p s a r e n o r m a l l y d i v e r t e d t o hog  and  l o g can  log-chipping activities  e s t i m a t e , f o r f i n e p a r t i c l e s recovered from  activities  of  d i f f e r e n t l o g c a t e g o r i e s i n the model.  i s assumed t h a t t h e r e i s 100  The  experts,  the  specific  The  number o f  i s v e r y l a r g e , b u t many c a n  be  r e a d i l y e l i m i n a t e d i n t h e m o d e l as i m p r a c t i c a b l e a l t e r n a t i v e s .  57 Anon. C o n v e r s i o n F a c t o r s f o r P a c i f i c N o r t h w e s t F o r e s t Products, I n s t i t u t e of Forest Products, S e a t t l e , Washington, ( J u n e , 1957).  57 The D o u g l a s - f i r p l y w o o d s  i n t h i s model a r e based  upon  Canadian Standards A s s o c i a t i o n s p e c i f i c a t i o n s w i t h regard t o the p a r t i c u l a r veneer grades i n each plywood.  The a c t u a l  percentage o f each veneer grade i n a p a r t i c u l a r  plywood  depends upon v e n e e r t h i c k n e s s and p a n e l t h i c k n e s s . plicity,  F o r sim-  a s t a n d a r d p a n e l t h i c k n e s s o f 3 / 8 i n c h i s assumed  and t h e r e l a t i v e p r o p o r t i o n s o f e a c h g r a d e o f v e n e e r i n t h e v a r i o u s plywoods  i s b a s e d o n d a t a p r o v i d e d b y l o c a l manu-  facturers. The  r e m a i n i n g plywood p r o d u c t i o n a c t i v i t i e s  m i x e d - s p e c i e and n o n - D o u g l a s - f i r , s i n g l e - s p e c i e  concern  plywoods.  These a r e n o t i n f a c t produced t o any l a r g e e x t e n t on t h e c o a s t and m a n u f a c t u r i n g s p e c i f i c a t i o n s a r e n o t r e a d i l y available. fir  E s t i m a t e s were o b t a i n e d h o w e v e r b a s e d o n D o u g l a s -  specifications. The  plywood-production a c t i v i t y  shown i n T a b l e 5*k.  coefficients are  These a r e c a l c u l a t e d  on a d r y - v e n e e r  b a s i s , a c c o u n t i n g f o r a n assumed volume s h r i n k a g e o f 8 p e r cent f o r a l l  veneers i n t h e drying  S a n d i n g l o s s e s o f Ik  stage a f t e r  p e r c e n t o f t h e g r e e n - v e n e e r volume  for a.3/8 inch panel are included f o r a l l cept D o u g l a s - f i r s h e a t h i n g grade unsanded plywood).  peeling.  plywoods ex-  ("sheathing grade"  infers  These a d j u s t m e n t s l e a d t o a r e q u i r e -  ment o f a p p r o x i m a t e l y 1 . 2 8 c u b i c f e e t g r e e n v e n e e r t o p r o d u c e one c u b i c f o o t o f s a n d e d p l y w o o d , a n d 1 . 0 9 c u b i c  feet  5 8 D o u g l a s F i r P l y w o o d - CSA/0121/1961, C a n a d i a n S t a n d a r d s A s s o c i a t i o n , Queen's P r i n t e r s , O t t a w a , ( 1 9 6 1 ) .  58 g r e e n v e n e e r t o p r o d u c e one ing  plywood.  The  plywood p r o d u c t i o n  veneer are expressed veneer r e q u i r e d per (b)  c u b i c f o o t of unsanded or  c u b i c f o o t of plywood produced. Activities. seven pulp p r o d u c t i o n  model are based r o u g h l y  production Since  o f one  the pulp  outputs the  The  activities  on t h e p r i n c i p a l t y p e s  r e n t l y produced i n B r i t i s h Columbia. hypothetical.  c o e f f i c i e n t s f o r green  on a b a s i s o f t h e c u b i c f e e t g r e e n  Pulp Production Three of the  sheath-  activity air-dried  The  of pulp  remainder  c o e f f i c i e n t s are based ton of pulp  chip inputs are  i n each  cur-  are on  activity.  i n v o l u m e - u n i t s and  i n weight u n i t s , a conversion  in this  activity  factor is built-in  c o e f f i c i e n t s t o a c c o u n t f o r t h i s change i n u n i t s .  calculated activity (c)  c o e f f i c i e n t s are  to The  5.5.  shown i n T a b l e  Log-selling Activities. One  u n i t of l o g i n p u t i s o b v i o u s l y necessary  u n i t of output from each l o g - s e l l i n g Figure  I).  The  activity  per  ( a s shown i n  u n i t - l e v e l of each l o g - s e l l i n g  activity  t h e r e f o r e depends upon the u n i t - v o l u m e s e l e c t e d i n the intermediate (d)  activities.  Lumber-selling The  Activities.  lumber produced from the l o g s i n the model  be  considered  It  i s assumed t h a t no p h y s i c a l t r a n s f o r m a t i o n  selling input  as a n i n p u t t o t h e  activities  and  may  lumber-selling a c t i v i t i e s . occurs  hence e a c h c u b i c f o o t of  ( l u m b e r ) r e s u l t s i n e x a c t l y one  intermediate  cubic foot of  s o l d , so t h a t t h e l u m b e r - s e l l i n g a c t i v i t y  i n the  lumber  coefficients  each  59 have a value selling ing (e)  o f one.  activity  a total  of  f o r each intermediate  lumber i n p u t , g i v - .  activities  are constructed  t o the l u m b e r - s e l l i n g a c t i v i t i e s .  assumed t h a t no p h y s i c a l t r a n s f o r m a t i o n p e e l i n g and s e l l i n g sanded  veneer).  distinct  Activities.  veneer s e l l i n g  manner s i m i l a r  and  twelve.  Veneer-selling The  There i s a separate  veneer ( t h e market  occurs  It is between  i s f o r green un-  Each cubic f o o t of intermediate  a veneer-selling activity  input  c o r r e s p o n d s t o e x a c t l y one  f o o t o f v e n e e r s o l d , so t h a t t h e v e n e e r - s e l l i n g c o e f f i c i e n t s have a v a l u e activity  f o r each d i f f e r e n t  giving a total (f)  o f one.  of nine  intermediate  cubic  activity  separate  veneer  input  Chip-selling Activities.  responding to the three  chip-selling activities,  log species.  i s produced by t h e i n t e r m e d i a t e  The  total  chip  activities, efficient  chip-supply  inputs.  c h i p p i n g and  s e l l i n g , and one c u b i c f o o t o f c h i p s  Hog-fuel S e l l i n g An a c t i v i t y  supply  of the selling  has a t e c h n i c a l c o -  no p h y s i c a l c h a n g e s  r e q u i r e s one c u b i c f o o t o f c h i p s  produced  L i k e the other  each c h i p - s e l l i n g a c t i v i t y  o f one, t h e r e b e i n g  cor-  a c t i v i t i e s , sawing, p e e l -  and c h i p p i n g , e a c h o f w h i c h c o n t r i b u t e s t o one  intermediate  (g)  There i s a  to  veneer-selling activities.  There are o n l y three  ing  in a  between sold  input.  Activity.  t o a c c o u n t f o r t h e d i s p o s a l o f hog  i n t h e s a w i n g and p e e l i n g a c t i v i t i e s  fuel  i s required  60 t o make t h e m o d e l c o m p l e t e .  Like the other  selling  activi-  t i e s , one c u b i c f o o t o f hog f u e l s o l d r e q u i r e s one c u b i c foot input. II.  i s t h e r e f o r e one.  UNIT-LEVEL RETURNS OF THE A C T I V I T I E S  The be  The t e c h n i c a l c o e f f i c i e n t  u n i t - l e v e l returns of the various a c t i v i t i e s  discussed  discussed  i n t h e same o r d e r a s t h e t e c h n i c a l c o e f f i c i e n t s  i n the preceding  s e c t i o n , beginning  mediate a c t i v i t i e s which produce outputs the remaining The zero  final  with the i n t e r -  f o r consumption by  activities.  l o g supply  cost.  will  i n t h e m o d e l i s assumed g i v e n , a t  The o b j e c t i v e f u n c t i o n t h e r e f o r e c o n s i s t s o f  e n t r e p r e n e u r i a l p r o f i t p l u s economic r e n t t o t h e l o g supply. be  A d i s c u s s i o n o f t h e p u r e l y p r o f i t - m a x i m i z i n g case  found i n chapter  will  s i x , d e a l i n g w i t h an a p p l i c a t i o n o f  t h i s model t o t h e l o g - a l l o c a t i o n p r o b l e m o f a n i n t e g r a t e d firm. Intermediate (a)  Activity Unit-level  Sawing A c t i v i t y  Returns,  Returns.  When a v a r i e t y o f l o g s a r e p r o c e s s e d no  i n a sawmill  a t t e m p t i s made t o d e t e r m i n e t h e l u m b e r o u t p u t p e r l o g .  I n d e e d , t h e c o l l e c t i o n o f s u c h d a t a w o u l d be p r a c t i c a l l y i m p o s s i b l e i n most s a w m i l l s w i t h o u t duction.  s e r i o u s l y d i s r u p t i n g pro-  Hence most p r o d u c t i o n d a t a i s r e p o r t e d  average-log  basis.  Rather than attempt t o assess each type  on a n  the sawing cost f o r  a n d g r a d e o f l o g i n v o l v e d i n t h e m o d e l i t w i l l be  assumed t h a t s a w i n g c o s t s p e r u n i t v o l u m e o f l o g a r e c o n s t a n t .  61  I n t e r - i n d u s t r y comparisons o f l o g - c o n v e r s i o n g i v e a n average f i g u r e o f $26.00 per  Rankin^  c o s t s by  thousand  feet  b o a r d m e a s u r e ( a b b r e v i a t e d MBM) o f l u m b e r p r o d u c e d , f o r sawing  costs i n the c o a s t a l r e g i o n o f B r i t i s h Columbia.  This  f i g u r e i n c l u d e s s e l l i n g , a d m i n i s t r a t i o n , d e p r e c i a t i o n and a l l manufacturing To  c o s t s , but  convert  this  i s exclusive oflog costs.  f i g u r e t oa log-volume b a s i s an aver-  age  lumber y i e l d  f i g u r e f o r a l l l o g s i n c l u d e d i n the  was  c a l c u l a t e d from the data  o fTable 5 . 2 . T h i s ,  model  multiplied  by R a n k i n ' s a v e r a g e s a w i n g - c o s t f i g u r e gave a n a v e r a g e l o g sawing c o s t o f $20.00 per type  o f l o g i n the model.  (b)  Peeling-activity Cost data  Figure I .  f o r plywood p r o d u c t i o n are a l s o o n l y  c a l c u l a t e log-sawing  located  See  Returns.  able on an average-log  estimate  hundred c u b i c f e e t o f l o g , f o r each  basis.  avail-  The method o u t l i n e d a b o v e t o  c o s t s o n a l o g - v o l u m e b a s i s was u s e d t o  p e e l i n g costs per u n i t o f each specie o f l o g a l t othe p e e l i n g a c t i v i t i e s .  The c a l c u l a t i o n gave a n  average p e e l i n g c o s t o f $6.00 per hundred c u b i c f e e t o f l o g peeled (c)  for a l l peeling a c t i v i t i e s  i n t h e m o d e l . See  Figure I .  C h i p p i n g - a c t i v i t y Returns. Chipping  c o s t s i n the model are based on r e c e n t  given by M c B r i d e ^ f o r chipping  i n the  interior  data  region of  59 A. G. R a n k i n , " C o s t - P r i c e R e l a t i o n s h i p s i n t h e F o r e s t I n d u s t r y , " The F o r e s t r y C h r o n i c l e , v . 3 9 , ( M a r . 1 9 6 3 ) , PP. 6 9 77.  60 C. F. M c B r i d e , " B a r k i n g and C h i p p i n g i n t h e I n t e r i o r o f B r i t i s h C o l u m b i a , " C a n a d a Lumberman, v.83 , ( J u l y , 1 9 6 3 ) ,  pp. 53-55  .  62 B r i t i s h Columbia, and on the estimates of personnel i n the industry.  A cost of $2.00 per 100 cubic feet of log chipped  was adopted f o r a l l logs included i n the model, see Figure I . Recombination A c t i v i t y U n i t - l e v e l Returns. These a c t i v i t i e s represent plywood production and pulp production,and chips.  use the intermediate inputs, veneer and  The u n i t - l e v e l returns of these a c t i v i t i e s are based  on recent market prices, (a)  Plywood Production A c t i v i t y Returns. U n i t - l e v e l returns f o r the pure Douglas-fir plywoods  are based on November, 1963 prices quoted by a major Vancouver producer f o r 3/8 inch panels.  The prices were con-  verted to a 100 cubic foot plywood basis to correspond to the units used i n the veneer-peeling  activities.  See  Figure I . Table 5.7 shows the price data used f o r calculating u n i t - l e v e l returns f o r the Douglas f i r , hemlock, spruce and mixed-specie plywoods i n the model.  The hemlock, spruce and  mixed-specie price data are quite a r b i t r a r y . The u n i t - l e v e l return of each plywood-production a c t i v i t y was calculated by subtracting plywood manufacturing cost from market price.  Manufacturing  cost i s the cost  of a l l stages of plywood production beyond the veneer-sell i n g stage ( i . e . , after the veneer has been peeled and chipped into standard facture) .  sizes suitable f o r shipping or further manu-  The veneer-peeling  a c t i v i t i e s , as explained ear-  l i e r , incorporate manufacturing costs up to the green-veneer  63 s e l l i n g stage. Plywood-production  costs are taken from published  data (which unfortunately was several years old) and from 61 the estimates of experts.  Costs incurred i n the various  stages of plywood production are expressed as percentages of  sales price i n Table 5 . 7 .  From these, the u n i t - l e v e l  return values i n Table 5.6 are calculated by deducting plywood manufacturing  costs comprising drying, lay-up and  pressing, trimming, patching, sanding (where applicable) and shipping costs from the market price, (b)  Pulp Production A c t i v i t y Returns. Pulp production u n i t - l e v e l returns i n the model  are calculated by deducting pulp production costs, excluding  the cost of chips, from recent market prices.  pulp-manufacturing  The  cost adopted i n the c a l c u l a t i o n i s  14-3.00 per air-dry short ton of pulp, for a l l pulp-production a c t i v i t i e s i n the model. for  This i s an average  figure  t y p i c a l kraft pulp m i l l s i n the coastal region, based on 62  estimates by an expert i n the f i e l d .  The market prices f o r  pulp are s i m i l a r i l y based on well-informed estimates.  Since  there i s no large open market f o r t h i s product, these f i g ures are no more than estimates of recent average 61to'.E. Mayhew, "A New Method of Allocating Costs to Veneer by Grades," For. Prod. Journ., v. 8 , (Aug. 1 9 5 8 ) , pp.  27A-30A.  62 Ian Hudson, Senior Development Engineer, Sandwell & Co. Ltd., Consulting Engineers, Vancouver, B.C.  64  prices.^  Most p u l p s produced i n N o r t h A m e r i c a are s o l d  in  t h e U n i t e d S t a t e s a t a u n i f o r m d e l i v e r e d - p r i c e anywhere i n the country.  P u l p p r i c e s a t the m i l l  are t h e r e f o r e g r e a t l y 6U  i n f l u e n c e d by t h e p r o x i m i t y o f t h e m i l l s '  customers.  F o r t h e p u r p o s e o f t h i s a n a l y s i s an a v e r a g e  mill-net  p r i c e o f $115.00 p e r a i r - d r y s h o r t - t o n o f p u l p i s a d o p t e d . Using  this  v a l u e as a b a s e , market p r i c e s a r e e s t i m a t e d  each of the s e v e r a l p u l p s i n the model. Selling Activity Unit-level The  selling  See  Table  for  5.8.  Returns.  a c t i v i t y u n i t - l e v e l r e t u r n s are  simply  t a k e n f r o m r e c e n t m a r k e t p r i c e s , o r e s t i m a t e s where m a r k e t p r i c e s are not a v a i l a b l e . o f p l y w o o d and previous  returns  p u l p - p r o d u c t i o n a c t i v i t i e s d i s c u s s e d i n the  s e c t i o n , a c t u a l m a r k e t d a t a a r e much more  available i n published (a)  U n l i k e the u n i t - l e v e l  form,  Log-selling Activity The  readily  Returns.  unit-level returns for log-selling a c t i v i t i e s  are  b a s e d on c u r r e n t l o g p r i c e s p u b l i s h e d i n t h e B r i t i s h C o l u m 65  b i a Lumberman.  S i n c e most l o g p r i c e s i n t h i s  reference  63 M o s t wood p u l p i n N o r t h A m e r i c a i s s o l d u n d e r c o n t r a c t a t p r i c e s a n n o u n c e d q u a r t e r l y by t h e p r o d u c e r s . Most s a l e s a r e c o n d u c t e d t h r o u g h a g e n t s whose s t a n d a r d f e e i s t h r e e p e r cent of s e l l i n g p r i c e , l e s s f r e i g h t , u n l e s s s a l e s are to a c a p t i v e market i n w h i c h case c o m m i s s i o n s a r e not p a i d . 64 For example, a pulp m i l l i n the c o a s t a l r e g i o n f a c e s about a t e n d o l l a r d i f f e r e n t i a l i n i t s m i l l - n e t p r i c e s bet w e e n E a s t e r n and W e s t e r n U n i t e d S t a t e s m a r k e t s ; and up t o t w e n t y d o l l a r s d i f f e r e n t i a l b e t w e e n E a s t e r n U n i t e d S t a t e s and o t h e r w o r l d m a r k e t s where f r e i g h t c o s t s , p a i d by t h e p r o d u c e r , c u t more s e v e r e l y i n t o m i l l - n e t p r i c e . 65 R o b e r t S c h u l t z & Co. L t d . , Log P r i c e R e p o r t , B r i t i s h C o l u m b i a Lumberman, v. 47 ( O c t o b e r , 1963)? p. 80.  show a $10,00 s p r e a d b e t w e e n h i g h e s t and l o w e s t p r i c e s p a i d , t h e a v e r a g e o r m e d i a n o f t h e p r i c e s shown was See T a b l e  5.9.  selec-  ted  f o r the model.  A conversion factor of  six  f e e t - b o a r d - m e a s u r e l o g s c a l e e q u a l s one c u b i c f o o t , i s  used t o convert l o g values t o the u n i t s used i n the model.^ (b)  Lumber-selling A c t i v i t y  Returns.  Unit-level returns f o r lumber-selling a c t i v i t i e s are based on r e t a i l coastal region. (c)  p r i c e s quoted by a major p r o d u c e r See T a b l e  5.10.  Veneer-selling Activity  Returns.  M a r k e t - p r i c e data f o r veneers although t h i s product the United S t a t e s .  i n the  i s difficult  to obtain  i s marketed t o a l i m i t e d extent i n  The u s e f u l n e s s o f t h e a v a i l a b l e d a t a i s  f r e q u e n t l y l i m i t e d by t h e grouping s i n g l e average p r i c e s .  o f veneer grades under  Moreover, hemlock and spruce  are very r a r e l y s o l d as such.  veneers  Most o f t h e data i n Table  5.11  a r e e s t i m a t e s , p a r t i c u l a r l y t h e v a l u e s f o r hemlock and spruce.  Neither of these l a t t e r  s p e c i e s i s used f o r f a c e -  v e n e e r a t p r e s e n t , so t h a t t h e &. and B g r a d e p r i c e s a r e assumed t o be e q u i v a l e n t t o D o u g l a s f i r C and D  grades,  w h i c h a r e used e x c l u s i v e l y as plywood " c o r e " m a t e r i a l .  66 6 FBM l o g s c a l e = 1 c u b i c f o o t i s t h e g e n e r a l l y a c cepted conversion f a c t o r f o r the c o a s t a l region. I n the i n t e r i o r o f B.C., a n o f f i c i a l c o n v e r s i o n f a c t o r o f 5.75 FBM l o g s c a l e = 1 c u b i c f o o t i s u s e d . See C o n v e r s i o n F a c t o r s f o r P a c . N.W. F o r . P r o d u c t s , I n s t i t u t e o f F o r e s t P r o d u c t s , S t a t e o f W a s h i n g t o n , j O j A n d e r s e n H a l l , S e a t t l e 5, W a s h i n g t o n , 1957.  66 (d)  C h i p - s e l l i n g A c t i v i t y Returns. The u n i t - l e v e l returns of c h i p - s e l l i n g a c t i v i t i e s  are based on chip prices recently paid i n the Vancouver chip market.  These prices are available on a "unit"  67  basis,  and a conversion factor of 'one unit equals  67  cubic feet solid wood' i s used to convert the date to cubi c feet, to meet the requirements of the model. Table  See  5.12. III.  RESTRAINTS  A d i s t i n c t i o n has already been drawn between the primary input r e s t r a i n t s , which comprise the available supp l y of logs, and the intermediate input r e s t r a i n t s , which stipulate that a l l intermediate products  (lumber, veneer  and chips) are to be completely consumed as input to f i n a l activities.  Since intermediate products are e n t i r e l y con-  sumed by f i n a l a c t i v i t i e s i t follows that the values of the intermediate r e s t r a i n t s must be zero.  I t remains there-  fore to discuss the sources of data for the primary input restraints.  67 A "unit" of chips i s defined as 200 cubic feet gross, volume of uncorapacted chips. The s t i p u l a t i o n 'uncompacted' i s i n d e f i n i t e , for the several methods of storing and transporting chips lead to various degrees of compaction. A more rigorous q u a n t i f i c a t i o n that i s finding increasing acceptance i s the "bone-dry u n i t , " defined as the quantity of pulp chips which w i l l weigh 24-00 pounds i n an oven-dry condition.  67 The  \  log supply data are based on the annual log scale  of the B r i t i s h Columbia coastal region forest industry.  Log  scale data for each specie i n the model are available i n the 1962  Annual Report of the B r i t i s h Columbia Forest  Service.  In addition, a breakdown of the log scale by log-grades obtained from industry personnel and  statisticians.  supply data are summarized i n Table  5.1.  IV.  was  The  log  METHOD OF SOLUTION  Elementary l i n e a r programmes involving only a  few  a c t i v i t i e s and r e s t r a i n t s can be solved by hand using 68  the  simplex method.  ma-  More complicated programmes require  chines to handle the very large quantities of data  involved.  A machine solution of the l o g - a l l o c a t i o n model presented i n this thesis was  carried out on the IBM  1620  d i g i t a l com-  puter i n the computing centre of the University of B r i t i s h Columbia. In this chapter we s h a l l b r i e f l y describe and  the format  special features of the machine programme employed i n  obtaining a solution to the model.  Three variations of the  model that were solved to demonstrate i t s p r a c t i c a l a p p l i cation w i l l then be outlined. w i l l be presented and discussed IBM  1620  Results of these solutions l a t e r i n chapter s i x .  Computer Programme.  The machine programme used i s i d e n t i f i e d as: 68 M. J. Baumol, Economic Theory and Operations Analysis, Prentice H a l l Inc., C a l i f . , (June, 1962) , ch. !?.  68  "1620 L i n e a r Programming Code f o r Card Input/Output," byN i c h o l s , N i c k e l and D a v i s . P r o c e d u r a l d e t a i l s and mathematical elements of  the  programme are f u l l y d i s c u s s e d i n the above r e f e r e n c e , and need not be repeated h e r e . characteristics  However,  some important p r o p e r t i e s and  of the programme which are of i n t e r e s t  particular application, S p e c i a l Features  to  this  follow.  of the Machine Programme.  The programme i s designed f o r input from c a r d s .  All  output i s on the t y p e w r i t e r although an o p t i o n a l f i n a l m a t r i x punch-out on cards i s a v a i l a b l e .  The s i z e of problem  which can be handled by t h i s programme i s l i m i t e d by memoryc a p a c i t y of the computer a c c o r d i n g to the f o l l o w i n g  relation-  ship. (m + 2 ) where:  (n + 3)  *  m i s the number of  memory - 3920 10  restrictions,  n i s the number of ' r e a l '  activities,  and  'memory' i s equal to 40,000 f o r the p a r t i c u l a r machine i n the U n i v e r s i t y  comput-  ing c e n t r e . The term ' r e a l ' the  'disposal'  a c t i v i t i e s r e f e r s to those other  activities.  The l a t t e r are a c t i v i t i e s d e -  signed to convert the i n e q u a l i t y r e s t r a i n t equalities.  than  For the intermediate  expressions into  input r e s t r a i n t s ,  selling  a c t i v i t i e s were i n c l u d e d as the corresponding d i s p o s a l a c t i v i t i e s and f o r computational purposes these  selling  69 a c t i v i t i e s cannot t h e r e f o r e mathematical sense. i n Figure  as ' r e a l ' ,  to give  i n the  F o r t h e l o g - a l l o c a t i o n p r o b l e m shown  a r e m = 37 r e s t r a i n t s a n d n = 57  I there  activities,  be c o n s i d e r e d  a value  of the c a p a c i t y expression hand s i d e o f t h e e x p r e s s i o n There are three  'real'  o f 2340 f o r t h e l e f t - h a n d above.  The v a l u e  side  of the r i g h t -  i s 3908.  special features  of t h i s  computer  programme w h i c h make i t q u i t e v e r s a t i l e , a n d p a r t i c u l a r l y u s e f u l t o the l o g - a l l o c a t i o n problem under  discussion.  (i)  activities, i n  C o s t o r p r i c e changes f o r t h e v a r i o u s  terms o f the o r i g i n a l data, reload  or re-solve  c a n be made w i t h o u t h a v i n g t o  the o r i g i n a l matrix.  These changes a r e  i n s t i t u t e d by i n s e r t i n g a s p e c i a l deck o f c a r d s ,  referred  t o a s t h e ' C o s t C h a n g e r ' d e c k , i n t o t h e o v e r - a l l programme, u s u a l l y behind the o r i g i n a l - d a t a cards. programme i n t o t h e m a c h i n e a s t o p C o s t Changer e n t r y  the  typewriter.  i s executed a f t e r the  and t h e r e q u i r e d  c h a n g e ) d a t a c a n t h e n be e n t e r e d An u n l i m i t e d  When e n t e r i n g t h e  cost  change ( p r i c e  e i t h e r by c a r d  input  o r by  number o f c o s t c h a n g e s may be  made i n a n y s i n g l e r u n . (ii) out  The r e s t r a i n t s o f t h e p r o b l e m c a n a l s o be v a r i e d reloading  or re-solving the o r i g i n a l matrix.  with-  These  c h a n g e s a r e a c h i e v e d i n e x a c t l y t h e same manner a s c o s t changes, by i n s e r t i n g a s p e c i a l deck o f c a r d s r e f e r r e d t o as  the ' R H 3 Changer', ( r i g h t - h a n d  f o r RHS  c h a n g e s may be e n t e r e d  s i d e changer) deck.  b y c a r d s o r by  Data  typewriter  f o r a n u n l i m i t e d number o f c h a n g e s i n a n y s i n g l e r u n . B o t h  70  c o s t a n d RHS C h a n g e r d e c k s c a n be i n c l u d e d (iii)  i n t h e programme,  The o v e r - a l l programme c o n s i s t s o f s e v e r a l  ly  i n d e p e n d e n t sub-programmes w h i c h c a n be d e l e t e d  ed  i n many r e s p e c t s w i t h o u t  programmes.  Sequential  automatic.  relativeor a l t e r -  i n t e r f e r e n c e w i t h other sub-  l o a d i n g o f t h e sub-programmes i s  This feature enables a s k i l l e d  grammer t o m a n i p u l a t e t h e v a r i o u s  computor  pro-  sub-programmes t o make  adjustments i n the a c t u a l s o l u t i o n procedure. Programme O u t p u t - F o r m a t . I f d e s i r e d , t h e r e s u l t s of each i t e r a t i o n i n the s o l u t i o n o f t h e p r o b l e m may b e t y p e d put.  out as p a r t o f the out-  A l t e r n a t e l y , t h e c o u r s e o f t h e s o l u t i o n may be m o n i -  t o r e d by s e t t i n g an a p p r o p r i a t e ically. sists  s w i t c h o n and o f f p e r i o d -  The i n f o r m a t i o n m o n i t o r e d f o r e a c h i t e r a t i o n  o f t h e i t e r a t i o n number, v a l u e  of the objective  f u n c t i o n , t h e p a r t i c u l a r v a r i a b l e ( a c t i v i t y ) removed the previous  con-  from  s o l u t i o n , and t h e p a r t i c u l a r v a r i a b l e i n s e r t e d  into the l a t e s t solution. The  value  of the objective f u n c t i o n increases  maximizing problem) w i t h each s u c c e s s i v e the  f i n a l or optimal  been obtained cards (i) (ii)  or typed The f i n a l  value.  (in a  i t e r a t i o n up t o  When t h e o p t i m a l  s o l u t i o n has  a F i n a l B a s i s Output i s e i t h e r punched on out, containing value  the f o l l o w i n g  information:  of the objective function.  The i d e n t i f i c a t i o n number a n d i n p u t p r i c e ( c o s t ) o f  each a c t i v i t y  i n the Final Basis.  (These a c t i v i t i e s  r e s p o n d t o t h e ones t o be e m p l o y e d t o r e a c h  cor-  a n optimum  71 value  of the o b j e c t i v e f u n c t i o n ) .  (iii)  The " l e v e l " a t w h i c h e a c h a c t i v i t y i n t h e F i n a l  i s t o be o p e r a t e d , "unit-level" (iv) ity  Basis  expressed as a m u l t i p l e o f the a c t i v i t y ' s  defined  i n the o r i g i n a l  problem.  The u p p e r and l o w e r l i m i t s t o t h e l e v e l o f e a c h  activ-  i n t h e F i n a l B a s i s , b e y o n d w h i c h t h e a c t i v i t y w o u l d be  d r o p p e d f r o m t h e F i n a l B a s i s and r e p l a c e d w i t h a F i n a l NonBasis a c t i v i t y . (v)  The F i n a l N o n - B a s i s a c t i v i t i e s w h i c h w o u l d  F i n a l B a s i s i n t h e e v e n t t h a t one o f t h e F i n a l activities The  exceeded  remainder of the optimal s o l u t i o n c o n s i s t s of a containing the f o l l o w i n g information.  The i d e n t i f i c a t i o n number a n d i n p u t p r i c e ( c o s t ) o f  each a c t i v i t y i n the F i n a l (vii) value  Basis  one o f i t s l i m i t s .  F i n a l Non-Basis Output (vi)  enter the  Non-Basis.  The "shadow p r i c e " o f e a c h n o n - b a s i s a c t i v i t y . represents  This  t h e p e n a l t y t o t h e whole system i f a u n i t  of t h i s a c t i v i t y i s forced i n t o the f i n a l  solution.  other words, i f a non-basis a c t i v i t y (excluded  In  from the  o p t i m a l plan) i s i n f a c t used or f o r c e d i n t o the f i n a l  plan  of a c t i v i t i e s (contrary t o optimal conditions) i tw i l l  incur  a l o s s t o t h e s y s t e m e q u a l t o i t s shadow p r i c e p e r u n i t o f the a c t i v i t y used. (viii)  The u p p e r and l o w e r l i m i t s t o t h e l e v e l a t w h i c h  a c t i v i t y c o u l d be f o r c e d i n t o t h e s o l u t i o n .  this  As more and  more o f t h i s a c t i v i t y i s u s e d t h e l o s s i n c u r r e d goes u p , until  e v e n t u a l l y some o t h e r  forced out.  a c t i v i t y i n the F i n a l Basis i s  72 (ix) tion  The F i n a l B a s i s v a r i a b l e s w h i c h w o u l d l e a v e t h e s o l u (be f o r c e d o u t ) f o l l o w i n g  the events  of ( v i i i )  A punch-out on cards o f t h e complete is  optional.  comes c o m p l e t e for  final  above.  matrix  When o b t a i n e d , t h e m a t r i x , d e c k p u n c h - o u t w i t h c o n t r o l cards, i n a format  suitable  d i r e c t r e l o a d i n g by the normal Data Loader  routine.  Transformation of Results. The  output  format  o f t h e s o l u t i o n programme, o u t -  l i n e d above, i s d i f f i c u l t  to interpret.  An a u x i l i a r y  gramme was w r i t t e n t h e r e f o r e t o t r a n s f o r m t h e o u t p u t  prodata  i n t o a f o r m more c o n s i s t e n t w i t h t h e l o g - a l l o c a t i o n m o d e l and  more e a s i l y u n d e r s t o o d Using the f i n a l  by t h e i n t e r e s t e d  s o l u t i o n as i n p u t , on c a r d s ,  programme a d j u s t s a c t i v i t y l e v e l s basis,computes  reader.  to a  this  hundred-cubic-foot  t o t a l r e t u r n f o r each a c t i v i t y and d i s c a r d s  t h e F i n a l Mom-Basis v a r i a b l e - l i m i t s . c o l l e c t e d and r e a r r a n g e d  The s o l u t i o n d a t a i s  i n t o a more r e a d a b l e f o r m .  Maxi-  mum v a l u e o f t h e o b j e c t i v e f u n c t i o n a n d number o f i t e r a t i o n s r e q u i r e d t o r e a c h a s o l u t i o n a r e shown, a n d e a c h c o l u m n o f f i g u r e s i s given a c l e a r l y understood the a p p r o p r i a t e u n i t s . gramme o u t p u t V.  heading  including  A sample o f t h e t r a n s f o r m a t i o n p r o -  i s shown i n A p p e n d i x I t o t h i s SOLUTION OF LINEAR  thesis.  PROGRAMME  Three v a r i a t i o n s o f t h e l o g - a l l o c a t i o n l i n e a r gramme m o d e l p r e s e n t e d follows:  i nthis  t h e s i s were s o l v e d , a s  pro-  A P P E N D I X T HA  P T E R  0 F I V E  73  Case  I . U s i n g t h e data p r e s e n t e d i n c h a p t e r f i v e , as shown i n F i g u r e I .  Case  I I . U s i n g t h e same d a t a as i n Case I but with modified a c t i v i t y  coefficients  f o r t h e No. 3 hemlock l o g - s a w i n g activity. Case I I I .  U s i n g the same d a t a as i n Case I I but with a modified l o g supply.  D e t a i l s o f t h e m o d i f i c a t i o n s i n Case I I and Case I I I a r e shown i n T a b l e s 5.13 and 5.14 r e s p e c t i v e l y . A p a r t from d e m o n s t r a t i n g t h a t t h e Cost Changer subprogramme works e f f e c t i v e l y , these m o d i f i c a t i o n s i n Case I I and Case I I I p r o v i d e a u s e f u l i n s i g h t i n t o p r a c t i c a l  appli-  c a t i o n s o f the model, which we s h a l l d i s c u s s i n t h e next chapter.  7 4  TABLE 5 . 1 THE LOG SUPPLY IN THE COASTAL REGION OF BRITISH COLUMBIA 1962 PERCENTAGE DISTRIBUTION BY GRADES AND AVAILABLE TOTAL SUPPLY IN MILLIONS OF CUBIC FEET *  Log Description Douglas F i r # 1 peeler .t  u  #  .i  # 3  it  II  "  "  2  #k  II  # 2 sawlog  Distribution (percent)  Available Supply ( m i l l i o n cubic feet)  3  6.1  7  1 4 . 2  14  2 8 . 4  9  1 8 . 3  2 3  46.7  it  4 4  8 9 . 5  T o t a l Douglas F i r :  1 0 0  • 2 0 3 . 2  5  1 3 . 8  1 8  5 0 . 0  7 7  213.6  1 0 0  2 7 7 . 4  4  1 . 3  11  ..  .,  # 3  Hemlock # 1 sawlog it  #  "  2  # 3  T o t a l Hemlock: Spruce # 1 sawlog II  # 2  "  3 5  1 1 . 4  "  # 3  "  61  1 9 . 8  T o t a l Spruce Sources:  1 0 0  3 2 . 5  D i s t r i b u t i o n based on data by industry s t a t i s t i c i a n s . See text pp. **Available supply on data from: BCFS.  Annual Report,  TABLE 5.2 LOG SAWING ACTIVITY TECHNOLOGICAL COEFFICIENTS PERCENT YIELD OF LUMBER, CHIPS AND HOG FUEL  Douglas F i r Log Output  \^  1  #  2  #  3  %  *2  sawlogs  sawlogs  sawlogs  peelers #  Spruce  Hemlock  #  # 2  *2  3  #  3  Lumber: Clear  38  32  18  11  11  k  22  11  5  33  16  7  Sel/Merch.  13  14  21  17  17  19  16  16  10  14  17  12  Const/std.  15  15  23  29  29  32  26  27  26  12  26  28  Util/Econ.  6  10  8  9  9  9  6  9  13  8  6  8  Chips:  13  lk  16  22  20  22  15  23  32  18  20  25  Hog Fuel:  15  15  lk  13  lk  14  15  14  14  15  15  14  Source:  See Text pp. 51-54.  TABLE 5 . 3 LOG-PEELING A C T I V I T Y COEFFICIENTS PERCENT Y I E L D S OF GREEN VENEER, CHIPS AND HOG Douglas F i r \Log  peelers  Output \ v  #  #  #  sawlogs #  #  #  #  Hemlock  Spruce  sawlogs  sawlogs  #  12  6  12  12  12  12  -  29  34  29  3>+  18  -  20  20  20  20  23  25  -  27  28  27  28  8  8  -  8  8  8  8  2  17  10  6  -  12  8  9  10  12  -  23  28  33  38  39  Chips  22  21  20  19  Hog  17  19  21  8  8  8  A  30  24  B  8  C  Fuel  Shrinkage  Source:  See T e x t pp. 5 4 - 5 6 .  #  6  k  1  3  #  2  3  2  #  1  2  1  FUEL  3  #  3  T A B L E 5.4 PLYWOOD PRODUCTION A C T I V I T Y COEFFICIENTS CUBIC FEET OF GREEN VENEER REQUIRED PER CUBIC FOOT OF F I N I S H E D PLYWOOD  \  Piy-  \woods Ve\ n e e r s \ ^ G2S Douglas F i r - A .776 " 11  Hemlock  G/Sol  G1S  S2S  .388 .388  -  B  .388  C .504  .504  -  S I S Sh'g  2  F/H/S  F/H  F/S  H/S  .776  -  -  .388  -  -  .892  -  .388  .892 1.090 .388  "  B  .388  "  C  .504 .504  .776  .388  -  B  .388 . 7 7 6  C  .504 .504  .504  -  -  - Canadian Standards Association  -  -  .504 .892  F i g u r e s o n a g r e e n v e n e e r b a s i s a l l o w i n g a v e r a g e lh% s a n d i n g l o s s (where and 8% s h r i n k a g e l o s s i n d r y i n g . S e e t e x t p p . 56-58. Douglas f i r plywoods CSA 0121 - 1961.  -  .504  .388  Spruce A  Source:  S/H  .776  -  A  "  1 2  .388  . 7 7 6 .388  .892 .504  1  Publication,  appropriate)  TABLE 5  -  5  PULP PRODUCTION ACTIVITY COEFFICIENTS CUBIC FEET OF CHIPS (SOLID VOLUME) PER AIR-DRY TON OF PULP  Chip Specie  Yield of Pulp (*)  Density (lb/CF)*  Chip Compositions f o r each Pulp  Wood Conspt n 1  F H (CF/ADT) "40/60  F  H  5 0 / 5 0  F  H S  3 0 / 5 0 / 2 0  F  H S  4 5 / 4 5 / 1 0  F 100  Douglas F i r  4 2 . 3  28.0  1 5 2  63.5  79.0  49.0  7 2 . 0  1 5 2  Hemlock  41.4  26.5  164  9 5 . 5  79.0  8 1 . 5  7 2 . 0  Spruce  41.4  24.0  181  -  -  32.8  16.0  Moisture-free weight, green volume. Sources:  -  -  H 100  S 100  —  —  164  -  -  181  ADT = A i r Dry Ton  1. Wood Properties - Canadian Woods - Their Properties and Uses, Appendix Tables, Queen's P r i n t e r s , Ottawa. 2.  Chip Compositions - data supplied by industry personnel.  (See text pp. 58  TABLE  5.6  PLYWOOD MANUFACTURING COSTS AS PERCENT OF SALES  Production  Step  Cost %  1.  Logs  47  2.  Peeling  10  3.  Drying  4.  L a y - u p and P r e s s i n g  5.  Trimming  2  6.  Panel  Patching  7  7.  Panel  Sanding  6  8.  Warehouse &  9  Shipping  15  4  100%  Source:  See T e x t p p . 62-63.  PRICE  TABLE 5.7 PLYWOOD PRODUCTION ACTIVITY UNIT-LEVEL RETURNS CALCULATION OF UNIT-LEVEL RETURNS FROM MARKET PRICE & MANUFACTURING COST DATA D e s c r i p t i o n Market Price $ per L Species Grade cu.ft.  Plywood  Manufacturing Costs $/cu.ft. 3/8" plywood  Unit-level Return $/cu.ft. 3/8" plywood  5.00  2.40  2.60  G/Sol  4.50  2.40  2.10  D o u g . f i r i 1 G2S ^ II  u  it  I I  G13  4.00  1.80  2.20  II  it  S2S  4.40  2.00  2.40  tt  I I  SIS  3.90  1.80  2.10  it  it  Sheathing  2.30  1.00  1.30  Hemlock  -  3.00  2.40  0.60  u  -  2.50  2.00  0.50  -  3.00  2.40  0.60  -  2.50  2.00  0.50  -  4.00  1.80  2.20  -  4.30  2.00  2.30  4.25  2.00  2.25  2.80  1.80  1.00  2.90  1.80  1.10  Spruce it  Fir/Hem /Spruce Fir/Hem  Hem/Sprc  -  Sprc/Hem  -  Fir/Sprc  See t e x t pp. 6 2 - 6 3 .  8 1  TABLE 5  .  8  PULP PRODUCTION A C T I V I T Y UNIT-LEVEL RETURNS CALCULATION OF UNIT-LEVEL RETURNS FROM MARKET PRICES AND MANUFACTURING COST DATA  Pulp  Chip Mix (cu.ft.per ADT p u l p * ) D.F. Hem. S p r u c e  a  64  9 5  b  7 9  7 9  -  c  4 9  81  3  d  7 2  7 2  16  e  1 5 2  -  -  -  f g  164  -  3 '  1 8 1  ADT = a i r d r y t o n Source;  S e e t e x t p p . 63-64.  Manufacturing Cost $/ADT p u l p  Activity Unit-level Return $/ADT p u l p  1 1 5 . 0 0  4 3 . 0 0  7 2 . 0 0  1 1 5 . 0 0  4 3 . 0 0  7 2 . 0 0  1 2 5 . 0 0  4 3 . 0 0  8 2 . 0 0  1 2 5 . 0 0  4 3 . 0 0  8 2 . 0 0  1 1 0 . 0 0  4 3 . 0 0  6 7 . 0 0  1 1 0 . 0 0  4 3 . 0 0  6 7 . 0 0  1 1 0 . 0 0  4 3 . 0 0  6 7 . 0 0  Assumed Price $/ADT p u l p  TABLE 5  .  9  LOG S E L L I N G A C T I V I T Y UNIT-LEVEL RETURNS  Log  Description  Market P r i c e Dec. 1 9 6 3 $/MBM L o g S c a l e  Douglas F i r # 1 peeler  Activity UnitLevel Return $ / 1 0 0 cu. f t .  1 2 0 . 0 0  7 2 . 0 0  II  it  #2  •  »  1 1 0 . 0 0  66.00  ii  ii  #  3  "  1 0 0 . 0 0  60.00  ti  II  #  4  "  9 0 . 0 0  5 4 . 0 0  ti  II  #  2 sawlog  7 0 . 0 0  42.00  it  II  #  3  60.00  36.00  1s a w l o g  5 5 . 0 0  3 3 . 0 0  n  5 0 . 0 0  3 0 . 0 0  II  4 5 . 0 0  2 7 . 0 0  1 sawlog  7 0 . 0 0  42.00  it  55.oo  3 3 . 0 0  ii  45.oo  2 7 . 0 0  Hemlock; # # 2 # 3  Spruce # "  #  2  "  #  3  Source:  "  See t e x t pp. 64-65.  TABLE  5.10  LUMBER S E L L I N G A C T I V I T Y UNIT-LEVEL RETURNS  Activity UnitLevel Return  Specie  Grade  Market P r i c e $/MBM  Douglas F i r  Clear  195.00  235.00  Sel/Mer  110.00  132.00  Cons/Std  95.00  11H-.00  Util/Econ  35.00  42.00  120.00  144.00  Sel/Mer  85.00  102.00  Cons/Std  75.00  90.00  Util/Econ  35.00  42.00  225.00  270.00  Sel/Mer  80.00  96.00  Cons/Std  70.00  84.00  Util/Econ  35.00  42.00  Hemlock  Spruce  Source:  Clear  Clear  S e e T e x t p. 65.  $/CCF  lumber  84 TABLE  5.11  VENEER SELLING A C T I V I T Y U N I T - L E V E L RETURNS  Veneer Grade  Specie  Douglas F i r ti  II  Hemlock u Spruce it  *  Market P r i c e , ($/M/l6ths)-* •  9.00  173.00  5.75  110.00  A ,B  5.75  110.00  C  4.50  86.50  A ,B  5.75  110.00  C  4.50  86.50  A ,B C  1 1 M/I6ths = 1000 x l 6 x 12  Source:  Activity UnitLevel Return $/100 c u . f t . v e n e e r  S e e t e x t p p . 65-66.  cubic  feet.  TABLE 5.12 PULP CHIP SELLING ACTIVITY UNIT-LEVEL RETURNS  Specie  Market Price 1/200 cu.ft."unit"  A c t i v i t y Unit-Level Return 1/100 cu.ft.of chips  Douglas F i r  12.00  18.00  Hemlock  14.00  21.00  Spruce  14.00  21.00  Source:  See Text p. 66.  TABLE 5.13 MODIFIED COEFFICIENTS OF ACTIVITY NO. 9; FOR CASE II  Modified sawing a c t i v i t y c o e f f i c i e n t s f o r No. 3 hemlock l o g . VOLUME OF PRODUCT PER CUBIC FOOT OF LOG CONSUMED Original ^ Coefficients (Case I)  Modified ^ Coefficients (Case II and Case III)  Clear  0.05  0.02  Sel/mer  0.10  0.05  Coast/std  0.26  0.14  util/econ  0.13  0.12  Chips  0.32  0.40  Hog Fuel  0.14  0.27  Lumber:  * Industry-average  data.  * * A r b i t r a r i l y assumed c o e f f i c i e n t s .  TABLE 5.1k VOLUME OF LOGS IN MILLION CUBIC FEET, BY SPECIES AND GRADE  Log D e s c r i p t i o n  60  142  140  2 8 4  3 0 0  1 8 3  2 5 0  4 6 7  5 5 0  8 9 5  1 0 0 0  1 sawlog  1 3 8  1 5 0  5 0 0  7 5 0  2 1 3 6  1 3 5 0  1 3  5 0  »  1 1 4  2 0 0  "  1 9 8  3 0 0  II  ii  Hemlock #  1 peeler »  #  2  #  3  ..  ..  #k  "  #  2 sawlog  II  #  3  II  a  "  #  2  "  #  3  #  1 sawlog  Spruce  #2 #  Modified * Log Supply (Case III)  61  Douglas F i r #  "  O r i g i n a l Log Supply (Case I and Case II)  3  " 11  C o a s t a l r e g i o n d a t a , 1962. **Arbitrarily  (See  assumed l o g s u p p l y .  t e x t pp. 67  88  CHAPTER VI RESULTS AND DISCUSSION I.  RESULTS  The IBM 1620 computer programme outlined i n chapter f i v e performed  smoothly and no d i f f i c u l t y was encountered  ing a solution.  i n obtain-  Case I required 28 i t e r a t i o n s to reach an o p t i -  mal solution; running time f o r the main solution programme was approximately twelve minutes with i t e r a t i o n times ranging from ten seconds to 45 seconds per i t e r a t i o n .  The solution and  f i n a l matrix for Case I were punched out on cards.  Solutions  f o r Case II and Case III were obtained more e a s i l y , since i t was quite possible to start with the Case I f i n a l matrix, i n sert the required modifications via the appropriate changerprogramme, and reach an optimal solution i n two or three i t e r ations. As described i n chapter f i v e the f i n a l solution for each case was obtained on cards, rather than typed-out, so that i t could be used as input to the solution-transformation programme.  A sample of the transformed data i s presented i n  Appendix I to this thesis. For each case, an optimum solution to the model comprised a maximum value for the objective function and a l i s t i n g of the f i n a l basis and non-basis variables (or a c t i v i t i e s ) .  The  fi-  nal basis variables specify optimum a c t i v i t i e s and a c t i v i t y l e v e l s , necessary to achieve a maximum value for the objective function.  The non-basis variables represent a c t i v i t i e s ex-  cluded from an optimal solution.  39  V a r i a b l e s numbered f r o m one to  intermediate  activities  t o 37  inclusive,  correspond  i n t h e m o d e l , see F i g u r e  I.  Those  s p e c i f i e d among t h e f i n a l b a s i s v a r i a b l e s c o m p r i s e t h e  opti-  mum  l o g - a l l o c a t i o n p l a n f o r the p a r t i c u l a r case.  The  ing  v a r i a b l e s , numbered f r o m 33 t o 9  correspond  to  final activities,  and  those  s p e c i f i e d among t h e  v a r i a b l e s c o m p r i s e t h e optimum m i x i n the p a r t i c u l a r case.  As  inclusive,  L  final  of f i n a l products  explained  i n chapter  programme s o l u t i o n i n c l u d e s u p p e r and  lower  limits  f i n a l non-basis v a r i a b l e that w i l l  when e i t h e r l i m i t Compiled  enter  to  specifies  the s o l u t i o n  the  t h e r e s u l t s f r o m e a c h c a s e i t w i l l be s o l u t i o n data  f i n a l product  shows t h e t o t a l  and  I I I by e a c h u t i l i z a t i o n  and  pulp  production.  I t should  be  r e t u r n f o r cases I , I I namely lumber, plywood  These net r e t u r n f i g u r e s  f o r the  represent  costs, excluding  noted t h a t the pulp  include a deduction  peeling a c t i v i t i e s .  net  category,  r e t u r n s , l e s s manufacturing  production  the  production  not  cost  figures  cost of chips from sawmill  S i m i l a r l y , the lumber p r o d u c t i o n  wood p r o d u c t i o n r e t u r n s do  The  allocations,  mixes, s a l e s volumes, e t c .  T a b l e 6.1  chips to pulp  use-  i n t a b l e s , shown b e l o w ,  s e t t i n g f o r t h c o m p a r i s o n s between the optimum l o g  not  the  i s exceeded.  evaluate  f u l to compile  logs.  the  Results  To  gross  basis  produced  five,  u n i t - l e v e l r e t u r n f o r e a c h f i n a l b a s i s v a r i a b l e , and the  remain-  and  i n c l u d e r e t u r n s from the  of do and  ply-  sale  of  activities.  optimum l o g - a l l o c a t i o n p l a n s  f o r e a c h c a s e are shown  90  i n Table 6.2,  as the percentage  of the s u p p l y of each type  o f l o g t h a t i s consumed i n each u t i l i z a t i o n c a t e g o r y . F i n a l l y , T a b l e s 6.3,  6.4  and 6.5  show the f i n a l o u t -  put of lumber, plywood and p u l p , r e s p e c t i v e l y , f o r each case. These f i g u r e s i n d i c a t e the type and q u a n t i t y of each f i n a l p r o d u c t (lumber, plywood, veneer, p u l p , and c h i p s ) t h a t would be produced  w i t h an optimum a l l o c a t i o n o f l o g s , i . e . , a t a  maximum v a l u e f o r the o b j e c t i v e f u n c t i o n . D i s c u s s i o n of R e s u l t s . The p r a c t i c a l s i g n i f i c a n c e o f these r e s u l t s i s l i m i t e d by the s i m p l i f y i n g assumptions o f the model.  a p p l i e d i n the c o n s t r u c t i o n  I t i s p o s s i b l e n e v e r t h e l e s s t o observe some  r e l e v a n c i e s t o the r e a l w o r l d . F o r example, a c c o r d i n g t o the model ( a l l cases) no l o g s s h o u l d be s o l d ; i t i s more p r o f i t a b l e t o c o n v e r t the t o t a l g i v e n l o g s u p p l y than s e l l any p a r t o f i t .  Similarly,  c h i p s s h o u l d be s o l d , i n c l u d i n g those produced and plywood m i l l waste.  no  from s a w m i l l  S i n c e the model i s based on the  e n t i r e l o g s u p p l y o f the c o a s t a l r e g i o n we must i n f e r t h a t any s a l e s would be t o markets o u t s i d e the c o a s t a l r e g i o n . o f these n o - s a l e c o n d i t i o n s are s u b s t a n t i a l l y met  Both  i n practice  70  a t .the p r e s e n t t i m e . 70 Log e x p o r t s i n 1962, from the whole p r o v i n c e , were app r o x i m a t e l y 1.5% o f the c o a s t a l r e g i o n l o g s c a l e . Chip e x p o r t s from the p r o v i n c e were a p p r o x i m a t e l y 0.5% o f the c o a s t a l r e g i o n l o g s c a l e . Annual R e p o r t , B r i t i s h Columbia F o r e s t S e r v i c e . P r o v i n c e of B r i t i s h Columbia, Dept. of Lands and F o r e s t s , V i c t o r i a , B.C., (1962).  91 With respect to log a l l o c a t i o n , the figures f o r Case I i n Table 6.2 show almost two-thirds of the log supply going to sawmills.  In practice approximately 82 percent of the combined  f i r , hemlock and spruce supply for the coastal region i n 1962 71 was  converted  to lumber.  On the other hand, the percentage  of logs allocated to plywood production i n Case I of the model i s s i g n i f i c a n t l y higher than industry practice, (the increase 72  i s equal to the difference i n lumber production noted above). The percentage of logs allocated to chipping i n the model (Case I) i s the same as industry practice for 1962.  Insofar  as the technological information and simplifying assumptions i n the model are reasonable,  the r e s u l t s of case I indicate  that the coastal region forest industry i n 1962 misallocated logs to lumber production^which might otherv/ise have been more p r o f i t a b l y u t i l i z e d i n the manufacture of plywood. In case I I , a s l i g h t v a r i a t i o n i n technological coeff i c i e n t s of the No. 3 hemlock log sawing a c t i v i t y results i n a s i g n i f i c a n t l y modified l o g - a l l o c a t i o n plan. the main a c t i v i t y accounting  Chipping  i s now  for almost half of the log input.  This pattern of log a l l o c a t i o n c l e a r l y does not correspond 71 Annual Report, 1963, B r i t i s h Columbia Lumber Manufacturers Association, Vancouver, (1964). 72 L. Read, Economist and S t a t i s t i c i a n , Council of Forest Industries, Vancouver, (1964) - personal correspondence. 73  Ibid.  92  c l o s e l y w i t h that a c t u a l l y observed  i n the r e g i o n .  The  sig-  n i f i c a n t p o i n t however i s t o observe  t h a t the  problem  l a r g e volume o f No.  i s dominated  hemlock l o g s .  by a r e l a t i v e l y  T h u s , i f t h e q u a l i t y o f No.  log-allocation  3 hemlock l o g s  d e c l i n e s as p o s t u l a t e d i n t h e m o d i f i e d a c t i v i t y  coefficients  o f c a s e I I , t h e e n t i r e a l l o c a t i o n o f t h e s e l o g s may ed f r o m l u m b e r  to  3  be  shift-  chips.  I n p r a c t i c e of course such a wholesale t r a n s f e r of l o g s f r o m one u t i l i z a t i o n p r o c e s s t o a n o t h e r i s l i m i t e d  t o the l o n g -  r u n , where u t i l i z a t i o n c a p a c i t i e s f o r e a c h p r o c e s s may v a r i e d . Furthermore, may  i t i s possible that a given log supply  be o p t i m a l l y d i v i d e d b e t w e e n two  gories.  be  o r more u t i l i z a t i o n c a t e -  T h i s i s e v i d e n t i n c a s e I I I where t h e s u p p l y o f No.  3  s p r u c e i s a l l o c a t e d b e t w e e n s a w i n g , 10 p e r c e n t , and c h i p p i n g , 90 p e r c e n t . The  output of Douglas  (Table 6.3)  f i r lumber  specified  i s 25 p e r c e n t below the a c t u a l output  i n Case I , i n 1962  in  7k the c o a s t a l r e g i o n . allocated  t o plywood  cussed above.  T h i s r e f l e c t s the l a r g e r p o r t i o n of l o g s p r o d u c t i o n i n t h e c a s e I s o l u t i o n as  H e m l o c k and  spruce lumber  dis-  p r o d u c t i o n i s moder-  a t e l y h i g h e r i n case I than a c t u a l e x p e r i e n c e would  indicate,  75  but the p r o p o r t i o n s are reasonably c l o s e . t w e e n c a s e I and c a s e I I show t h a t D o u g l a s  Comparisons f i r and  b e r o u t p u t i s u n a f f e c t e d by t h e m o d i f i e d a c t i v i t y  7k Annual Report 1963, B r i t i s h Columbia f a c t u r e r s A s s o c i a t i o n , Vancouver ( 1 9 6 4 ) . 75  Ibid.  be-  spruce  lum-  coefficients  Lumber Manu-  93  o f No. 3 hemlock  logs.  In plywood p r o d u c t i o n each case of the model s p e c i fied  two Douglas f i r plywoods and one mixed-specie plywood.  As d i s c u s s e d e a r l i e r , mixed-specie plywoods have only a l i m i ted market i n B r i t i s h Columbia.  In a d d i t i o n , however, the  model s p e c i f i e d d i r e c t s a l e s of each grade of hemlock veneer. As f a r as can be a s c e r t a i n e d from a v a i l a b l e data there i s no market f o r hemlock veneer, per se, i n the c o a s t a l We  region.  must conclude t h e r e f o r e that the veneer and plywood pro-  d u c t i o n data i s i n a c c u r a t e r e l a t i v e to the lumber and p u l p p r o d u c t i o n data.  T h i s i s not s u r p r i s i n g i n view of the  d i v e r g e n t sources of data i n v o l v e d i n the model.  I t i s of  i n t e r e s t however to observe t h a t i n each case hemlock neer i s i n v o l v e d i n two separate f i n a l b a s i s hemlock  ve-  activities;  v e n e e r . s a l e s and hemlock - Douglas f i r mixed-specie  plywood.  T h i s i s an i l l u s t r a t i o n of the interdependence be-  tween these two  activities.  The s o l u t i o n data on upper and lower l i m i t s to u n i t l e v e l r e t u r n s , and the c o r r e s p o n d i n g l i m i t i n g v a r i a b l e s f o r each f i n a l b a s i s v a r i a b l e , are a u s e f u l guide t o the r e l a t i v e importance of each a c t i v i t y i n the optimum s o l u t i o n .  For ex-  ample, a c t i v i t y number s i x (sawing No. 3> Douglas f i r sawlogs) i s a f i n a l b a s i s v a r i a b l e w i t h a u n i t - l e v e l r e t u r n ( c o s t ) of -$20.00; see Appendix I .  The lower l i m i t to t h i s  unit-level  r e t u r n f i g u r e i s -$31.22, beyond which i t would be more p r o f i t a b l e , from the p o i n t of view of t o t a l net r e t u r n t o the l o g supply,  94 i  ••  "i  t o e m p l o y a c t i v i t y number 29 ( c h i p p i n g No. 3 , D o u g l a s f i r s a w l o g s ) . T h e r e i s a " c u s h i o n " h e r e o f more t h a n $11.00. tivity limit  Conversely, ac-  number 16 w i t h a u n i t - l e v e l r e t u r n o f -$6.00 h a s a o f -$6.99, b e l o w w h i c h i t w o u l d be r e p l a c e d b y  number 14.  The " c u s h i o n " h e r e i s $0.99.  a relatively  l a r g e (56 p e r c e n t )  decrease  lower  activity  Clearly, i tw i l l i n unit-level  ( i n c r e a s e i n c o s t ) o f a c t i v i t y number s i x b e f o r e  return  i t i s replaced,  w h e r e a s a c t i v i t y number s i x t e e n w i l l be r e p l a c e d f o l l o w i n g similar  a  c h a n g e o f o n l y 16.5 p e r c e n t . It  s h o u l d be n o t e d  able t o e i t h e r of these if  take  t h a t t h e r e i s no u p p e r - l i m i t i n g v a r i -  intermediate a c t i v i t i e s .  t h e i r u n i t - l e v e l r e t u r n s a r e any h i g h e r  no b e t t e r a l t e r n a t i v e . and  lower  limiting  and  other f i n a l  Normally,  (lower cost) there i s  each a c t i v i t y has b o t h  upper  v a r i a b l e s a s e v i d e n t i n a c t i v i t y number 3 8 , 76  a c t i v i t i e s with positive unit-level returns.  Two c o n c l u s i o n s f o l l o w f r o m t h e s e d i f f e r e n t cases  I n other words,  o f the model.  First,  o b s e r v a t i o n s on t h e  t h e v a l i d i t y o f any p r a c t i -  c a l c o n c l u s i o n s drawn f r o m t h e s o l u t i o n o f t h e model depends h e a v i l y on t h e q u a l i t y o f t h e d a t a u s e d .  The f u l l  value of the  m o d e l c a n n o t be r e a l i z e d u n l e s s a c c u r a t e d a t a on y i e l d s , p r i c e s and  costs are available. Second, g i v e n confidence  nificant  i n the q u a l i t y of the data,  sig-  c h a n g e s i n t o t a l n e t r e t u r n and o p t i m u m u s e o f t h e l o g s  may r e s u l t f r o m a r e l a t i v e l y m i n o r change i n y i e l d s , p r i c e s o r costs.  I n an example, a decrease  hemlock l o g r e s u l t e d  i n t h e lumber y i e l d  i n a $3.2 m i l l i o n d e c r e a s e  f r o m a No. 3  i n t o t a l net  r e t u r n ( s e e T a b l e 6.1, c a s e s I and I I ) . I t a l s o r e s u l t e d i n a 76 Some a c t i v i t i e s , s u c h a s No. 11, h a v e a n u p p e r - l i m i t i n g v a r i a b l e b u t t h e programme f a i l s t o s p e c i f y a m e a n i n g f u l u p p e r u n i t - l e v e l r e t u r n f i g u r e , due t o i n s u f f i c i e n t s p a c e f o r l a r g e r n u m b e r s i n t h e m a c h i n e programme f o r m a t .  95 major adjustment i n the II.  l o g - a l l o c a t i o n p l a n (see  APPLICATIONS OF THE  In t h i s study the  Table 6 . 2 ) .  MODEL  a c q u i s i t i o n of a c c u r a t e data and  c l u s i o n of a l l p o s s i b l e  variables  i n the model was  the  in-  considered  of secondary importance to p r e s e n t i n g a c l e a r demonstration of the  application  blems.  of l i n e a r programming to l o g - a l l o c a t i o n pro-  Many s i m p l i f y i n g  assumptions were i n c l u d e d  t h i s demonstration as simple as p o s s i b l e . we  s h a l l consider relaxing  t i o n s to make the  In t h i s  section  some of these s i m p l i f y i n g  assump-  model more v a l i d .  In chapter four we and  to make  distinguished  c o r r e l a t i o n assumptions i n the  assumptions are b a s i c  between fundamental  model.  The  fundamental  to l i n e a r programming and  l a x e d without d e s t r o y i n g the  l i n e a r i t y of the  cannot be  model.  The  r e l a t i o n assumptions however serve merely to s i m p l i f y the position.  We  assumptions, by the  may  conveniently relax  considering  some of the  an a p p l i c a t i o n  l o g - a l l o c a t i o n problem faced by an  Log-Allocation We  latter  individual  firm.  approach of modifying the  simplified to conform  l o g - a l l o c a t i o n problem of an i n t e g r a t e d  This w i l l involve  (a)  re-defining  the  objective  function  firm. and  some o r i g i n a l assumptions,  A P r o f i t Objective-Function. The  first  ex-  of the model to  l i n e a r programme model presented i n t h i s t h e s i s  relaxing  cor-  L i n e a r Programme f o r an I n t e g r a t e d F i r m .  s h a l l take the  more w i t h the  re-  step i s to deduct l o g c o s t s from the  total  96  net  return objective function.  An o p t i m a l  s o l u t i o n then  r e s p o n d s t o maximum e n t r e p r e n e u r i a l p r o f i t , e x c l u d i n g rent by  t o the supply  adding l o g costs  of logs.  This  t o the u n i t - l e v e l r e t u r n of each  inter-  or by deducting  age  l o g cost  The  f o r m e r p r o c e d u r e i s t h e more a c c u r a t e  an aver-  from t h e u n i t - l e v e l r e t u r n of each f i n a l  to apply.  return of l o g - s e l l i n g zero  economic  c o r r e c t i o n may be made e i t h e r  mediate ( i . e . , l o g c u t t i n g ) a c t i v i t y ,  i s probably simpler  ( o r a negative  cor-  activity.  although the l a t t e r  I n e i t h e r case the u n i t - l e v e l  a c t i v i t i e s w o u l d h a v e t o be a d j u s t e d  value  i fexpected salvage  were l e s s t h a n p u r c h a s e p r i c e ) t o a v o i d  values  to  f o r logs  double-costing  of  logs. (b)  U t i l i z a t i o n Capacity The  Restraints.  next b a s i c m o d i f i c a t i o n i s t o account f o r the l i m i -  ted u t i l i z a t i o n capacity of a s i n g l e f i r m i n the short-run. Previously, the long-run condition of unlimited assumed.  c a p a c i t y was  I n p r a c t i c e i ti s the short-run l o g - a l l o c a t i o n  problem that i s of i n t e r e s t to the firm's current with long-run considerations and  operations,  a p p l i c a b l e more t o i n v e s t m e n t  p o l i c y d e c i s i o n s , which are discussed  later.  U t i l i z a t i o n c a p a c i t y r e s t r a i n t s c a n be r e a d i l y i n c o r porated  i n t o t h e l o g - a l l o c a t i o n m o d e l i f no more t h a n t h e  t o t a l capacity and  chipping)  requires  o f each u t i l i z a t i o n category (sawing, need be s p e c i f i e d .  Each c a p a c i t y r e s t r a i n t  an a d d i t i o n a l row i n t h e m a t r i x  of the model,  a c t i v i t y c o e f f i c i e n t s o f u n i t y f o r each intermediate a f f e c t e d by t h e r e s t r a i n t .  peeling  Thus, the s a w m i l l i n g  with  activity  capacity  97 restraint  (row) would have a 'one' i n each l o g - s a w i n g i n t e r -  mediate a c t i v i t y column. u t i l i z a t i o n category, mary i n p u t s i s entered expressions  T o t a l a v a i l a b l e c a p a c i t y f o r each  e x p r e s s e d i n t h e same u n i t s as the p r i i n the r e s t r a i n t column.  (inequalities)  The r e s t r a i n t  f o r each l i m i t e d u t i l i z a t i o n c a -  p a c i t y t a k e the same form as the p r i m a r y i n p u t r e s t r a i n t exp r e s s i o n s ; i . e . , t o t a l consumption o f each u t i l i z a t i o n - c a p a c i t y must be l e s s - t h a n o r e q u a l - t o  the a v a i l a b l e u t i l i z a t i o n capa-  city. D i s p o s a l a c t i v i t i e s c o r r e s p o n d i n g t o the " u s e " o f i d l e c a p a c i t y a r e r e q u i r e d f o r each u t i l i z a t i o n - c a p a c i t y  restraint.  The u n i t - l e v e l , r e t u r n s f o r these c a p a c i t y - d i s p o s a l o r i d l e capacity a c t i v i t i e s are given negative  values  corresponding  t o t h e c o s t o f i d l e c a p a c i t y , w h i c h s u b t r a c t s from t o t a l profit. A more e x a c t model would i n c l u d e s e p a r a t e c a p a c i t y r e s t r a i n t s f o r some or a l l o f t h e i n t e r m e d i a t e  activitiesi n  the model, but t h i s would make i t c o n s i d e r a b l y more cumbersome.  To s p e c i f y c a p a c i t y r e s t r a i n t s on each o r i g i n a l i n t e r -  mediate a c t i v i t y would add as many new r e s t r a i n t s , and as many new ( d i s p o s a l ) a c t i v i t i e s , as t h e r e were o r i g i n a l i n t e r mediate a c t i v i t i e s , (c)  Log C o s t s . I n t h e s i m p l i f i e d i n t e g r a t e d - i n d u s t r y model o f t h i s  s t u d y we assumed t h a t l o g c o s t s were e s t a b l i s h e d on the open market.  T h i s i s a r e a s o n a b l e a s s u m p t i o n f o r any f i r m  i n g w i t h i n the Vancouver l o g market.  I n t h e event  operat-  however  t h a t a f i r m does have a c c e s s t o l o g s ( o r i n t e r m e d i a t e  products  98  s u c h as  c h i p s ) of  more d i f f e r e n t t h e s e must be one  the  same g r a d e and  s o u r c e s a t two treated  w i t h i t s own  as  q u a l i t y but  f r o m two  o r more d i f f e r e n t p r i c e s ,  separate i n p u t s to the  then  model.  corresponding sawing, peeling,  and  or  Each  chipping  activities. Applications A as  the  of  f i r m can  one  run)  the  s e p a r a t e ways:  lacking  and  in  the  Applications. s h o r t - r u n the  l e v e l of  any  (a)  long-run.  f i r m seeks to maximize i t s  p r o f i t s subject to given p r i c e s ,  cities  technology.  costs,  t a k e c e r t a i n d a t a as  1.  Log  Supply:  (i)  (ii) Activities: (iii)  given,  grade.  Log  prices  Available  on  capa-  firm,  the  market,  by  species  namely:  Volume o f a v a i l a b l e and  (short-  production  I n t h i s c o n t e x t , the  m o n o p o l y o r monopsony i n f l u e n c e  can  2.  Problems of a Firm.  a b o v e , i n two  i n the  Short-run In  Model t o the  u s e f u l l y a p p l y a l o g - a l l o c a t i o n model such  outlined  s h o r t - r u n , (b) (a)  the  logs,  (delivered  to the  firm).  u t i l i z a t i o n processes  and  capacities, (iv)  T e c h n o l o g i c a l c o e f f i c i e n t s of utilization  (v) 3.  Products  (vi)  Unit-costs  process, f o r each u t i l i z a t i o n  Demand p r i c e s final  for intermediate  process. and  products.  G i v e n t h i s i n f o r m a t i o n the  f i r m can  a l o g - a l l o c a t i o n programme s i m i l a r t o i n t h i s t h e s i s , w i t h the  each  the  c o n s t r u c t and one  solve  described  appropriate modifications  outlined  99 earlier. profit  T h i s m o d e l w o u l d be u s e d t o d e t e r m i n e  t h e maximum  t h e f i r m c o u l d e a r n and t h e l o g - a l l o c a t i o n p l a n t o be  followed  i n attaining this  profit.  T h e s e two r e l a t e d p i e c e s o f i n f o r m a t i o n , maximum p r o fit  and optimum l o g - a l l o c a t i o n p l a n , would s e r v e a s u s e f u l  guides and  to current operations of the f i r m , i n d i c a t i n g  w h e r e , a d d i t i o n a l p r o f i t s m i g h t be e a r n e d  efficient The  t h r o u g h more  log allocation. e f f e c t o f a change i n c o m p o s i t i o n  p l y o r a change i n p r o d u c t solving  whether,  o f t h e l o g sup-  p r i c e s c o u l d be i n v e s t i g a t e d b y  t h e m o d e l a s e c o n d t i m e w i t h t h e new d a t a ,  demonstrated w i t h cases  I I and I I I i n t h i s  study).  ( a s we Changes  i n maximum p r o f i t and optimum l o g - a l l o c a t i o n p l a n c o u l d be noted (b)  and e v a l u a t e d w i t h r e s p e c t t o t h e o r i g i n a l  solution,  Long-run A p p l i c a t i o n s . L o n g - r u n c h a n g e s may be a n a l y z e d  through  t h e same p r o -  cedure o u t l i n e d above, namely, by o b s e r v i n g changes i n maximum  p r o f i t a n d optimum l o g a l l o c a t i o n .  I n t h e l o n g r u n , how-  e v e r , u t i l i z a t i o n c a p a c i t i e s and t e c h n o l o g i c a l c o e f f i c i e n t s may vary a l s o , r e s u l t i n g  i n a change i n t h e b a s i c m a t r i x o f t h e  model. I f u t i l i z a t i o n - c a p a c i t y r e s t r a i n t s are excluded the model e n t i r e l y , as i n t h e model p r e s e n t e d  i n this  from thesis,  t h e n t h e optimum l o n g - r u n l o g - a l l o c a t i o n p l a n c o r r e s p o n d s an i d e a l c o m b i n a t i o n processes.  This  of u t i l i z a t i o n capacities of the various  s o l u t i o n , c e t e r u s p a r i b u s , would p r o v i d e t h e  f i r m w i t h a u s e f u l guide expansion.  to  f o r investment  plans i n future  100 A l t e r n a t e l y , t h e f i r m may  investigate different  util-  i z a t i o n c a p a c i t y c o m b i n a t i o n s r e s u l t i n g f r o m a g i v e n amount o f investment i n p l a n t s , f o l l o w i n g a b e n e f i t - c o s t a n a l y s i s  proced-  77 ure  f o r each proposed investment The  plan.  model a l l o w s a d i r e c t comparison between b e n e f i t -  cost r a t i o s f o r d i f f e r e n t investment t h e r on a c e t e r u s i n other  paribus  ( e x p a n s i o n ) schemes, e i -  b a s i s or i n c l u d i n g f o r e c a s t changes  c o n d i t i o n s ( s u c h as p r i c e s o r l o g  supply).  F i n a l l y , t h e f i r m c o u l d e m p l o y a l i n e a r programme m o d e l s u c h as t h i s t o e v a l u a t e novation.  The  b e n e f i t s from t e c h n o l o g i c a l i n -  i n d u s t r i a l research  c o n s t a n t l y f a c e s a problem of r e s e a r c h endeavour.  An  justifying  estimate  d e v e l o p m e n t s i n wood c o n v e r s i o n on  t o t a l n e t r e t u r n and  great The  group ( o r i t s e q u i v a l e n t ) v a r i o u s avenues  of the e f f e c t techniques,  that  of  future  e t c . , m i g h t have  optimum l o g a l l o c a t i o n w o u l d be  of  value.  L o g - A l l o c a t i o n L i n e a r Programme R e f e r e n c e was  made e a r l i e r  Dual.  to the  "mathematical dual"  o f a l i n e a r programme m o d e l and  i t s particular interpretation  i n the  To  the  l o g - a l l o c a t i o n problem.  l o g - a l l o c a t i o n d u a l we  illustrate  the  s h a l l consider a simple  nature  problem  i n w h i c h l o g s a r e consumed d i r e c t l y i n t h e p r o d u c t i o n wood p r o d u c t s ; will  be  complications  of intermediate  of  products,  of  basic  etc.,  ignored.  77 J . D a v i s , D. W. R o s s , A. D. S c o t t and W. R. D. S e w e l l , B e n e f i t - C o s t A n a l y s i s H a n d b o o k , Queen's P r i n t e r , O t t a w a ,  1962.  new  101 I n the primary problem, in this  similar  i n form t o the model  s t u d y , the o b j e c t i v e i s t o maximize the r e t u r n t o a  g i v e n supply of l o g s .  P r o d u c t p r i c e s a r e known and  c o n s t a n t ; the l o g supply i s f i x e d .  The  assumed  v a r i a b l e s i n the  pro-  blem are the l e v e l s of p r o d u c t i o n of v a r i o u s l o g - c o n v e r s i o n k  processes  or a c t i v i t i e s ,  s o l u t i o n to the primary  problem  comprises  s e l e c t i n g t h e most p r o f i t a b l e c o m b i n a t i o n  of l o g -  c o n v e r s i o n p r o c e s s e s , and levels  specifying  their  of p r o d u c t i o n , s u b j e c t t o the l i m i t a t i o n s  a restricted, fixed, S u p p o s e now  supply of  propor-  t h e r e s o u r c e owner ( e . g . f i r m ) owes t o To do  this  the  accounting p r i c e s f o r these logs which  h i g h enough t o g i v e t o t h e s e to the t o t a l p r o f i t a f t e r paying these  by  logs.  each type of l o g i n the g i v e n s u p p l y . s e t up  imposed  t h a t i t i s r e q u i r e d t o f i n d what  t i o n of i t s p r o f i t s  will  corresponding  imputed  I n programming terms,  the problem  just  equal  That i s , the f i r m ' s p r o f i t s  p r i c e s f o r l o g s w o u l d be  f o r the l o g s which minimize t h e s e r e s o u r c e s , and  are  i n p u t s a combined v a l u e  of the f i r m .  firm  i s to f i n d  zero.  imputed  prices  the t o t a l accounting c o s t of  y e t i n v o l v e an i m p u t e d  o f e a c h w o o d - p r o d u c t no l e s s  l o g - c o s t per  than the p r o f i t per u n i t  unit  of each  wood-product. The  d i s t i n c t i o n may  be  l i n e a r programme o u t l i n e s as  clarified follows:  by c o n s i d e r i n g two  1 0 2  The  P r i m a r y Problem. Maximize p r o f i t : P  =  p X  +  I  1  Subject to resource  the requirement  2  X II  and  +  p X  2  3  3  limitations:  a  +  a  1  2  a  p X  1  X  12  l  X  +  +  a  2 2  a  2  X ^ b  13 2  X  +  a  3 2  1 X 3  3 *  b  2  t h a t no a c t i v i t y l e v e l s be n e g a t i v e . X  l  -  °>  ~  X 2  °'  -  X 3  0  The Dual Problem. M i n i m i z e Account C o s t s : C  =  b  1  (Imputed  +  Y  1  b  Y  p  S u b j e c t t o t h e requirement  prices).  2  that a l l p r o f i t s are  imputed: a  Y 11  a  a  +  13  Y  2 2  Y  +  p 1  —  Y  23  p  2  P  2  a  1  — 2  a  1  a  Y  21  Y 1 2  and the requirement  + 1  ^  p  3  3  t h a t no a c c o u n t i n g p r i c e s be n e g a t i v e : Y  1  ^  0  '  , Y  2  — 0 , Y — 0 . '  3  I t should be noted t h a t the same m a t r i x elements a p p l y i n t h e p r i m a r y and the d u a l model.  The o n l y changes a r e t h a t  rows i n the p r i m a r y become columns i n the d u a l (and c o n v e r s e l y ) ; the i n e q u a l i t y  s i g n s i n the r e s t r a i n t e x p r e s s i o n s a r e r e v e r s e d ,  and the o b j e c t i v e f u n c t i o n becomes one o f m i n i m i z i n g r a t h e r  103  than maximizing.  There i s no d i f f e r e n c e i n the s o l u t i o n t e c h -  nique . A p p l i c a t i o n s o f the D u a l . The d u a l l o g - a l l o c a t i o n problem d e s c r i b e d above i s p r o b a b l y of more v a l u e t o a r e s o u r c e owner than t o a r e s o u r c e e x p l o i t e r , s i n c e i t c o n s i d e r s l o g c o s t as the o p t i m i z i n g v a r i a b l e r a t h e r than p r o d u c t o u t p u t . r e s o u r c e owner may  I n t h i s sense, the  term  encompass t h r e e c l a s s e s o f owner:  the  P r o v i n c i a l Government which owns almost the e n t i r e  resource  78  i n B r i t i s h Columbia;  the l a r g e i n t e g r a t e d f i r m w i t h i t s own  h o l d i n g s of t i m b e r ; the l o g - b u y e r f o r a f i r m p u r c h a s i n g l o g s on the open-market. The l o g - b u y e r i n t e r p r e t a t i o n i s the most r i g o r o u s app l i c a t i o n of the l o g - a l l o c a t i o n d u a l , f o r two F i r s t l y , the l o g - b u y e r i s concerned or t i m b e r ) .  reasons.  o n l y w i t h l o g s (not t r e e s  S e c o n d l y , the l o g - b u y e r i s p r e d o m i n a n t l y c o s t -  oriented. The  l i s t o f imputed  l o g p r i c e s generated  i n the d u a l  s o l u t i o n would i n d i c a t e to the r e s o u r c e owner the  relative  v a l u e of l o g s t o h i s p a r t i c u l a r l o g - u t i l i z a t i o n complex.  78 T h i s i s our o r i g i n a l i n t e r p r e t a t i o n of the term r e s o u r c e owner, used throughout the e a r l i e r p a r t of t h i s t h e s i s .  A P P E N D I X T 0 C H A P T E R  S I X  TABLE 6.1 TOTAL NET RETURNS, IN LUMBER, PLYWOOD, AND PULP PRODUCTION C a l c u l a t e d as t o t a l g r o s s r e t u r n s l e s s m a n u f a c t u r i n g  costs,  e x c l u d i n g the c o s t o f l o g s . FIGURES IN MILLIONS OF DOLLARS Utilization  Category-  CASE I  CASE I I  CASE I I I  Lumber P r o d u c t i o n  120.0  64.7  46.3  Plywood P r o d u c t i o n and Veneer S a l e s  134.4  134 A  160.3  70.5  125.6  110.5  3.6  5.6  8.2  333.5  330.3  325.3  Pulp Production and Chip S a l e s Hog-Fuel  T o t a l Net R e t u r n •  TABLE 6.2 OPTIMUM LOG ALLOCATION Showing percentage  of a v a i l a b l e  l o g supply a l l o c a t e d t o v a r i o u s u t i l i z a t i o n - by s p e c i e s and grade -  CASE I Saw' g Doug. F i r #1 p e e l e r u  #  "  " II  #3 #1+  "  II  "  #3  "  "  "  Hemlock '*  Spruce II  "  -  "  2  --  II  #2 sawl'g  100  #1 sawl'g  #2 #3  100  -  11  "  #1 sawl'g  100 100  II  #3  "  Peel'g 100 100 100 100 100  -  100  -  CASE I I Chip'g Sav/' g  — —  —  — —  -  100 100  —  —  -  100  100 100  —  100  Peel'g 100 100 100 100 100  CASE I I I Chip'g Saw' g  — —  -  _  a  -  —  _  -  100  processes,  —  100 100  —  —  -  100  Peel'g 100 100 100 100 100  -  Chip'g _ _ _  -  _  100  -  _  100  100 100 9.7  — —  90.3  h  142.9  205.0  162.1  k5.5  28.0  40.0  —  —  100  _  —  T o t a l Los Consumptn. . million  cu.ft.  percentage ACTUAL CONSUMPTION 1962 - B. C. COAST  329.6  163.7  19.8  116.0  163.7  64.0  32.0  4.0  22.5  32.0  82.0  14.0  4.0  .  233.  32.0  TABLE 6 . 3 LUMBER SALES BY SPECIES AND GRADE Volume o f lumber s a l e s by f o u r grade c a t e g o r i e s ,  i n MILLION c u b i c f e e t , and v a l u e o f  lumber s a l e s by s p e c i e , i n MILLIONS o f d o l l a r s CASE I FIR  HEM  CASE I I SPRU  FIR  HEM  CASE I I I SPRU  FIR  HEM  SPRU  3.580  13.716  2.253  3.580  3.036  2.253  1.945  1.358  1.743  Sel/Mer  17.005  23.568  2.120  17.005  2.208  2.120  14.290  2.133  1.245  Cons/Std  28.64-0  59.124  3.120  28.640  3.588  3.120  23.620  7.842  1.079  8.055  28.596  0.788  8.055  0.828  0.788  6.670  8.010  0.205  Million cu.ft.  57.280  125.004  8.281  57.280  9.660  8.281  46 . 525 19.843  4.272  Percent  30  65  5  76  Million Dollars  66.678  Clear  Util/Econ Totals  ACTUAL 1962  PRODN.  40  103.541  57  11.064 6 6 . 6 7 8  3  * See t e x t p. 51 f o r lumber g r a d e s .  13 10.171  11  75  11.064 5 2 . 9 9 7  21  15.093  4 10.087  1 0 7  TABLE 6 . 4 PLYW00D AND VENEER SALES Volumes of finished plywood and green veneer sold, in hundreds of cubic feet Only a c t i v i t i e s (products) specified i n the solution are shown. Product Description  CASE I  CASE II  CASE III  (Hundreds of Cubic Feet) Plywoods Douglas F i r "  »  Fir/Hem mix  G 1 S 8  1  S  3 7 8 , 8 1 4  413,917  7 2 , 1 1 6  106,822  1 1 3 , 6 0 7  1 1 3 , 6 0 7  1 1 9 , 2 6 9  3 0 , 0 0 0  3 0 , 0 0 0  4 , 9 5 0  3 7 8 , 8 1 4  72,116  Veneers Hemlock A • "  B  60,000  60,000  9 0 , 0 0 0  "  C  112,740  112,740  194,838  1 0 8  TABLE 6  .  5  PULP SALES Volumes of pulp produced and s o l d , Pulps  Pulp  i d e n t i f i e d by t h e i r  I  CASE  4 1  5 F i r / 4 5 Hem/10 0  0 Hemlock  Spruce Spruce  5 9 1 , 3 1 6  1 7 5 , 0 3 5  1 7 5 , 0 3 5 l , 0 0 7 , l  k  III  tons)  5 9 1 , 3 1 6  1 2 1 , 4 8 1  CASE  II  (air-dry 3 0 / F i r / 5 0 Hem/20  tons  chip-mixtures.  CASE  Produced  in air-dry  0  841,857  6 6 8 , 1 0 7  109  CHAPTER  VII  SUMMARY AND CONCLUSION . The f o r e s t i n d u s t r y of B r i t i s h Columbia f a c e s competition i n i t s  t r a d i t i o n a l markets from other world  ducers and from s u b s t i t u t e p r o d u c t s .  pro-  To meet t h i s compe-  tition it  i s e s s e n t i a l t h a t the i n d u s t r y reduce i t s  and r a i s e  the economic e f f i c i e n c y  cesses.  strong  of i t s  unit-costs  log-conversion pro-  One aspect of t h i s r e q u i r e d e f f i c i e n c y  is  to  ensure  t h a t each l o g i s consumed i n a manner that maximizes t o t a l  net  r e t u r n to the log s u p p l y . As f a r as can be a s c e r t a i n e d , procedures i n the i n d u s t r y r e s u l t  current  i n considerable  This arises  from two c a u s e s ; i n s u f f i c i e n t  and y i e l d s ,  and the absence of an e f f e c t i v e  i n g the data  log-allocation inefficiency.  data on l o g c o s t s technique f o r h a n d l -  available.  The problem of determining an optimal d i s t r i b u t i o n of l o g s among a l t e r n a t e  c o n v e r s i o n processes i s amenable to a  linear  programme s o l u t i o n .  A p p l i c a t i o n s of l i n e a r programming to  var-  i o u s o p t i m i z a t i o n problems i n each s e c t o r of the i n d u s t r y have 79 SO 8x been d e s c r i b e d i n the l i t e r a t u r e / " ' '  The c o n t r i b u t i o n of  79 F. H. C u r t i s , " L i n e a r Programming the Management of a F o r e s t P r o p e r t y , " J o u r n a l of F o r e s t r y , v. 60, (Sept. 1962), p p . 611-616. 80 N. D. Jackson & G. ¥ . Swinton, " L i n e a r Programming i n Lumber P r o d u c t i o n , " F o r . Prod. J o u r , v. X I , (June, 1961), p p . 272-274. 81 E. K o e n i g s b e r g , " L i n e a r Programming A p p l i e d to the P l y wood I n d u s t r y , " F o r . Prod. J o u r , v. XI, (Sept. I 9 6 0 ) , Dp. 481486. ~"  no' this  t h e s i s i s a demonstration  programming  of the a p p l i c a b i l i t y of  t o t h e l o g - a l l o c a t i o n p r o b l e m f a c e d by t h e i n d u s -  t r y as a w h o l e , e n c o m p a s s i n g a l l o f t h e p r i n c i p a l tion  linear  utiliza-  alternatives. Fundamental d i f f e r e n c e s i n p r o d u c t i o n processes  between  exist  v a r i o u s l o g - u t i l i z a t i o n s e c t o r s of the i n d u s t r y .  P r i n c i p a l l y , lumber p r o d u c t i o n i n v o l v e s a s i n g l e  breaking-  down o p e r a t i o n ( s a w i n g ) t o p r o d u c e a f i n a l p r o d u c t ,  whereas  p l y w o o d and p u l p p r o d u c t i o n r e q u i r e a b r e a k i n g - d o w n  process  ( p e e l i n g and c h i p p i n g ) f o l l o w e d by a r e c o m b i n a t i o n ( g l u e i n g and p u l p i n g ) t o p r o d u c e f i n a l p r o d u c t s .  process, Reconciling  t h e s e d i f f e r e n c e s i n a l i n e a r programme m o d e l r e q u i r e d ducing  the concept of intermediate Intermediate  other a c t i v i t i e s  activities.  a c t i v i t i e s were viewed as p r o c e s s e s  produced intermediate products i n the model.  which  t o be consumed a s i n p u t s t o They were i n c l u d e d i n t h e  w i t h n e g a t i v e a c t i v i t y c o e f f i c i e n t s and n e g a t i v e (i.e., costs).  products  p r o d u c e d w o u l d be consumed; i . e . , t h e r e w o u l d be  The  of intermediate  assumed t h a t a l l i n t e r m e d i a t e no  products.  s c o p e o f t h e m o d e l was  of B r i t i s h Columbia.  model  activity  returns,  accumulation  I t was  intro-  limited  t o the c o a s t a l r e g i o n  D a t a were a s s e m b l e d f r o m r e s e a r c h  jour-  n a l s , t r a d e j o u r n a l s and f r o m p e r s o n a l d i s c u s s i o n s b e t w e e n  the  author  of  and p e r s o n n e l  i n the i n d u s t r y w i t h e x p e r t knowledge  c u r r e n t operations i n the f o r e s t i n d u s t r y . S o l u t i o n s o f the model were o b t a i n e d t h r o u g h  the s e r v i c e s  of the computing c e n t r e a t the U n i v e r s i t y of B r i t i s h Columbia. V a r i a t i o n s i n the model demonstrated i t s p r a c t i c a l v a l u e i n  Ill analyzing the effects  o f c h a n g i n g l o g s u p p l i e s and c h a n g i n g  technological coefficients, log  allocation.  for  investigating  grated forest  on t o t a l n e t r e t u r n a n d optimum  I t was shown t h a t t h e m o d e l i s a p o w e r f u l  s h o r t - r u n and l o n g - r u n c h a n g e s i n t h e i n t e -  products  firm.  I t c a n be c o n c l u d e d t h a t ,  as a comparative  economic model, the l o g - a l l o c a t i o n  statics  l i n e a r programme p r o v i d e s a n  e f f i c i e n t means o f e v a l u a t i n g t h e c o n s e q u e n c e s o f c h a n g i n g nomic v a r i a b l e s  tool  i n the i n d u s t r y or f i r m .  eco-  Once c o n s t r u c t e d , t h e  m o d e l may be s o l v e d a n i n d e f i n i t e number o f t i m e s t o i n v e s t i gate v a r i o u s combinations of v a r i a b l e s  of i n t e r e s t  to the  analyst. The many s i m p l i f y i n g  a s s u m p t i o n s on w h i c h t h e m o d e l h a s  b e e n c o n s t r u c t e d c a n be r e m o v e d , t h o u g h t o do so w o u l d more d a t a a n d i n v o l v e i n c r e a s i n g solution. ear  non-linear log-allocation  The p r i n c i p a l i n this thesis  be removed b y c o n s t r u c t i n g a  problem, but t h i s degree o f complex-  i s beyond t h e scope o f t h i s  thesis.  l i m i t a t i o n t o t h e l i n e a r programme  has been the q u a l i t y  v a l i d i t y of the r e s u l t s , quality  c o m p l e x i t y and c o s t i n t h e  I n d e e d , some o f t h e f u n d a m e n t a l a s s u m p t i o n s o f l i n -  p r o g r a m m i n g may u l t i m a t e l y  ity  which i s governed s u b s t a n t i a l l y  The  by t h e  o f the data employed, determines the u s e f u l n e s s o f the  the p r i n c i p a l  size  described  of the data a v a i l a b l e .  m o d e l a s a p r a c t i c a l e c o n o m i c t o o l o f management. of  require  T h u s , one  c o n t r i b u t i o n s o f t h i s s t u d y h a s b e e n t o empha-  the value of c o l l e c t i n g accurate data i n the f o r e s t  ducts industry.  T h i s q u e s t i o n has a l r e a d y r e c e i v e d  pro-  considerable  a t t e n t i o n w i t h i n the i n d u s t r y and e f f o r t s are being d i r ected towards s o l v i n g the fundamental problem of d e s c r i b i n g and grading logs and log products lumber).  8 1  >  8 2 , 8  3  adequately  (notably  However, much of the data c o l l e c t e d i s of  the wrong type f o r t h i s kind of a n a l y s i s , and s e v e r a l new kinds of data must be c o l l e c t e d i n order to e x p l o i t the p o t e n t i a l of linear-programming a n a l y s i s .  full  The f o u n d a t i o n  of a l l o c a t i o n models such as the one d e s c r i b e d i n t h i s  thesis  p r o v i d e a guide to the p r o d u c t i o n data r e q u i r e d .  81 P. H. Lane, " E v a l u a t i n g Log and Tree Q u a l i t y f o r Wood P r o d u c t s , " F o r . P r o d . J o u r . , v. XIV, (Mar. 1963), pp. 89-93. 82 C. k. Newport, C. R. Lockard and C. L. Vaughan, "Log and Tree Grading as a Means of Measuring Q u a l i t y , " Rept. Working Group as approved by The N a t i o n a l Log Grade Committee, Madison, May, 1958, F o r e s t S e r v i c e , U.S. Dept. of A g r i c . Wash., D . C . , (May, 1959). 83 J . H. J e n k i n s , "Grade Marking of Canadian Lumber," Report No. I 8 9 , F o r . P r o d . Res. Branch,.Canada Dept. of F o r . , Ottawa, (Sept. 1962).  A P P E N D I X  I  A*  0  L O G  A  L  L  O  N U M b E R  M  A  X  I  M  U  M  C  A  T  I  O F  V  A  L  O I  U  A  R I  A  b  L  E  '  i  R  L  I  N  E  A  R  A  T  I  O  N  S  O  B  J  E  C  T  I  V  E  O  P  T  I  M  U  M  A  C  T  I  V  I  L  E  V  E  L  C  .  C  O F  I  L  (  E  E  U N V  N  T  P  R  O  =  G  R  A  M  M  E  -  R  E  S  U  L  T  S  2 9  F  U  N  C  L O G  T  I A  O  N  =  3>  L  L  O  C  A  T  .  T  O  T  A  L  R  E  T  U  R  3 3 0 > I  O  N  P  3 L  5 A  9  >  3  0  0  Y  P E R  E  A  R  N  i 1  T  E  V  E  L  R  E  T  U  R  N  /  C  .  C  .  F  o  )  (  .  T  F  Y  .  )  L O W E R N  L (  ( i X l . O O O )  I  W  M C  I .  L I  T C  V .  F  .  1 I T . 1 A  R  I  A  b  N G '  U  P  P  E  R  L  L  I  M  I  T  i  /  C  .  C  E  )  (  '  .  F  .  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I  CA» £ ^  <ji a  ca  «D ' T "  I I  00  CO CO CM O O CM CM <f CM CM - - i  \0 I <t- <r o <f  CM CM  s  <t" <t" CM i n vO O ! CM CM i n rH  m  [O  O rH CA CT> (<i  H  o r^-  c n c j > %o <ri cn m rH  CO CO  o co co i n < r  un co m <t-. co o m <t I*"- O rH CM v£) o O .I - CO I  s  OO  rH ON O  vO  co r- loo r-  O  O  o o o o  rH. CM CO  O  o o o o o o o o CO  o o n o o CA j cn vO  o o o o o m  o <—i O o XI o o <J- o o I- o o ~M s  —1 —1  o o o o o CO o CO o  o o o o o o o o o o o o o o o o o o O O •£> <—i <—I CO  m  vo  r-  CO CO CO  O  \0  Oi  rH CO rH  CO O CO O  <f CA  CO  r**  tO  LO  "af CO  NON- bAb I VARIAbLE • . 1 • 2 3 4 5 8 . 9 12 13 14 20 "22 23 '24 25 26 27 28 29 30 '• 31 33 34 36 37 39 41 42 43 44 45 48 49 50 51 52 . 55 57  4 3  UN IT L E V E L -20.000 -20.000 -20.000 -20.000 -20.000 -20.000 -20.000 -20.000 -6.000 -6.000 -6.000 -6.000 • -6.000 -2.000 -2.000 -2.000 -2.000 -2.000 -2.000 -2.000 -2.000 -2.000 : ' -2.000 260.000 210.000 240.000 13 0.000 60.000 50.000 60.000 50.000 225.000 100.000 110.000 72.000 72.000 67.000 67.000  Kc TURN  S  VARIADLES  SHADOW  PRICE  29.4954 23.7199 2 7.9281 32.9924 24.8572 3.3643 14.5122 3.8068 7.5323 .9923 5.1173 43.6560 15.0928 86.7777 70.4006 60.3058 50.2109 45.2788 11.2185 22.4743 • 15.1570 50.6392 19.8760 12.5782 52.5782 12.5782 12.5700 68.7040 78.7040 82.9860 107.2681 4.9999; '•• 19.3920 9.73.60 5.1137 7.5543 . 23.9689 4 0.4097  "  -  •  58 59 60 I 61 62. 63 64 65 66 67, 68 69 82 ' 83 . -. 84 89 91 92 93  72.000 66.000 60.000 54.000 42.000 36.000 33.000 30.000 27. 000 42.000 33.000 2 7. 000 173.000 173. 000 110.000 110.000 18.000 2 1 . 000 21.000  ' '  "  '  72.6257 62.2486 58 . 1538 54.0589 61.1268 3 3 . 0665 28.328Q 24.0107 1 1 .8536 65.9816 44.2184 30_. 3424_ 93."30 9 2 6 7 . 5360 20.7982 36.8095 41.8480 _ _ 1 L » JL ?Jk. 38.3424 5  BIBLIOGRAPHY BOOKS Baumol, W. J . Economic Theory and Operations A n a l y s i s . P r e n t i c e H a l l , C a l i f . (1962). Charnes, A. ¥., Cooper, W. N., and Henderson, A. An I n t r o d u c t i o n to L i n e a r Programming. W i l e y & Sons Inc. New York, (I960). Dorfman, R., Samuelson, P.A., and Solow, R.M. Linear Programming and Economic A n a l y s i s . McGraw H i l l , New York, (1958). D a v i s , J . , Ross, D. W., S c o t t , A. D. and S e w e l l , W. R. B e n e f i t - C o s t A n a l y s i s Handbook. Queen's P r i n t e r , Ottawa, (1962).  D.  G u t h r i e , John A., and Armstrong, George, R. Western F o r e s t I n d u s t r y - An Economic Outlook. The John Hopkins P r e s s , B a l t i m o r e , (1961). Moore, A. M i l t o n . F o r e s t r y Tenures and Taxes i n Canada. Canadian Tax Foundation, Toronto, (1957). S c o t t , Anthony. N a t u r a l Resources - The Economics C o n s e r v a t i o n . Univ. Toronto P r e s s , (1955). Zaremba, Joseph.  Economics  of  of American Lumber I n d u s t r y .  JOURNAL ARTICLES C u r t i s , F. H. " L i n e a r Programming the Management of a F o r e s t P r o p e r t y . " J o u r n a l of F o r e s t r y , v. 60, Sept. 1962), pp. 611-616. Hamlin, M. E. "Experience Report - Wastewood and Chip Volume Measurement." Amer. Pulpwood Assoc. Northe a s t Tech. Comm. Minutes, (1956;, pp. 12-14. Jackson, N. D., and Swinton, G. W. " L i n e a r Programming i n Lumber P r o d u c t i o n . " F o r . Prod. Jour, v. X I , (June, 1961). Koenigsberg, E., " L i n e a r Programming Applied t o the P l y wood I n d u s t r y . " F o r . Prod. Journ., v. XI, (Sept. I960), pp. 481-486. Lane, P a u l . " E v a l u a t i n g Log and True Q u a l i t y f o r Wood P r o d u c t s . " F o r . Prod. Journ., v. XIX, (Mar. 1963), PP. 89-93.  Mayhew, W. E. "A New Method o f A l l o c a t i n g C o s t s t o Veneer by Grades." F o r . P r o d . J o u r , v. 3 , (Aug. 1  9  5  8  )  , pp. 27A-30A.  M c B r i d e , C. F., and K i n g h o r n , J . M. "Lumber Degrade Caused by jAmbrosia B e a t l e s . " B r i t i s h Columbia Lumberman, v. 4 4 , ( J u l y , i 9 6 0 ) , pp. 80-83. M c B r i d e , C. F. " B a r k i n g and C h i p p i n g i n t h e I n t e r i o r o f B r i t i s h Columbia." Canada Lumberman, v. 8 3 , ( J u l y , 1  9  6  3  )  , PP.  5  3  -  5  5  .  P a u l l , A. E. " L i n e a r Programming - A Key t o Optimum N e w s p r i n t P r o d u c t i o n . " P u l p and Paper Mag, o f Canada, v. 5 7 , ( 1 9 5 6 ) , pp. 1 4 5 - 1 5 1 . " R a n k i n , A. G. " C o s t - P r i c e R e l a t i o n s h i p s i n t h e F o r e s t I n d u s t r y . " The F o r e s t r y C h r o n i c l e , v. 3 9 , (Mar. 1  9  6  3  )  , PP.  6  9  -  7  9  .  S c o t t , Anthony, D. "The Development o f t h e E x t r a c t i v e I n d u s t r i e s . " The Can. J o u r n . Econ. and P o l . S c i e n c e , v.  2  8  ,  (Feb.  1  9  6  2  )  .  GOVERNMENT AND INSTITUTIONAL PUBLICATIONS Anon. C o n v e r s i o n F a c t o r s p e r P a c i f i c Northwest F o r e s t P r o d u c t s . I n s t i t u t e o f F o r e s t P r o d u c t s , S e a t t l e , Wash., ( 1 9 5 7 ) .  A n n u a l R e p o r t 1962. B r i t i s h Columbia F o r e s t S e r v i c e , B.C. Dept. o f Lands and F o r e s t s , V i c t o r i a , (1963). B r i t i s h Columbia Dept. of Lands and F o r e s t s . C o n t i n u o u s F o r e s t I n v e n t o r y o f B r i t i s h C o l u m b i a , V i c t o r i a , (195^8). B r i t i s h Columbia F o r e s t S e r v i c e . " P r o g r e s s t o September, 1962, and f u t u r e P r o s p e c t s o f t h e B r i t i s h Columbia S u s t a i n e d Y i e l d F o r e s t r y Program." S u b m i t t a l t o Tari f f Commission o f t h e U n i t e d S t a t e s o f A m e r i c a , Wash., D.C , v. I . B r i t i s h Columbia F o r e s t S e r v i c e . "The C o n d i t i o n and O p e r a t i o n o f t h e Open Log-Market and Chip and S m a l l Wood M a r k e t i n g i n t h e Vancouver F o r e s t D i s t r i c t . " R e p t . t o t h e S e l e c t S t a n d i n g Committee o f F o r e s t r y o f the L e g i s l a t i v e Assembly o f B r i t i s h C o l u m b i a , V i c t o r i a , ( J a n . 1962) - s u p p l i e d i n c o n f i d e n c e t o t h e a u t h o r . B r i t i s h Columbia Lumber M a n u f a c t u r e r s R e p o r t , 1963. Vancouver, (1964).  Association.  Annual  C l a r k e , E. H. "Lumber Grade Recovery from Old-Growth Douglas F i r a t a Northwestern Oregon S a w m i l l ^ " U.S. Dept. of A g r i c , P a c N.W. F o r e s t and Range E x p t . Sta. Research Note No. 1 9 1 , P o r t l a n d , Oregon,(Oct. I960). C l a r k e , E. H., and Knauss, A. C. "Veneer Recovery from Douglas F i r Logs." U.S. Dept. o f A g r i c , Pac. N.W. F o r e s t and Range Expt. S t a . Research Paper No. 2 3 , P o r t l a n d , Oregon, ( 1 9 5 7 ) . Canadian Standards A s s o c i a t i o n . Douglas F i r Plywood CSA/0121/19. Queen's P r i n t e r s , Ottawa, ( 1 9 6  1 )  .  Dominion Bureau of S t a t i s t i c s . C a t l ' g . No. 3 5 - 2 0 6 . Veneer and Plywood M i l l s . Queen's P r i n t e r s , Ottawa, ( 1 9 6 3 ) .  Dominion Bureau of S t a t i s t i c s . C a t l ' g . No. 3 6 - 2 0 4 . Pulp and Paper M i l l s . Queen's P r i n t e r s , Ottawa, ( 1 9 6 3 ) .  Dominion Bureau of S t a t i s t i c s . C a t l ' g . No. 3 5 - 0 0 3 . P r o d u c t i o n , Lumber M i l l s . Queen's P r i n t e r s , Ottawa. Dobie, J . "A M i l l i n g Study of 1 5 0 - y e a r Old Douglas F i r . " F o r e s t Products Research Branch P u b l i c a t i o n No. 1 0 3 2 . Canada Dept. of F o r e s t r y , Ottawa, ( 1 9 6 2 ) . Dowdle, Barney, and B a i n , Robert. "Lumber or C h i p s A Comparison of S m a l l - l o g U t i l i z a t i o n A l t e r n a t i v e s . " V.S. Dept. of A g r i c , N o r t h e a s t e r n F o r . Expt. S t a . (I960). Guernsey, F. Columbia a t o r y of Affairs,  W. "Some Conversion F a c t o r s f o r B r i t i s h F o r e s t P r o d u c t s . " F o r e s t Products LaborCanada P u b l i c a t i o n No. V - 1 0 2 7 , Dept. Nth. Ottawa, ( 1 9 5 9 ) .  J e n k i n s , J . H. "Grade Marking of Canadian Lumber." Report No. 1 8 9 . F o r . Prod. Research Branch, Can. Dept. of F o r e s t r y , Ottawa, (Sept. 1 9 6 2 ) . Matson, E. E. "Lumber Grade Recovery from Oregon Coast Type Douglas F i r . " U.S. Dept. of A g r i c u l t u r e , P a c N.W. F o r e s t and Range Expt. S t a . Research Paper No. 3 , P o r t l a n d , Oregon, (May, 1 9 5 2 ) . Matson, E. E. '.'-Lumber Grades from Young-Growth Douglas F i r . ' " U.S. Dept. of A g r i c , Pac. N.W. F o r e s t and Range Expt. S t a . Research Note No. 7 9 , P o r t l a n d , Oregon, (Sept. 1 9 5 2 ) .  Matson, E. E. "Lumber Grades from Douglas F i r P e e l e r Logs." U.S. Dept. o f A g r i c , Pac. N.tf. F o r e s t and Range E x p t . S t a . , R e s e a r c h Note No. 8 3 , P o r t l a n d , Oregon, (Nov. 1  9  5  2  )  .  Matson, E. E. "Lumber Grades from Old-Growth Douglas F i r S a w m i l l Logs." U.S. Dept. o f A g r i c , Pac. N.W. F o r e s t and Range E x p t . S t a . , R e s e a r c h Note No. 1 2 5 , ( J a n . 1 9 5 6 ) .  Newport, C a r l , A., L o c k a r d , C. R., and Vaughan, C. L. Log and Tree Grading as a Means o f Measuring Q u a l i t y . " Rept. o f Working Group as approved by the N a t i o n a l Log Grade Committee, Madison, Wis. May, 1 9 5 8 . - F o r e s t S e r v i c e , U.S. Dept. o f A g r i c , Wash. D.C. (May, 1 9 5 9 ) . UNPUBLISHED PAPERS M c B r i d e , C. F. " C o n v e r s i o n F a c t o r s f o r B. C. C o a s t F o r e s t I n d u s t r y . " - Mimeo Notes f o r L e c t u r e , ( 1 9 6 2 ) . Z i n u v s k a , John, A. "The F u t u r e f o r Wood i n a C o m p e t i t i v e M a r k e t . " Paper f o r p r e s e n t a t i o n a t j o i n t meeting Puget Sound and Columbia R i v e r s e c t i o n s , S o c i e t y o f A m e r i c a n F o r e s t e r s , Longview, Wash. (May 4 , 1 9 6 3 ) .  NTERME  PRIMARY  T5  N PU  DIATE  Hi  •3>  i—  8  J-  ><  <-»  4>  .i  rv  i i  Oo  ro  .i  J  O  0  . 1  X  .  ,  O J  co  x  2  X  -x  .i  . 1 .1 . 1 • = > » ^» = ° c, A, —r 1 —!  . 1  J*  0~-»  ,4  X  .1  c  a-  . 1  I  —  J_  !  <-C  H5  ?>  r-o  0~>  T .i .i  rv. —  —  . 1  — Ca *n c»  to — J  r%  K  X  s  "J-  OJ I N  . 1 . 1 O J;l —.  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