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Linear programming analysis applied to a selected plywood manufacturing firm Lee, Meng-Hye 1968

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LINEAR PROGRAMMING APPLIED  ANALYSIS  TO A SELECTED  PLYWOOD MANUFACTURING  .  by Meng-Hye  B.A.  (Hons,  FIRM  Lee  i n E c o n . )> U n i v e r s i t y of M a l a y a ,  1965  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F THE REQUIREMENTS  FOR THE DEGREE OF  M A S T E R O F BUSINESS  i n the  ADMINISTRATION  Faculty of  C o m m e r c e and B u s i n e s s  Administration  W e a c c e p t t h i s t h e s i s as c o n f o r m i n g to required  the  standard  T H E UNIVERSITY  O F BRITISH  April,  1968  COLUMBIA  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I request the Library to make i t available for reference and study only after receiving prior approval from the Head of my department or his representative.  This restriction in circulation of this thesis may  end May 1, 1970.  After May 1, 1970, I agree that the library shall  make this thesis freely available for reference and study.  I further  agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  I t i s understood that copying or publication of this thesis  for financial gain shall not be allowed without my written permission.°  Faculty of Commerce and Business Administration The University of British Columbia Vancouver 8, Canada.  ABSTRACT  A c o m b i n a t i o n of m a n y g r a d e s  of v e n e e r m a y be j o i n t l y  p r o d u c e d b y p e e l i n g a n y one t y p e of l o g s .  T h i s m e a n s that the  plywoo  m a n u f a c t u r e r c a n not r e a l l y k n o w the p r o f i t m a r g i n s of the p a n e l s produces.  A n d f o r m o s t of the m a n u f a c t u r e r s ,  he  the c o s t of the l o g s  c o n s t i t u t e s about 6 5 % of the t o t a l c o s t o f p r o d u c i n g the p l y w o o d p a n e l s Consequently,  the m a n u f a c t u r e r finds it v e r y d i f f i c u l t to s e l e c t h i s  s a l e s s t r a t e g y a n d to p r i c e h i s  panels.  T h e p l y w o o d m a n u f a c t u r e r a l s o h a s o p p o r t u n i t i e s to m i n i m i z e his log cost and p r o c e s s i n g  c o s t b y s e l e c t i n g the r i g h t c o m b i n a t i o n  of l o g s to p e e l a n d u s i n g the r i g h t c o n s t r u c t i o n s  i n l a y i n g u p the  panels.  L i n e a r p r o g r a m m i n g techniques  a r e u s e d i n t h i s s t u d y to  p r o v i d e an a p p r o a c h to the a b o v e m e n t i o n e d p r o b l e m s f o r a s e l e c t e d plywood manufacturer.  T h r o u g h this,  it i s h o p e d as w e l l to p r o v i d e  an e x a m i n a t i o n of the w a y to u s e l i n e a r p r o g r a m m i n g t e c h n i q u e s an e v a l u a t i o n o f t h e i r u s e f u l n e s s as m a n a g e m e n t manufacturing.  tools in plywood  and  iv  A s u r v e y of the r e p o r t e d e x p e r i e n c e  of s o m e p l y w o o d m a n u -  f a c t u r e r s i n d i c a t e d that the u s e o f L . P . h a d b e e n i n s t r u m e n t a l i n s a v i n g s o m e hundreds of thousands  of d o l l a r s p e r a n n u m f o r s o m e m a n u -  facturers.  An L .P.  m o d e l was c o n s t r u c t e d f o r the l a r g e s t o f the f o u r  m i l l s o f the C a s e C o m p a n y , f o r the y e a r 1967.  u s i n g the o p e r a t i n g s i t u a t i o n s  predicted  S u c h p r o b l e m s ( a n d t h e i r s o l u t i o n s ) as  encountered in defining,  were  i d e n t i f y i n g a n d m e a s u r i n g the v a r i a b l e  p r o c e s s c o s t s a n d the n e e d f o r m a k i n g s i m p l i f y i n g a s s u m p t i o n s  were  examined.  The L . P .  m o d e l s e e k s to o p t i m i z e the c h o i c e of p a n e l output,  the c h o i c e o f l o g i n p u t a n d the c h o i c e of p a n e l c o n s t r u c t i o n s  simul-  t a n e o u s l y b e c a u s e t h e s e t h r e e d e c i s i o n s a r e i n t e r r e l a t e d and s o m e what  interdependent.  The L . P .  analysis  s u g g e s t s that about 30% of the d o l l a r s a l e s  of the C a s e M i l l i n 1967 w e r e m a d e i n u n p r o f i t a b l e (thin) E v e n after allowing for p o s s i b l e variable processing  cost,  panels.  over estimation in measuring  this m a y c a l l for a thorough  o f the s a l e s s t r a t e g y a n d the p a n e l p r i c i n g  the  re-examination  system.  T o p r o d u c e the p a n e l output s e l e c t e d f o r 1967,  the b e s t l o g  c o m b i n a t i o n a p p a r e n t l y i n c l u d e s the u s e of a m u c h h i g h e r p r o p o r t i o n  V  of F i r P e e l e r #2 a n d S a w l o g #3,  Interior F i r and H e m l o c k - B a l s a m  M i x t h a n was u s e d b y the C o m p a n y i n i t s m i l l . s u g g e s t s p r o p o r t i o n s of F i r P e e l e r #1,  Also,  the m o d e l  #4 a n d S. F . P . m i g h t b e m u c h  l o w e r t h a n what the C o m p a n y t e n d e d to u s e .  T h e s e tentative findings  m a y have significant implications for choosing log acquisition p o l i c i e s .  T h e m o d e l s u g g e s t s the c h o i c e i n p a n e l c o n s t r u c t i o n m a y be to p e e l P e e l e r l o g s f o r . 104" h i g h q u a l i t y v e n e e r , veneer  a n d o t h e r l o w q u a l i t y l o g s f o r . 171" c o r e v e n e e r .  suggests down-grading some veneer constructions the l o g s  I n t e r i o r F i r f o r . 130" It a l s o  and u s i n g s o m e s u b s i d i a r y p a n e l  s o as to u t i l i z e f u l l y the t o t a l s u p p l y o f v e n e e r  from  peeled.  T h e u s e f u l n e s s of the L . P . a n a l y s i s i s f u l l y r e a l i z e d b y m a k i n g a c o m p r e h e n s i v e p o s t - o p t i m a l a n a l y s i s of the s e n s i t i v i t y o f the o p t i m a l i t y of the s o l u t i o n to v a r i o u s c h a n g e s i n the l o g s u p p l y a n d / o r panel demand a n d / o r p r o c e s s i n g cost situations.  This analysis  e n a b l e the c o m p a n y to d e t e r m i n e w h i c h of the o p e r a t i n g f a c t o r s c r u c i a l i n d e t e r m i n i n g the p r o f i t a b i l i t y o f the p a n e l s c o n s t i t u t e the b e s t l o g c o m b i n a t i o n to u s e .  may seem  a n d what m a y  F r o m this,  the m a n u -  f a c t u r e r c o u l d p o s s i b l y k n o w w h e n a n d h o w to a d a p t h i s p r o g r a m o f operation in response  to any f u t u r e c h a n g e s i n ( o r any r e v i s i o n i n  the f o r e c a s t of) the o p e r a t i n g s i t u a t i o n .  T h i s a n a l y s i s is also helpful  i n g a u g i n g the i m p o r t a n c e of the a s s u m p t i o n s the m o d e l .  made when constructing,  N o c o m p r e h e n s i v e s e n s i t i v i t y a n a l y s i s was c a r r i e d out i n t h i s study.  However,  optimal analyses  Lastly,  recommendations regarding appropriate postare presented.  the s t u d y c o n c l u d e s b y p r e s e n t i n g a n L . P .  m o d e l of  p o s s i b l e u s e to a n a l y s e the f o u r m i l l s o f the C o m p a n y t o g e t h e r , r e c o g n i z i n g the p o s s i b i l i t i e s the m i l l s .  of s p e c i a l i z a t i o n a n d c o o p e r a t i o n a m o n g  TABLE OF  CONTENTS  HAPTER I.  II.  PAG  INTRODUCTION  1  D e f i n i t i o n of the P r o b l e m  1  O b j e c t i v e o f the S t u d y  2  M e t h o d of Study  3  Thesis  4  Chapter L a y - o u t  A NOTE ON T H ECONCEPT O F LINEAR PROGRAMMING  5  L i n e a r P r o g r a m m i n g a n d the T h e o r y of the E c o n o m i c s of the F i r m UJ.  7  A REVIEW O F REPORTS ON T H E SUCCESSFUL APPLICATION O F T H ELINEAR  PROGRAMMING  T E C H N I Q U E IN T H E P L Y W O O D I N D U S T R Y  12  I n d u s t r i a l A p p l i c a t i o n o f L . P'. T e c h n i q u e . . .  13  A n E a r l y Attempt  14  A Later Attempt  15  The  E x p e r i e n c e of S i m p s o n T i m b e r C o m p a n y , Seattle,  The  Washington,  U . S. A  E x p e r i e n c e of B o i s e C a s c a d e C o m p a n y , U.S. A  The  21  E x p e r i e n c e of W e y e r h a e u s e r  Company,  U.S. A The  18  23  E x p e r i e n c e of T o c c o a C a s k e t C o m p a n y , Georgia,  Summary  U . S. A  24 25  viii  CHAPTER IV.  PAGE T H E PLYWOOD MANUFACTURING PROCESS  -  WITH S P E C I A L R E F E R E N C E T O T H E C A S E COMPANY The  27 Softwood P l y w o o d M a n u f a c t u r i n g Process  V.  27  Process Flow-Chart  28  M a t e r i a l F l o w i n the C a s e C o m p a n y  33  A N o t e o n the M a c h i n e r y  48  The  50  S y s t e m of P r o d u c t i o n Scheduling. . . .  FORMULATING A LINEAR  PROGRAMMING  M O D E L T O B E U S E D IN A N A L Y S I N G T H E C A S E COMPANY  53  C o n f i g u r a t i o n of the L . P .  M a t r i c e s i n the  Model  54  The V a r i a b l e P r o c e s s Cost and V a r i a b l e Revenue The  Coefficients  64 of the O b j e c t i v e F u n c t i o n  L o g r C o s t not A l l o c a t e d VI.  DATA PREPARATION FOR LINEAR  68 PROGRAM-  M I N G A N A L Y S I S IN T H E C A S E C O M P A N Y The  Importance  66  of R e l i a b l e D a t a  70 70  S e l e c t i n g the P l a n n i n g P e r i o d  71  P l y w o o d Sale O p p o r t u n i t i e s  72  Minimum Market Commitment  76  L o g Supplies  76  ix  CHAPTER  PAGE Opening V e n e e r and P l y w o o d P a n e l s Inventories  83  Closing Veneer Inventories Constraints  87  Veneer Purchasing  88  Veneer Recovery from Log-peeling  95  Manufacturing Process Cost  104  I d e n t i f y i n g the V a r i a b l e P r o c e s s C o s t I t e m s  106  Direct Production Labour Cost  107  Direct Maintenance  Labour & Direct Mainte-  nance M a t e r i a l Cost  Ill  Indirect Production Cost  116  The  119.  C o s t of W a t e r C o n s u m p t i o n  Plant Service  Cost and O i l & G r e a s e  Cost  119  C o s t of F o r k l i f t T r u c k S e r v i c e  119  Direct Production M a t e r i a l Cost  123  S u m m a r y of P r o c e s s C o s t s  127  Other Production Costs  129  Other Operating Costs  129  Log  135  Peeling  Veneer  - T i m e Study  D r y i n g - T i m e Study  Veneer-Patching Veneer  136  - T i m e Study  Edge-gluing  - T i m e Study  138 :  141  X  CHAPTER  PAGE Panel Lay-up & Panel Pressing  - T i m e Study  P a n e l F i n i s h i n g - T i m e Study  148  Panel Structure Alternatives  152  Coefficients  157  of the O b j e c t i v e F u n c t i o n  Process Centre Capacity VII.  A N INTRODUCTION  T O T H E 'LP-ITI,  157 IBM  7040/7044' C O M P U T E R P R O G R A M . . . , General Features  INTERPRETATION ANALYSIS  IX.  163  of the P r o g r a m  Selected Sub-routines VIII.  148  163  f r o m the L P - I I I S y s t e m  164  O F FINDINGS F R O M T H E L . P .  OF THE CASE COMPANY  170  Introduction  170  P r o f i t a b i l i t y of P l y w o o d P a n e l s  173  O p t i m u m L o g Input  180  O p t i m u m Plywood Panel Constructions  183  Appropriate Post Optimal Analysis  186  AREAS F O R F U R T H E R INVESTIGATION  IN T H E  CASE COMPANY Economics  190 of the L . P .  Analysis  190  O p t i m u m C e n t r a l A l l o c a t i o n of P r o d u c t i o n O r d e r s a n d L o g S u p p l y to the Individual M i l l s Panel Down-grading X.  CONCLUSIONS  192 195 196  xi  PAGE BIBLIOGRAPHY  199  APPENDICES  202  xii  LIST O F  APPENDICES  TITLE I  II  PAGE  A S A M P L E OF T H E L O G GRADING S Y S T E M IN B R I T I S H C O L U M B I A A SAMPLE OF PANEL  202  PRESSING  INSTRUCTIONS III  204  A S A M P L E OF V E N E E R GRADING  SYSTEM  A T PRESS IV  206  A SAMPLE OF PLYWOOD PANEL  CONSTRUC-  TION A L T E R N A T I V E S V  VI VII  208  THE COMPONENTS OF SOME OF THE COEFFICIENTS OF T H E O B J E C T I V E FUNCTION210 CODE NAMES FOR COMPUTER-RUN F O R T R A N INSTRUCTIONS FOR  213  COMPUTER  2.15  RUN VIII  OPTIMUM PLYWOOD PANEL SALE MARGINAL PROFITABILITY PANELS  IX  OF  AND  PLYWOOD  ,  218  PLYWOOD P A N E L SALE PRICE  226  OPTIMUM LOG INPUT  228  XI  OPTIMUM P A N E L CONSTRUCTION  231  XII  HISTORY  X  O F T H E L . P.  7044 C O M P U T E R  R U N ON T H E  IBM 237  xiii  LIST O F  CHARTS  TITLE  I  PLYWOOD MANUFACTURING  PAGE  PROCESS  FLOW CHART II  29  AN ILLUSTRATION OF THE MILL LAY-OUT  34  III  L O G I N - F E E D A T M I L L (Boom)  36  IV  FLOW OF VENEER  42  xiv  LIST OF DIAGRAMS  TITLE I II  PAGE  THE STRUCTURE OF A PLYWOOD P A N E L  45  P L Y W O O D BUSINESS C A P T I V I T Y GROUPING  54  XV  LIST OF  FIGURES  TITLE I  CONFIGURATION OF THE L. P.  II  PAGE  OF THE  MATRIX  MODEL  A REPRESENTATION  56 OF THE  PLYWOOD-  BUSINESS L I N E A R P R O G R A M M I N G M O D E L  58  IH  A MODIFIED  60  IV  A N L . P.  L . P.  MODEL  M O D E L -OPTIMISING A L L O C A T I O N  OF PRODUCTION  ORDERS  SUPPLIES TO THE MILLS  AND  LOG 193  xvi  LIST O F GRAPHS  PAGE I  V E N E E R INVENTORIES  41  I-X  DOUGLAS FIR PLYWOOD  PRODUCTION,  BRITISH C O L U M B I A I-Y  78  DOUGLAS FIR PLYWOOD  SHIPMENT,  BRITISH COLUMBIA II-A  A T PRESS-DIRECT C O S T vs.  II-B  79 PRODUCTION  PRODUCTION  LABOUR  LEVEL  109  A T BOOM PROCESSING-DIRECT T I O N L A B O U R C O S T vs.  PRODUC-  PRODUCTION  LEVEL IH-A  110  A T BOOM PROCESSING-DIRECT N A N C E L A B O U R C O S T vs.  MAINTE-  PRODUCTION  LEVEL III-B  112  A T DRYERS-DIRECT L A B O U R C O S T vs.  III-C  PRODUCTION  AT GREEN-END-DIRECT L A B O U R C O S T vs.  TH-D  MAINTENANCE  MILL TOTAL -  LEVEL..  PLYWOOD  PANEL OUTPUT  V  115  MILL TOTAL - ELECTRICAL POWER vs.  COST  PLYWOOD PANEL OUTPUT  117  MILL T O T A L - P L A N T SERVICE COST  vs.  PLYWOOD PANEL OUTPUT VI  MILL T O T A L - OIL & GREASE (labour & material) vs. OUTPUT  114  MAINTENANCE  C O S T (labour & m a t e r i a l ) vs.  IV  113  MAINTENANCE  PRODUCTION  DIRECT  LEVEL. .  120 COST  PLYWOOD  PANEL 121  xvii  PAGE VII  M I L L T O T A L - F O R K L I F T C O S T (labour & fuel) v s .  VIII-A  VDJ-B  PLYWOOD PANEL OUTPUT. . .  122  A T DRYERS - DIRECT PRODUCTION M A T E R I A L C O S T vs. P R O D U C T I O N L E V E L  125  A T PRESS - DIRECT M A T E R I A L C O S T vs.  126  PRODUCTION PRODUCTION L E V E L  LIST O F  TABLES  TITLE I  II IH  IV V-A V-B  PAGE  PLYWOOD SALE OPPORTUNITIES  FOR  1967  75  MINIMUM M A R K E T C O M M I T M E N T  77  L O G SPECIES A V A I L A B L E TO  BRITISH  COLUMBIA PLYWOOD MANUFACTURERS  81  LOG SUPPLY  82  TO CASE COMPANY  YEAR-BEGINNING INVENTORY. .  GREEN  VENEER 84  Y E A R - B E GINNING D R Y  VENEER  INVENTORY... VI  85  YEAR-BEGINNING  FINISHED  P A N E L INVENTORY VII VIII-A  VUI-B  INVENTORY  PLYWOOD 86  4  STORAGE CAPACITY  STRATEGIC MINIMUM V E N E E R . INyjENX.QELY  G R E E N AND  DRY 90  AN A V E R A G E ONE H A L F SHIFT OF A PRODUCT  89  PRODUCTION  MLX R E P R E S E N T A T I V E  OF  1966 VIII-C  91  STRATEGIC PLYWOOD  IX-A  & B  XI  YEAR-END!FINISHED  PANEL INVENTORY  VENEER RECOVERY FROM A/B  X  MINIMUM  ...  PURCHASED  MLX V E N E E R  V E N E E R R E C O V E R Y F R O M LOGS P E E L E D BY-PRODUCT  RECOVERY  92  93 96 105  xix PAGE XK  THE PROPORTION ITEMS  XIII  OF  1966  O F T H E VARIOUS  COST  T R E A T E D AS V A R I A B L E . . .  T H E R E L A T I V E SIGNIFICANCE OF  THE  VARIOUS COST ITEMS XIV  XV  124  THE RELATIONSHIP  AMONG  VARIABLE PROCESS  COST ITEMS  PROCESS  118  VARIOUS  CENTRES)  (BY -  VARIABLE PRODUCTION  PROCESS  128 COST  P E R SHIFT  130  XVI  OTHER PRODUCTION  COST ITEMS  133  XVII  L O G - P E E LING TIME  137  XVIII  VENEER-DRYING  TIME  139  XIX  VENEER-DRYING  TIME  140  XX  VENEER-PATCHING  TIME  142  XXI  VENEER-PATCHING  TIME  144  XXII  VENEER EDGE-GLUING TIME  145  XXIII  VENEER EDGE-GLUING TIME  247  XXIV  PANEL-PRESSING  149  TIME  XXV  PANEL-FINISHING TIME.  XXVI  PANEL STRUCTURE ALTERNATIVES  XXVII  151 AND  G L U E COST  153  PLANT CAPACITY  158  ACKNOWLEDGEMENT  T h i s c a s e s t u d y was m a d e p o s s i b l e  o n l y b e c a u s e of the  g e n e r o u s c o o p e r a t i o n of s o m e c o m p a n y o f f i c i a l s  i n the C a s e C o m p a n y .  In p a r t i c u l a r , the a u t h o r i s v e r y g r a t e f u l f o r b e i n g e n t r u s t e d w i t h v e r y c o n f i d e n t i a l t y p e s of i n f o r m a t i o n on the o p e r a t i o n s However,  o f the  company.  a t t e m p t s to h i d e the i d e n t i t y of the c o m p a n y m a k e it  i m p o s s i b l e to l i s t the n a m e s of the i n d i v i d u a l s to w h o m the a u t h o r i s greatly  indebted.  Dr.  B . E . B u r k e of the U n i v e r s i t y of B r i t i s h C o l u m b i a ,  the c h a i r m a n o f the t h e s i s c o m m i t t e e , for  as  i s to be c r e d i t e d f o r a r r a n g i n g  the c a s e s t u d y a n d a l s o f o r m u c h h e l p f u l g u i d a n c e a n d e n c o u r a g e -  m e n t to the a u t h o r .  D r . J . S w i r l e s was  also indispensable  c o n s t r u c t i v e c r i t i c i s m and helpful guidance, techniques  Mr.  i n his  p a r t i c u l a r l y on the  of u s i n g l i n e a r p r o g r a m m i n g .  A . G . F o w l e r was m o s t g e n e r o u s a n d u n d e r s t a n d i n g i n  a p p r o v i n g s p e c i a l r u n s o n the c o m p u t e r . ,  M r . Peter Madderom,  also  of the C o m p u t i n g C e n t r e , m o s t g r a c i o u s l y c o n s e n t e d to r e m a i n a f t e r h i s r e g u l a r o f f i c e h o u r s i n o r d e r to s p e n d h o u r s h e l p i n g the a u t h o r  to d e b u g the p r o g r a m a n d to s u p e r v i s e the s p e c i a l n i g h t r u n s o n the c o m p u t e r a r r a n g e d f o r the s a k e of the a u t h o r .  CHAPTER I  INTRODUCTION  D e f i n i t i o n of the P r o b l e m ; The selection  s o f t w o o d p l y w o o d m a n u f a c t u r i n g p r o c e s s b e g i n s w i t h the  a n d p e e l i n g of l o g s into v e n e e r  dimension.  F r o m these veneer  m a y be l a i d u p .  sheets,  s h e e t s of s o m e  specified  a l a r g e v a r i e t y of p l y w o o d p a n e l s  T h e s e p l y w o o d p a n e l s m a y d i f f e r one f r o m a n o t h e r i n  their length and b r e a d t h , their thickness  and their quality.  The specifi-  c a t i o n s of a p l y w o o d p a n e l a r e i n t u r n d e t e r m i n e d b y the d i m e n s i o n , grades  the  a n d the n u m b e r of p l i e s of the v e n e e r u s e d i n l a y i n g up the p a n e l .  Also there are m a n y p o s s i b l e  c o m b i n a t i o n s of w n e e r  up a p a n e l of a n y p a r t i c u l a r s e t of  a v a i l a b l e for l a y i n g  specifications.  F r o m a n y one g r a d e o r s p e c i e s of l o g s , a c o m b i n a t i o n of m a n y different grades of v e n e e r is r e c o v e r e d .  So f a r , t h e r e i s no  satisfactory  m e t h o d f o r a l l o c a t i n g the c o s t of the l o g to the d i f f e r e n t g r a d e s of produced.  veneer  T h i s m e a n s t h a t the p l y w o o d m a n u f a c t u r e r d o e s not k n o w the  w o o d - c o s t of the d i f f e r e n t t y p e s of p a n e l s p r o d u c e d .  Consequently,  he  2  k n o w s n e i t h e r the p r o f i t m a r g i n of the v a r i o u s t y p e s of p a n e l s p r o d u c e d n o r how the e c o n o m i c s of the d i f f e r e n t a l t e r n a t i v e  c h o i c e s of v e n e e r  g r a d e s a n d v e n e e r t h i c k n e s s u s e d to l a y up a p a n e l c o m p a r e one  with  another.  T h e p r o b l e m of j o i n t w o o d c o s t l e a v e s the p l y w o o d with three i m p o r t a n t questions u n s a t i s f a c t o r i l y  answered.  manufacturer Namely,  what i s the m o s t p r o f i t a b l e s e t of p l y w o o d p a n e l s to p r o d u c e ? a r e the b e s t w a y s to c o n s t r u c t a p l y w o o d p a n e l ?  What  A n d what i s the b e s t  c o m b i n a t i o n of l o g s p e c i e s a n d l o g g r a d e s to u s e ?  Bearing in mind  t h a t the w o o d c o s t i n p l y w o o d p r o d u c t i o n as c o m p u t e d b y one  manufacturer,  c o n s i s t s of 60 to 70% of the t o t a l p r o d u c t i o n c o s t of the p l y w o o d  panels,  these are v e r y c r u c i a l questions.  O b j e c t i v e of the S t u d y : L i n e a r P r o g r a m m i n g technique has been p r o v e d suitable d e f i n i n g the b e s t p r o g r a m o f a c t i v i t i e s i n the e c o n o m i c business.^  for  s h o r t r u n for a  It c a n be u s e d to get a r o u n d the p r o b l e m w i t h j o i n t - c o s t  s i t u a t i o n s to a r r i v e at the o p t i m u m s e t of d e c i s i o n s .  When applying  L i n e a r P r o g r a m m i n g a n a l y s i s to the p l y w o o d m a n u f a c t u r i n g b u s i n e s s , the c o s t of the l o g s n e e d not be a l l o c a t e d to the i n d i v i d u a l g r a d e s of veneer in order  '''See R .  to a r r i v e at the o p t i m u m u s e of the l o g s .  D o r f m a n , A p p l i c a t i o n of L i n e a r P r o g r a m m i n g to the  T h e o r y o f the F i r m - I n c l u d i n g an A n a l y s i s of M o n o p o l i s t i c F i r m s b y Non-Linear Programming,  P h . D . T h e s i s , U n i v e r s i t y of C a l i f o r n i a ,  1951.  3 The  o b j e c t i v e of the s t u d y i s two f o l d :  firstly,  it a i m s  at  d e m o n s t r a t i n g how an L . P . m o d e l m a y b e c o n s t r u c t e d f o r u s e i n a plywood manufacturing business.  Secondly,  i t a i m s at e v a l u a t i n g the  e x t e n t to w h i c h the p r e s e n t p o l i c i e s i n l o g i n p u t , p a n e l output a n d c h o i c e of p a n e l l a y - u p a l t e r n a t i v e s i n the C a s e M i l l m a y d i f f e r f r o m the optimum.  T h i s m a y b e a d e m o n s t r a t i o n of the s i z e of the  a d v a n t a g e to b e o b t a i n e d f r o m u s i n g L . P . industry,  economic  a n a l y s i s i n the p l y w o o d  g r a n t e d that the s i t u a t i o n s m a y v a r y f r o m o n e f i r m to a n o t h e r .  M e t h o d of Study: T h i s c a s e s t u d y o f the a p p l i c a t i o n o f L . P .  a n a l y s i s to the p l y -  w o o d m a n u f a c t u r i n g b u s i n e s s i s m a d e p o s s i b l e o n l y t h r o u g h the c o o p e r a t i o n o f the C a s e C o m p a n y .  gracious  T h e w r i t e r w a s g i v e n a c c e s s to v e r y  c o n f i d e n t i a l t y p e s of i n f o r m a t i o n c o n c e r n i n g the o p e r a t i o n s o f the of the f o u r m i l l s of the C a s e C o m p a n y . this r e p o r t ,  However,  largest  i n the w r i t i n g of  s t e p s h a v e b e e n t a k e n to p r e v e n t a n y p o s s i b l e  d i v u l g i n g of  d e t a i l e d i n f o r m a t i o n c o n s i d e r e d c r i t i c a l to the i n t e r e s t of the  Case  Company.  The  s t u d y i n c l u d e s an a n a l y s i s of the o p e r a t i o n s of the  M i l l as the g r o u n d w o r k f o r c o n c e i v i n g a n L . P . the c o m p a n y .  The necessary  m o d e l a p p l i c a b l e to  d a t a a r e t h e n c o l l e c t e d w i t h the  of the c o m p a n y i n o r d e r to c o n s t r u c t the m o d e l .  cooperation  T h e m o d e l is then  o n the U n i v e r s i t y of B r i t i s h C o l u m b i a ' s c o m p u t e r , The  Case  m o d e l I B M 7044.  c o m p u t e r p r o g r a m e m p l o y e d f o r s o l v i n g the m o d e l i s the I B M  L - P S y s t e m III p r o g r a m .  solved  4 Thesis Chapter Lay-out: C h a p t e r II p r e s e n t s a b r i e f e x a m i n a t i o n of the c o n c e p t o f L i n e a r P r o g r a m m i n g f r o m the s t a n d p o i n t of the t h e o r y o f the f i r m . i s t h e n f o l l o w e d b y a b r i e f s u m m a r y a c c o u n t of s o m e s u c c e s s f u l c a t i o n s of the L . P .  This  appli-  t e c h n i q u e m a d e b y a few p l y w o o d m a n u f a c t u r e r s .  C h a p t e r I V a n a l y s e s the m a n u f a c t u r i n g s y s t e m o f the C a s e C o m p a n y f o r the p u r p o s e of c o n c e i v i n g an L . P . m o d e l f o r u s e i n the c o m p a n y . L. P.  The  m o d e l d e v e l o p e d f o r u s e i n the c o m p a n y i s p r e s e n t e d i n C h a p t e r V .  T h e r e q u i r e d data is c o l l e c t e d i n C h a p t e r V I .  Chapter VJJ gives a b r i e f  i n t r o d u c t i o n to the c o m p u t e r p r o g r a m , I B M L P - I I I , w h i c h w a s u s e d to s o l v e the m o d e l .  A n i n t e r p r e t a t i o n of the f i n d i n g s f r o m the L . P .  a n a l y s i s of the C a s e C o m p a n y i s f o u n d i n C h a p t e r VIII.  This is  b y r e c o m m e n d e d a r e a s f o r f u r t h e r r e s e a r c h a n d the f i n a l f r o m the s t u d y i n C h a p t e r s I X a n d X  respectively.  followed  conclusions  5  C H A P T E R II  A NOTE ON T H ECONCEPT OF LINEAR  PROGRAMMING  T h e r e a r e a l m o s t as m a n y w r i t e - u p s o n the t h e o r y o f l i n e a r p r o g r a m m i n g as we c a r e to r e a d .  T h e r e a r e a l s o a l m o s t as m a n y  d e f i n i t i o n s as t h e r e a r e a u t h o r s i n the f i e l d .  T h i s b r i e f note i s not a n  a t t e m p t to a d d to the a l r e a d y a d e q u a t e a m o u n t o f r e f e r e n c e s topic.  o n the  T h e e x i s t i n g l i t e r a t u r e o n L . P . i s w e l l a d a p t e d to the n e e d s o f  d i f f e r e n t c l a s s e s o f r e a d e r s who h a v e h a d v a r i o u s l e v e l s o f t r a i n i n g i n mathematica,  in economics  and in business.  T h e p u r p o s e o f t h i s note  i s to e m p h a s i z e the r e l e v a n c e o f the L . P . c o n c e p t to the b u s i n e s s and to the b u s i n e s s  firm  environment.  2 Writers like D. U . Greenwald L. P.  e m p h a s i z e d the p u r p o s e of  as one o f the p r o c e s s e s o f d e t e r m i n i n g the b e s t p r o g r a m o f  activities (among m a n y alternatives);  with given r e s t r i c t i o n s and given  2 D.U. N. Y. ,  1957.  Greenwald, Linear Programming, Ronald P r e s s Co.,  6 l i n e a r r e l a t i o n s h i p a m o n g the a c t i v i t i e s .  W. W. Garvin  the n a t u r e of the p r o b l e m , i . e.  problem,  r e s t r i c t i n g l i n e a r equations function.  R.  the L . P .  or inequalities  Dorfman, A . Samuelson,  3  emphasized  as d e f i n e d b y  a n d cln o b j e c t i v e  and R . M .  linear  Solow almost  equate  4 L . P . to the a n a l y s i s o f L i P . p r o b l e m s . e m p h a s i z e d the a n a l y s i s  These later  writers  o f the p r o b l e m r a t h e r t h a n m e r e l y p r o v i d i n g  a s o l u t i o n to the p r o b l e m .  P o s t - o p t i m a l a n a l y s i s o f the p r o b l e m i s  c o n s i d e r e d as m u c h a p a r t o f the w h o l e p r o g r a m as the f i n d i n g o f the o p t i m u m solution. 5 However,  G. B.  appropriate emphasis L . P.  Dantzig  a p p e a r s to h a v e g i v e n the m o s t  to the s u b s t a n c e of L . P .  H e f e l t that,  to m a n y ,  r e f e r s to the m a t h e m a t i c a l m e t h o d s f o r s o l v i n g the l i n e a r  inequality systems. problem,  . . w h i l e t h i s m a y be the c e n t r a l  it is not its definition.  H e d e f i n e d L . P . as a t o o l , a m e t h o d  o r a t e c h n i q u e f o r s t u d y i n g the b e h a v i o r o f s y s t e m s . i n v o l v e s the b u i l d i n g of a m o d e l to d e s c r i b e the a m o n g the c o m p o n e n t s  mathematical  of the l i n e a r  T h e technique  interrelationship  system.  3 W.W.  G a r v i n , I n t r o d u c t i o n to L i n e a r P r o g r a m m i n g , M c G r a w -  H i l l B o o k C o . Inc.,  I960.  4 R.  D o r f m a n & P . A . S a m u e l s o n and R. M . Solow,  Linear  P r o g r a m m i n g and E c o n o m i c A n a l y s i s , M c G r a w - H i l l C o . Inc., N . Y . 5 G. B . Dantzig, Princeton University.  L i n e a r P r o g r a m m i n g and E x t e n s i o n ,  1963,  1958.  7  It i s f e l t that D a n t z i g ' s r e m a r k v e r y w e l l p u t s the L . P . a p p r o a c h i n the r i g h t p e r s p e c t i v e as it is u s e d i n i n d u s t r i e s t o d a y .  The appli-  c a t i o n o f t h e L . P . t e c h n i q u e i n v o l v e s t h e c o n s t r u c t i o n o f a m o d e l to r e p r e s e n t the b u s i n e s s  situation.  T h e m o d e l h a s to t a k e i n t o a c c o u n t  a l l t h e r e l e v a n t v a r i a b l e s t h a t a f f e c t the b u s i n e s s .  In f a c t ,  constructing  the m o d e l i s the m o s t t i m e c o n s u m i n g a n d the m o s t t r y i n g p a r t o f the process.  E v e r y b u s i n e s s h a s i t s o w n c h a r a c t e r i s t i c s a n d t h e y h a v e to  b e p r o g r a m m e d as s u c h . .  T h e a c t i v i t i e s of the b u s i n e s s  and their  r e l a t i o n s h i p a n d the r e l e v a n t c o n s t r a i n t s h a v e to b e r e a l i s t i c a l l y d e f i n e d for each b u s i n e s s  situation.  H o w e v e r , the b e n e f i t s  a r e not j u s t l i m i t e d  to the d i s c o v e r y o f the o p t i m u m p r o g r a m o f a c t i v i t i e s f o r the  business,  as w i l l b e i n d i c a t e d i n C h a p t e r III.  L i n e a r P r o g r a m m i n g a n d the T h e o r y o f the E c o n o m i c s o f the The  Firm;  d e v e l o p m e n t of the t h e o r y o f the e c o n o m i c s of the f i r m  was  c l o s e l y r e l a t e d to t h e d e v e l o p m e n t o f the t h e o r y o f l i n e a r p r o g r a m m i n g . In f a c t ,  the b r a n c h o f e c o n o m i c s k n o w n as l i n e a r e c o n o m i c s  developed  i n the f o l l o w i n g p a t t e r n : - firstly,  g a m e t h e o r y ( a t t r i b u t e d to J . V . N e u m a n n , 1928),  - secondly,  input-output analysis (advanced by Leontif  1936),  - thirdly, linear p r o g r a m m i n g (advanced by Dantzig,  1947).  R.  the two  Dorfman,  R. D o r f m a n ,  i n his doctoral dissertation  discussed  A p p l i c a t i o n of L i n e a r P r o g r a m m i n g to the  Theory  of the F i r m - I n c l u d i n g an A n a l y s i s o f M o n o p o l i s t i c F i r m s b y N o n - L i n e a r P'rogramming,  P h . D . Thesis,  U n i v e r s i t y of C a l i f o r n i a ,  1951.  8 a p p r o a c h e s to the t h e o r y o f the f i r m . be t e r m e d m a r g i n a l - a n a l y s i s , input-output analysis.  O n e of the two a p p r o a c h e s  may  w h i c h we m a y a t t r i b u t e to L e o n t i f f s  T h e s e c o n d i s the l i n e a r p r o g r a m m i n g a p p r o a c h .  B o t h a p p r o a c h e s a t t e m p t to e x p l a i n the s h o r t - r u n e q u i l i b r i u m of the i n t e r m s of f a c t o r i n p u t a n d p r o d u c t o u t p u t .  M a r g i n a l analysis is  firm  more  c o n c e r n e d w i t h d e s c r i b i n g w h e n the f i r m h a s r e a c h e d i t s e q u i l i b r i u m (optimum).  It i s b a s e d o n the n o t i o n t h a t m a r g i n a l r e v e n u e m u s t be  e q u a t e d to m a r g i n a l ( v a r i a b l e ) c o s t s .  B u t i t d o e s n o t s h o w us h o w to  o r p r o v i d e us w i t h the m e a n s f o r the f i r m to a r r i v e at the e q u i l i b r i u m p r o g r a m of activities.  O n the o t h e r h a n d , the l i n e a r p r o g r a m m i n g  a p p r o a c h d o e s p r o v i d e the m e a n s p r o g r a m of a c t i v i t i e s .  f o r the f i r m to a r r i v e at the e q u i l i b r i u m  T h i s i s e s p e c i a l l y h e l p f u l w h e n the f i r m i s  with tens o r even h u n d r e d s of a l t e r n a t i v e s are produced. necessary  However,  the L . P .  faced  and also when j o i n t - p r o d u c t s  a p p r o a c h i s h i n d e r e d b y the  a s s u m p t i o n of a constant e c o n o m i c s  of s c a l e ,  d e f i n e d r a n g e of the l e v e l of e a c h of the a c t i v i t i e s i n the  A t the b e g i n n i n g o f a p l a n n i n g p e r i o d ,  at l e a s t f o r a firm.  a b u s i n e s s m a y be  as h a v i n g a s e t of f i x e d f a c t o r s o f p r o d u c t i o n at i t s d i s p o s a l .  viewed  It a l s o  h a s a c c e s s to c o m p e t i n g m a r k e t s i n w h i c h i t c a n p r o c u r e ( w i t h i n l i m i t s ) the v a r i a b l e f a c t o r s o f p r o d u c t i o n n e e d e d to c o m b i n e w i t h the factors.  fixed  A d e f i n e d s e t o f m a r k e t i n g o p p o r t u n i t i e s i s o p e n to the  firm.  T h e p r o d u c t i o n p r o c e s s i s d e f i n e d b y the n a t u r e of the p l a n t , the h u m a n resources  a n d the p r o d u c t l i n e s that the p l a n t c a n p r o d u c e .  A n input-  9 output r e l a t i o n s h i p f o r the f a c t o r s o f p r o d u c t i o n i s a s s u m e d k n o w n a n d l i n e a r i n nature within defined l i m i t s .  T h e n u m b e r of a l t e r n a t i v e u s e s  o p e n to the f i x e d f a c t o r s o f p r o d u c t i o n a r e a s s u m e d to be ' f i n i t e .  The  f i r m i s t h e r e f o r e f a c e d w i t h the p r o b l e m o f s e l e c t i n g the b e s t p r o g r a m of activities for itself,  so as to m a x i m i s e the r e t u r n s to i t s  fixed  f a c t o r s of p r o d u c t i o n .  T h i s s i t u a t i o n p a r t i c u l a r l y l e n d s i t s e l f to  a n a l y s i s b y the L . P . a p p r o a c h .  In the c a s e w h e r e j o i n t - p r o d u c t s a r e p r o d u c e d , b e i t at the f i n a l s t a g e o f the p r o d u c t i o n o r at a n i n t e r m e d i a t e s t a g e , approach is,  the L . P .  as f a r as the p r e s e n t a u t h o r k n o w s , the o n l y s u r e w a y of  d e t e r m i n i n g the b e s t p r o g r a m o f a c t i v i t i e s .  D o r f m a n c o n c l u d e d that l i n e a r p r o g r a m m i n g w a s d e v e l o p e d i n r e s p o n s e to t h e n e e d to s o l v e s p e c i f i c e c o n o m i c p r o b l e m s as t h o s e o f a f i r m d e s c r i b e d above.  T h e b a s i c a s s u m p t i o n o f l i n e a r p r o g r a m m i n g as a p p l i e d to a b u s i n e s s s i t u a t i o n m i g h t b e s t a t e d a l o n g the l i n e t a k e n b y D o r f m a n : -  1) t h e p r o d u c t i v e o p p o r t u n i t i e s ( a l t e r n a t i v e s )  o p e n to a  10  business  a r e d e f i n e d b y the  available.  resources  a n d the p r o d u c t i v e p r o c e s s e s  T h e q u a n t i t i e s o f at l e a s t s o m e o f the r e s o u r c e s  a r e finite  a n d so i s the n u m b e r o f p r o d u c t i v e p r o c e s s e s a v a i l a b l e .  2) a n y p r o d u c t i v e p r o c e s s ( a c t i v i t y ) m a y b e u s e d at a n y p o s i t i v e l e v e l c o n s i s t e n t w i t h the s u p p l y o f r e s o u r c e s of r e s o u r c e s  available.  The consumption  a n d the output o f a p r o d u c t i s p r o p o r t i o n a l to the l e v e l at  w h i c h a . a n a c t i v i t y i s c a r r i e d out ( i . e.  the r a t i o o f o u t p u t to i n p u t i s  a s s u m e d constant and known for e v e r y activity. )  3) •; s e v e r a l p r o d u c t i v e p r o c e s s e s m a y b e c a r r i e d o n s i m u l t a n eously,  i f the s u p p l y o f r e s o u r c e s i s a d e q u a t e .  If t h i s i s d o n e , t h e  c o n s u m p t i o n o f e a c h r e s o u r c e i s the s u m o f t h e c o n s u m p t i o n o f t h e individual p r o c e s s e s c a r r i e d on. t o t a l o f the o u t p u t o f the i n d i v i d u a l  T h e output o f the p r o d u c t i s the  sum  processes.  In L . P . , a p r o c e s s i s d e f i n e d as a p a r t i c u l a r m e t h o d o f producing a specific product.  A m e t h o d i s d e f i n e d as a p a r t i c u l a r  c o m b i n a t i o n of f a c t o r s of p r o d u c t i o n .  F o r example, i f a product is  p r o d u c e d f r o m 1 unit of f a c t o r A plus 2 units of B o r i s p r o d u c e d f r o m 2 o f A p l u s 1 o f B , t h e n t h e s e two m e t h o d s d i f f e r e n t a c t i v i t i e s ( p r o c e s s e s ) i n the L . P .  a r e p r o g r a m m e d as  two  analysis.  In a j o i n t - p r o d u c t s i t u a t i o n , s a y , f r o m 3 o f A p l u s 2 o f B we p r o d u c e 2 units of Y p l u s 3 units of X , o r f r o m a f a c t o r c o m b i n a t i o n of 4 u n i t s o f A p l u s 1 u n i t o f B , we get a n o u t p u t o f 3 o f Y p l u s 4 o f X , then,  we w i l l p r o g r a m as two d i f f e r e n t a c t i v i t i e s , f a c t o r  of 3 A p l u s 2 B a n d 4 A p l u s 1 B .  combinations  11  In other words an L. P. optimal solution i s based on the assumptions of constant economics of scale and static conditions for  8 the planning period.  Non-linear programming and 'dynamic programming' may be used to treat situations of non-constant economics of scale and dynamic situations. In most practical situations, these more sophisticated techniques are not required. Running the L. P. analysis again when important variables change substantially is often adequate for handling dynamic situations. Straight-line approximation of nonslinear relationships for a defined range can often do away with the need for using nonlinear programming.  12  CHAPTER in  A REVIEW O F REPORTS ON T H E APPLICATION O F T H E LINEAR  SUCCESSFUL PROGRAMMING  T E C H N I Q U E IN T H E P L Y W O O D  INDUSTRY  It i s n o t p o s s i b l e to e x p e c t that e v e r y a t t e m p t i n a p p l y i n g a m a n a g e m e n t t e c h n i q u e w i l l b e r e p o r t e d e x t e r n a l to the c o m p a n y concerned.  T h e a p p l i c a t i o n of the l i n e a r p r o g r a m m i n g t e c h n i q u e i n  the p l y w o o d i n d u s t r y i s no e x c e p t i o n .  T h o s e p e o p l e who f a i l i n t h e i r  a t t e m p t a r e l i k e l y to p r e f e r to k e e p q u i e t about the w h o l e a f f a i r .  Those  who s u c c e e d a n d a r e e n t h u s i a s t i c a b o u t i t m a y not b e too k e e n to l e t t h e i r c o m p e t i t o r s i n t o the s e c r e t u n t i l p e r h a p s a f t e r t h e y h a v e  securely  stolen a m a r c h on their c o m p e t i t o r s .  The  few r e p o r t s t h a t one m a y e n c o u n t e r i n p r o f e s s i o n a l  j o u r n a l s a n d s e m i n a r s e s s i o n s b y no m e a n s i n c l u d e a l l the applications. so r e p o r t e d . narration.  successful  N e i t h e r w o u l d one e x p e c t u n s u c c e s s f u l a t t e m p t s to b e Also,  t h e s e r e p o r t s a r e often b r i e f and g e n e r a l i n  T h e benefits  c l a i m e d f o r the t e c h n i q u e a r e o f t e n a j o i n t  13  r e s u l t of other m o v e s  as w e l l , not p u r e l y due to the u s e o f the L. P .  technique.  i t i s a l m o s t i m p o s s i b l e to a s s i g n the  Granted,  benefits  precisely.  However,  f r o m a n a n a l y s i s o f the few r e p o r t s a v a i l a b l e , one  m a y get a g o o d p i c t u r e o f the e x p e r i e n c e of the p l y w o o d i n d u s t r y w i t h the Li. P . t e c h n i q u e .  P e r h a p s , we m a y b e n e f i t f r o m the r e p o r t e d  e x p e r i e n c e b y l e a r n i n g i n w h i c h a r e a s o f d e c i s i o n m a k i n g the L . P . technique works well.  I n d u s t r i a l A p p l i c a t i o n of L . P .  Technique:  T h e m a t h e m a t i c a l c o n c e p t o f l i n e a r p r o g r a m m i n g i s now a  9 r e a s o n a b l y m a t u r e d concept.  T h e v i g o r o u s a p p l i c a t i o n o f the  c o n c e p t to d e f i n i n g a n d s o l v i n g p r a c t i c a l p r o b l e m s dates b a c k to the second world war, i n the N a v y .  w h e n D a n t z i g a p p l i e d i t to m a n a g e m e n t  problems  A n u m b e r of y e a r s l a t e r i n d u s t r i e s b e g a n to s e e  the  u s e f u l n e s s o f t h i s new t e c h n i q u e f o r s o l v i n g b u s i n e s s p r o b l e m s . the p a s t d e c a d e o r s o ,  the p r o f e s s i o n a l j o u r n a l s h a v e d e s c r i b e d l i n e a r  programming movements oil industry.  In  i n a v a r i e t y of i n d u s t r i e s ,  s t a r t i n g w i t h the  It does not t a k e too m u c h e f f o r t to v i s u a l i s e h o w the  s u c c e s s a c h i e v e d i n i t s u s e b y one i n d u s t r y o r b y one m a n a g e m e n t w o u l d c a u s e o t h e r s to s e e k to u s e i t t o o .  9 Mathematically,  the L . P .  c o n c e p t i s c o n c e i v e d as b e i n g the  m a x i m i s a t i o n ( m i n i m i s a t i o n ) of a l i n e a r f u n c t i o n , of l i n e a r i n e q u a l i t i e s .  s u b j e c t to the c o n s t r a i n t  In the e a r l i e r d a y s of the t e c h n i q u e , Pacific Coast, e m b r a c e it. Business  the p l y w o o d p e o p l e of the  l i k e those i n other i n d u s t r i e s , d i d not i m m e d i a t e l y  T h e o l d ways of m a k i n g decisions  was good.  handful of p r o d u c t s .  seemed  adequate.  "The soft-wood plywood industry made a m e r e The raw material, i.e.  l o g s , was h i g h g r a d e ,  old  g r o w t h D o u g l a s F i r - - i n f e r i o r g r a d e s a n d o t h e r s p e c i e s of w o o d w e r e simply by-passed.  . .  T h e r e w a s l i t t l e n e e d to w a t c h the p r o f i t m a r g i n . "  But times have changed.  T h e n u m b e r of p r o d u c t s has g r e a t l y i n c r e a s e d .  " C o m p e t i t i o n has f o r c e d down p r i c e s i n g e n e r a l . on the d w i n d l i n g s u p p l y o f o l d g r o w t h t i m b e r .  Pressure  mounted  Now there  are  m o r e alternatives  to c o m p e t e f o r the u s e of the l o g s a l s o .  these alternatives  m a d e d e c i d i n g w h a t b e s t to do i n the b u s i n e s s  increasingly complicated.  Consequently,  The o l d ways of m a k i n g d e c i s i o n  become i n c r e a s i n g l y inadequate.  A n E a r l y Attempt: O n e of the e a r l i e s t w r i t e - u p s o n a n a p p l i c a t i o n of the L . P . t e c h n i q u e i n the p l y w o o d i n d u s t r y was b y J . S . B e t h e l & , 12 i n 1956.  T h e r e p o r t was b a s e d on s o m e consulting w o r k they d i d for  R. H . Donnelly, facturing,  Co. Harrell,  Linear Programming in Plywood Manu-  the P r o c e e d i n g s of the I B M C o n f e r e n c e o n O p e r a t i o n s  R e s e a r c h i n the F o r e s t P r o d u c t Industry,  November,  1965.  R . H . D o n n e l l y m a d e t h e s e o b s e r v a t i o n s as a n i n s i d e p e r s o n i n the p l y w o o d i n d u s t r y . 12 P u b l i s h e d i n F o r e s t P r o d u c t s J o u r n a l , V o l . V J J , N o . 7, July, 1957.  15  a hard-wood plywood f i r m .  T h e y c l a i m e d t h a t as f a r as t h e y k n e w ,  a p p l i c a t i o n o f the L . P . t e c h n i q u e i n the w o o d - u s i n g i n d u s t r y w a s f i r s t one to b e m a d e .  their  the  T h e i r a r e a o f a p p l i c a t i o n s i g h t e d w a s i n the  s e l e c t i o n of the m o s t p r o f i t a b l e m i x of p l y w o o d p a n e l s to p r o d u c e , t a k i n g into c o n s i d e r a t i o n a c a p a c i t y c o n s t r a i n t and a m a r k e t c o n s t r a i n t .  A n o t a b l e o m i s s i o n i n the m o d e l u s e d w a s t h a t i t g a v e no e x p l i c i t c o n s i d e r a t i o n to the c o s t of the l o g s .  T h e a u t h o r s c o u l d not  h a v e d e d u c t e d the w o o d - c o s t f r o m the p r i c e o f the v a r i o u s g r a d e s  of  p l y w o o d p a n e l as t h e r e i s no r e l i a b l e w a y to a s s i g n t h e j j o i n t w o o d - c o s t to the d i f f e r e n t g r a d e c o m b i n a t i o n s of v e n e e r t h a t m a k e up the p l y w o o d panels.  T h i s p e r h a p s r e f l e c t e d the l a c k o f c o n c e r n f o r o t h e r u s e s f o r  the l o g s a p a r t f r o m p l y w o o d p r o d u c t i o n .  M o r e l i k e l y , i t r e f l e c t e d the  p r i m i t i v e s t a t e o f the a r t of a p p l y i n g the L i P . t e c h n i q u e i n the w o o d i n d u s t r y as w e l l as the l a c k o f a n e a s y a c c e s s to e f f i c i e n t facilities.  computing  T h e s i m p l e x m e t h o d w a s u s e d to s o l v e the p r o b l e m a n d the  c o m p u t a t i o n w a s done o n d e s k - c a l c u l a t o r s .  A Later Attempt: M a n y o t h e r a t t e m p t s at a p p l y i n g the L . P . t e c h n i q u e i n the soft-wood plywood industry followed.  O n e o f the r e p o r t s w o r t h y o f 13  m e n t i o n was that b y E . K o e n i g s b e r g i n I960.  T h e r e p o r t was  based  13 E. Industry,  K o e n i g s b e r g , A p p l y i n g L i n e a r P r o g r a m m i n g to the P l y w o o d  Forest Product Journal,  V o l . X , Sept.  I960.  16  o n a n u m b e r o f p i l o t s t u d i e s m a d e f o r a n u m b e r of  companies.  T h e a r e a s of application sighted include: - log purchasing - veneer production - product m i x selection. f i r s t a n d the t h i r d a r e a s ,  T h e r e p o r t o n l y d e a l t w i t h the  one i n d e p e n d e n t l y o f the  other.  T h e p r o d u c t m i x p r o b l e m was t r e a t e d with a g i v e n s u p p l y of the v a r i o u s g r a d e s of v e n e e r .  T h e p r o b l e m w a s to f i n d the b e s t  p l y w o o d p a n e l m i x to p r o d u c e out of the v e n e e r s u p p l y . c o s t was  No opportunity  c o n s i d e r e d a p a r t f r o m the p l y w o o d p r o d u c t l i s t e d i n the  problem.  No restrictions  the m a r k e t .  w e r e s e t o n the p r o c e s s i n g f a c i l i t i e s  T h e p r o b l e m was  solved using a computer.  In a d d i t i o n to f i n d i n g the o p t i m a l p r o d u c t m i x , the also generated  and  computer  ' s h a d o w p r i c e s ' w h i c h t o l d b y h o w m u c h the p r o f i t w o u l d  b e r e d u c e d i f one w e r e to b r i n g one u n i t o f one o f the n o n - o p t i m a l p r o d u c t s i n t o the o p t i m a l m i x , t h u s - . f o r c i n g out o n e of the o p t i m a l p r o d u c t s ( i . e.  the one w i t h the l e a s t i m p a c t , p r o f i t - w i s e . ) •  p r i c e ' t h e r e f o r e t o l d the c o m p a n y h o w m u c h a m a r k e t  The  'shadow  commitment  to p r o d u c e one u n i t of one o f the n o n - o p t i m a l p r o d u c t s w o u l d c o s t the company in terms  of s u b - o p t i m i s a t i o n .  T h e 'shadow cost'  developed  f o r the v e n e e r t o l d the c o m p a n y h o w m u c h m o r e o r l e s s p r o f i t i t w o u l d m a k e g i v e n one u n i t m o r e o r one u n i t l e s s of one o f the g r a d e s  of  veneer.  1  T h e 'shadow cost  1  o f the v e n e e r d o e s n o t h o l d t r u e f o r v e n e e r t h a t i s  already i n excess supply.  T h e s e c o n d a p p l i c a t i o n s i g h t e d w a s i n the c h o i c e o f the b e s t c o m b i n a t i o n of l o g s to p u r c h a s e a n d to p e e l i n o r d e r to m e e t a k n o w n r e q u i r e m e n t for veneer.  T h e m o d e l p r e s u p p o s e d that the u s e r knew  the v e n e e r y i e l d f r o m e a c h g r a d e o f l o g s . c o s t s the s a m e to p r o c e s s  It a l s o a s s u m e d that i t  any grade and any s p e c i e of l o g .  This  need  not b e t r u e as s o m e g r a d e s o f l o g r e q u i r e m o r e u p - g r a d i n g p r o c e s s i n g for the v e n e e r than o t h e r s .  T h e m o d e l a l s o d i d not c o n s i d e r t h e c h o i c  of v e n e e r t h i c k n e s s n o r a l t e r n a t i v e c o n s t r u c t i o n for the p a n e l s .  T h e a u t h o r d i d not s h o w h o w t h e two r e l a t e d m o d e l s a r e to b e tied together.  T h e f i r s t a s s u m e s a f i x e d s u p p l y of v e n e e r a n d t h e  o f the v e n e e r i s o p e n to c h o i c e .  use  The second assumes a fixed r e q u i r e -  m e n t f o r v e n e e r a n d the s u p p l y o f l o g s (thus v e n e e r ) i s o p e n to c h o i c e . T h e a l t e r n a t i v e u s e s o t h e r t h a n p l y w o o d - p r o d u c t i o n a v a i l a b l e to the l o g s a r e not c o n s i d e r e d .  H o w e v e r , this application definitely  s o m e p r o g r e s s o v e r the t i m e of B e t h e l & H a r r e l l .  T h e u s e o f the  c o m p u t e r a n d the d e v e l o p m e n t of 'shadow p r i c e s ' a n d 'shadow are commendable useful  achievements.  reflects  costs'  18 T h e E x p e r i e n c e of S i m p s o n T i m b e r C o m p a n y , S e a t t l e , W a s h i n g t o n ( U . S. A . ) : S i m p s o n T i m b e r C o m p a n y r e p o r t e d o n i t s s u c c e s s w i t h the  use  14 o f the c o m p u t e r a n d o p e r a t i o n s operations  r e s e a r c h techniques.  A n important  r e s e a r c h technique u s e d i n conjunction with its  manufacturing activities up its e x p e r i e n c e "Yes,  is l i n e a r p r o g r a m m i n g .  plywood  The report  summed  as:-  definitely,  . . . we h a v e b e e n s u c c e s s f u l .  The  c o m p a n y i s h e a v i l y c o m m i t t e d to the u s e o f m o d e r n m a n a g e m e n t which include operations  research, scientific  the c o m p u t e r ( d e f i n e d as E D P ) . . . .  methods  s y s t e m s a n d the u s e o f  W e see l o t s of o p p o r t u n i t y  a h e a d f o r p r o f i t a b l e u s e of E D P i n o u r p l y w o o d a n d o t h e r m a n u f a c t u r i n g operations.  M a n a g e m e n t has a p p r o v e d for p r o g r a m m i n g s i m i l a r E D P  applications i n o u r Insulating B o a r d P l a n t and i n our D o o r D i v i s i o n . . . . A new D e p a r t m e n t of C o r p o r a t e D e v e l o p m e n t , P r e s i d e n t was  created,  headed by a V i c e -  and a staff of i n d u s t r i a l engineers,  D i r e c t o r o f O . R . w i l l f o r m an i m p o r t a n t p a r t of t h i s n e w The company became Its e n g i n e e r i n g  headed by a 15 department."  a c q u a i n t e d w i t h the c o m p u t e r a r o u n d 1961.  s t a f f u s e d the I B M - 1 6 2 0 to s t u d y L . P .  models for  its  14 E.N.  G i l e s (the C h i e f S y s t e m s E n g i n e e r ) , T h e C o m p u t e r i n  P l y w o o d M a n u f a c t u r i n g at S i m p s o n T i m b e r C o m p a n y , an u n p u b l i s h e d r e p o r t p r e s e n t e d at a s e m i n a r s e s s i o n (no date a n d no l o c a t i o n ) .  This  i s a w e l l i n t e g r a t e d c o m p a n y , p r o d u c i n g a l a r g e v a r i e t y of p r o d u c t , including lumber,  plywood,  etc.  15 I b i d . , footnote #14  above.  plywood manufacturing activities.  S i n c e t h e n , the p l y w o o d L . P .  h a s i n c r e a s e d i n s c o p e a n d i n d e t a i l o v e r the y e a r s . report,  the m a t r i x o f the m o d e l u s e d was  model  A t the t i m e of the  340 x 1200 a n d w a s r u n o n a n  IBM-7094.  The L . P . mix,  model(s) is u s e d for d e t e r m i n i n g o p t i m u m p l y w o o d  l o g a l l o c a t i o n to v a r i o u s a l t e r n a t i v e u s e s ( p l y w o o d m a n u f a c t u r i n g  b e i n g one of t h e m ) a n d f o r p l a n t f a c i l i t i e s p l a n n i n g .  The report,  however,  o n l y d e a l t w i t h the f i r s t a r e a o f a p p l i c a t i o n i n a n y g r e a t d e t a i l .  T h e o p t i m u m p r o d u c t m i x o b t a i n e d i s u s e d to s e t (policies)(for  production and for s a l e s .  E a c h w e e k , the  guidelines  company's  s a l e s o r d e r s a r e s u m m a r i z e d a n d c o m p a r e d to the o p t i m u m p r o d u c t m i x b y the p r o d u c t i o n m a n a g e r a n d t h e n s u b m i t t e d to the s a l e s to g u i d e f u t u r e s a l e s  manager  activities.  T h e l e n g t h o f the p l a n n i n g p e r i o d u s e d b y the L . P . m o d e l not g i v e n i n the r e p o r t . half-yearly basis,  Presumably,  was  it is on a y e a r l y b a s i s o r even  a n d the s a l e p l a n i s r e v i s e d w h e n e v e r t h e r e  are  s i g n i f i c a n t c h a n g e s i n s o m e o f the r e l e v a n t v a r i a b l e s i n the m o d e l . T h o u g h not m e n t i o n e d ,  we m a y s p e c u l a t e t h a t the m o d e l c o v e r s m o s t o f  the v a r i a b l e s a f f e c t i n g the  company.  T h e p l y w o o d L . P . m o d e l w a s r e p o r t e d as u s e d b y the ment for evaluating plans and for setting objectives.  manage-  T h i s might also be  i n t e r p r e t e d as u s i n g the L . P . m o d e l f o r s u c h p u r p o s e s budgets into an o p t i m u m whole,  as t y i n g u p s u b -  for facilities investment planning,  In c o n n e c t i o n w i t h the a p p l i c a t i o n of the L . P . m o d e l ( s ) , other s u p p l e m e n t a r y O . R . techniques  were also successfully  R e l i a b l e v e n e e r - r e c o v e r y data w e r e c o l l e c t e d .  many  applied.  T h e c o m p u t e r was  to f i n d the b e s t c o n s t r u c t i o n f o r the p l y w o o d p a n e l s .  A useful  etc.  used  costing  s y s t e m was i n s t a l l e d and r e l i a b l e i n f o r m a t i o n o n p l a n t c a p a c i t i e s  were  collected.  T h e company also developed a s y s t e m for c e n t r a l l y allocating s a l e s o r d e r s to i t s v a r i o u s p l a n t s a c c o r d i n g to the ' b e s t fit. ' c o n t r o l was kept o v e r i n - p r o c e s s inventories.  veneer inventories  The inventory positions  A close  and plywood panel  a r e c o n s t a n t l y r e p o r t e d to  manage  ment.  In 1963,  the c o m p a n y d e c i d e d to b u i l d a n e w m o d e r n c e n t r a l  p e e l i n g p l a n t to s u p p l y v e n e e r to 3 s e p a r a t e p a n e l l a y - u p p l a n t s . r e p o r t d i d not i n d i c a t e to w h a t e x t e n t the c h a n g e - o f - f a c i l i t i e s w i t h the L i . P . m o d e l h e l p e d m a n a g e m e n t to a r r i v e at t h i s successful  move.  The  analysis  seemingly  P e e l i n g logs and allocating veneer f r o m a c e n t r a l  p l a n t do h e l p to c u t d o w n s u c h l o s s e s as t h o s e o c c u r i n g f r o m the d o w n 16 g r a d i n g of v e n e e r .  O n l y the r e q u i r e d v e n e e r i s s h i p p e d out to the  panel lay-up plants. ^ A g r a d e i n the  s h e e t o f v e n e e r i s d o w n - g r a d e d w h e n i t i s u s e d as a l o w e r panel l a y - u p than it actually i s .  21  T h e E x p e r i e n c e o f B o i s e C a s c a d e C o m p a n y ( U . S. A . ) : T h e e x p e r i e n c e of B o i s e C a s c a d e with L . P . and other O . R. 17 t e c h n i q u e s w a s r e p o r t e d i n a 1966 i s s u e of B u s i n e s s W e e k i n a s e m i n a r p a p e r p r e s e n t e d b y one o f i t s c o m p a n y o f f i c i a l s .  and also 1  The  8  l a t t e r s u m m e d up i t s s u c c e s s b y : " T h e r e s u l t s of this w o r k h a v e b e e n e x t r e m e l y W e (the c o m p a n y ) ,  too,  are enthusiastic.  our p r o d u c t i o n and sales people.  successful.  This enthusiasm is shared by  A l r e a d y , direct savings have been  r e a l i s e d m u c h i n e x c e s s o f the r e p o r t e d e x p e r i e n c e .  The potential  i s e x p a n d i n g as o u r m a n a g e m e n t l e a r n s h o w to l i v e w i t h L . P . a n d a p p l y i n g it i n new d i r e c t i o n s . "  19  T h e B u s i n e s s W e e k r e p o r t i n d i c a t e d that the u s e o f the L . P . m o d e l h a d h e l p e d o r m a d e i t p o s s i b l e f o r the c o m p a n y to t u r n a l o s s o f $100, 000 p . a.  at i t s P a y e t t e (Idaho) p l y w o o d p l a n t i n t o a s o l i d p r o f i t  r e c o r d e d at $55, 000 the f i r s t m o n t h .  In Idaho, the c o m p a n y h a r v e s t e d t r e e s f r o m f o u r f o r e s t L o g s w e r e s e n t to f i v e s a w m i l l s at B a r b e r ,  areas.  Cascade, Council, Eonmett  _ S e e B u s i n e s s W e e k , J a n u a r y 1st, to P r o f i t s i n L u m b e r . 18 I b i d . , footnote #10, p a g e 14 19 See also F o r e s t I n d u s t r i e s , F e b .  1966,  Computer Points Way  1966,  V o l . 16, N o .  O p e r a t i o n s R e s e a r c h - - T o o l f o r G r o w t h at B o i s e C a s c a d e .  2,  22  and M c C a l l ,  a n d a l s o to the P a y e t t e p l y w o o d m i l l .  m i l l capacities, opportunities,  log species,  T a k i n g into account  l o g s i z e s and l o g quality, and m a r k e t  the L . P . m o d e l c a m e . up w i t h the o p t i m u m l o g a l l o c a t i o n  to the m i l l s a n d to the v a r i o u s p r o d u c t l i n e s .  The L . P .  analysis indicated  that i n c r e a s e d t r a n s p o r t a t i o n c o s t s can be o f f - s e t b y g r e a t e r m i l l p r o f i t i f c e r t a i n l o g s b y - p a s s e d the n e a r e s t m i l l a n d w e r e u s e d i n s t e a d to i n c r e a s e the p r o d u c t i o n r a t e o f a n o t h e r .  T h e a n a l y s i s a l s o s h o w e d that  one o f the m i l l ' s p r o d u c t i v i t y c o u l d b e i n c r e a s e d i f i t s w i t c h e d f r o m w h i t e f i r to a n o t h e r s p e c i e o f l o g s .  O u t s t a n d i n g i m p r o v e m e n t to the  operations  of the P a y e t t e p l y w o o d p l a n t i n c l u d e d a r e d u c t i o n i n p e e l i n g D o u g l a s f i r for C o r e veneer,  a n d i n s t e a d u s i n g the f r e e d l o g s f o r l u m b e r .  The  p l y w o o d plant s t a r t e d taking i n other s p e c i e s of wood i n s t e a d . f o r i t s p r o d u c t i o n of s h e a t h i n g s ,  Also,  l o w e r g r a d e s of l o g s w e r e u s e d ,  r e l e a s i n g high grade logs for p r o d u c i n g high grade panels.  thus  The computer  a l s o a d v i s e d the p l a n t to c h a n g e i t s b a s i c p r o d u c t f r o m 5 - p l y p a n e l s  to  3 - p l y p a n e l s b e c a u s e the p l a n t h a d o n l y one g l u e - s p r e a d e r a n d i t w a s hamstringing production.  B u s i n e s s W e e k r e p o r t e d that these  a d d e d s o m e $1.50 to $2. 00 to the r e t u r n o f the m i l l f o r e v e r y  moves 1,000  b o a r d feet p r o d u c e d .  L; P.  a p p l i c a t i o n is often a p a c k a g e d e a l .  M a n y other  'supplementary' and ' c o m p l e m e n t a r y ' O . R . techniques have come with it since  1964.  A m o n g other things,  the c o m p a n y h a d to c a r r y o n m a n y  v e n e e r r e c o v e r y s t u d i e s f o r the L . P .  application.  In the p r o c e s s ,  the  c o m p a n y d e v e l o p e d a new s y s t e m f o r l o g g r a d i n g , a s y s t e m t h a t i s  more  h e l p f u l t h a n the e x i s t i n g one f o r c o n t r o l l i n g the p r o d u c t i o n p r o c e s s .  I n d e e d the c o m p a n y i s e n t h u s i a s t i c . i n a g r e a t e r u s e of L . P .  It i s o n l y the b e g i n n i n g  and other O . R . t e c h n i q u e s .  Future  possibilities  of the a p p l i c a t i o n of the O . R . t e c h n i q u e e x t e n d to e v e r y f a c e t of the company,  s t r e t c h i n g f r o m the o p e r a t i o n of the m i l l s r i g h t b a c k to a s t a n d  o f t r e e s i n the  forest.  Q u o t i n g the S e n i o r A n a l y s t , the c o m p u t e r was a b l e to c o m e up w i t h a l o n g l i s t of s m a l l c o s t s a v i n g s determined.  w h i c h no m a n a l o n e c o u l d h a v e  E a c h o f the m i n u t e d i f f e r e n c e s  f r a c t i o n of a c e n t p e r b o a r d foot o f l u m b e r .  might mean saving only a But, multiplying these  f r a c t i o n s b y the a n n u a l v o l u m e of m i l l i o n s o f b o a r d feet, the s u m c a n a d d u p to t h o u s a n d s o f d o l l a r s i n i n c r e a s e d p r o f i t .  T h e E x p e r i e n c e of W e y e r h a e u s e r C o m p a n y ( U . S . A . ) : 20 The same Business  Week report  a l s o m e n t i o n e d the  that the W e y e r h a e u s e r C o m p a n y h a d w i t h L . P . The applications ranged f r o m forecasting,  and other O . R .  success techniques.  facilities planning, scheduling  o f p r o d u c t i o n to p r o f i t - m a r g i n a n a l y s i s of p r o d u c t l i n e s .  The report  s p e c i f i c a l l y m e n t i o n e d that the c o m p a n y u s e s the c o m p u t e r i n the m a n a g e m e n t of i t s p l y w o o d , p u l p , p a p e r - b o a r d a n d c o n t a i n e r s —  I b i d . , footnote #17,  page 21.  divisions.  24  O n e p a r t i c u l a r a r e a of s u c c e s s w a s i n the a n a l y s i s o f the p r o f i t m a r g i n of the p r o d u c t l i n e s i n a m u l t i - p r o d u c t s i t u a t i o n .  T h e plant had  an a v e r a g e p r o f i t m a r g i n o f $2 / u n i t o f p r o d u c t , a n d i t w a s t h o u g h t that i t was doing r e a s o n a b l y w e l l .  However,  the a n a l y s i s p o i n t e d out that  a c t u a l p r o d u c t - l i n e c o n t r i b u t i o n r a n g e d f r o m a $48 / u n i t f o r one p r o d u c t to a l o s s of $ 3 6 A i n i t f o r a n o t h e r .  This discovery had drastically  the p a t t e r n o f p r o d u c t - l i n e e m p h a s i s  changed  i n the m a r k e t i n g d e p a r t m e n t o f the  company.  The  E x p e r i e n c e of T o c c o a C a s k e t C o m p a n y , G e o r g i a ( U . S . A . ) :  21  T h i s c o m p a n y w a s u s e d as a c a s e s t u d y i n the r e s e a r c h c a r r i e d 22 out f o r a D o c t o r a t e o f F o r e s t r y D i s s e r t a t i o n .  A s a result,  the  c o m p a n y c a m e to u s e l i n e a r p r o g r a m m i n g m o d e l s i n a n a l y s i n g i t s operations. The  Li. P .  m o d e l was u s e d to f i n d the b e s t p r o d u c t m i x ,  particular emphasis the c o m p a n y . labour,  and with  p l a c e d o n l o c a t i n g b o t t l e n e c k s i n the f a c i l i t i e s  of  A s t h i s i n d u s t r y e n g a g e s a v e r y h i g h l y - s k i l l e d t y p e of  c a p a c i t y u t i l i z a t i o n e x p a n s i o n i s b y no m e a n s a s h o r t - t i m e  Intthe a n a l y s i s ,  project.  b o t t l e n e c k s as w e l l as e x c e s s c a p a c i t y w e r e  p o i n t e d out i n the p r o d u c t i o n p r o c e s s . the flow of the o p e r a t i o n s  U p o n the s t r e n g t h of t h i s  for some products were changed.  analysis,  T h i s was  _ T h i s i s not i n the p l y w o o d i n d u s t r y . 22 W. C  Randel (Syracuse University, U . S . A . ,  Programming in a Small Forest Products  Firm.  1963,) L i n e a r  done  i n o r d e r to m i n i m i z e the i m p a c t o f the b o t t l e n e c k s o n the p r o d u c t i o n system.  T h e e x c e s s c a p a c i t y i n s o m e p a r t s o f the p r o d u c t i o n s y s t e m  was u s e d as a b a s i s f o r d e c i d i n g to i n t r o d u c e a new c a s k e t l i n e , w h i c h the m a n a g e m e n t a l s o b e l i e v e d to h a v e a g o o d m a r k e t .  T h i s is a good e x a m p l e of how a s m a l l c o m p a n y , without a c o m p u t e r of its own,  m a y a l s o b e n e f i t f r o m an a n a l y s i s o f i t s  w i t h the u s e o f a n L ; P . m o d e l . b y an o u t s i d e r ,  Such a one-time analysis,  operations  c a r r i e d out  c o u l d h e l p to i m p r o v e i t s o p e r a t i o n s u b s t a n t i a l l y .  Only  w h e n the c o n d i t i o n s a g a i n c h a n g e s u b s t a n t i a l l y n e e d the c o m p a n y s e e k further external consultation.  Summary: T h e few p r e c e e d i n g c a s e s s h o u l d s u f f i c e to i n d i c a t e that  since  the e a r l y q u a r t e r o f t h i s d e c a d e , the w o o d - p r o d u c t i n d u s t r y h a s c o m m i t t e d i t s e l f h e a v i l y to the u s e o f L . P . Simpson T i m b e r Company,  and other O . R . techniques.  B o i s e C a s c a d e C o m p a n y , and W e y e r h a e u s e r  C o m p a n y a r e s o m e o f the few l e a d i n g g i a n t s i n the f o r e s t p r o d u c t s i n d u s t r y i n the U . S . A .  N o r c a n we s a y that the s m a l l c o m p a n i e s  a r e e x c l u d e d f r o m the l i s t .  O f c o u r s e , t h e s e a r e not the o n l y c o m p a n i e s  i n the i n d u s t r y t h a t h a v e s u c c e s s f u l l y e x p e r i m e n t e d w i t h the new techniques. attempts  We c a n a l s o be c e r t a i n that t h e r e w e r e  as w e l l .  However,  p o t e n t i a l i t y of L . P . often,  unsuccessful  we c a n s e e the f e a s i b i l i t y a n d the  a n d o t h e r O . R . a p p r o a c h e s i n the i n d u s t r y .  Very  the a p p l i c a t i o n o f one t e c h n i q u e i s a n a t u r a l e x t e n s i o n f r o m t h a t o f  26  another technique.  Typical successful  a r e a s of a p p l i c a t i o n for the L . P .  approach  i n c l u d e d i n t e g r a t i n g sub-budgets into an o p t i m u m whole, o p t i m u m l o g a l l o c a t i o n to 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 , o p t i m u m p r o d u c t m i x , a n a l y s i s of p r o d u c t line contribution under conditions of joint costs, facilities bottleneck analysis, expansion,  etc.  facilities planning, product-line  27  C H A P T E R IV  THE PLYWOOD MANUFACTURING PROCESS WITH SPECIAL R E F E R E N C E TO T H E CASE  -  COMPANY  T h e Softwood P l y w o o d M a n u f a c t u r i n g P r o c e s s It i s not p o s s i b l e to s p e a k of the one ( s o f t w o o d ) p l y w o o d manufacturing process.  However,  as R . H . D o n n e l l y a p t l y p u t i t ,  " w h i l e the d e g r e e of m a c h i n i z a t i o n a n d p l a n t s i z e a r e v a r i a b l e , m o s t  23 softwood p l y w o o d is m a n u f a c t u r e d i n a s i m i l a r fashion. "  The present  w r i t e r h a d the o p p o r t u n i t y to o b s e r v e the p r o d u c t i o n m e t h o d s of 4 separate  m i l l s o p e r a t e d u n d e r two d i f f e r e n t o r g a n i z a t i o n s .  O n e of the  m i l l s i s a c c l a i m e d to b e the l a r g e s t s i n g l e p l y w o o d m i l l i n the w o r l d w h i l e the o t h e r t h r e e a r e o f a m u c h l o w e r c a p a c i t y .  Yet,  the w r i t e r  i s of the o p i n i o n that the 4 m i l l s d i f f e r o n l y i n t h e i r d e g r e e o f m e c h a n i sation,  t h e i r c a p a c i t y a n d the e f f i c i e n c y of t h e i r m a c h i n e r y .  2*3  I b i d . , footnote #10,  page  14  In e v e r y  28  one o f t h e m ,  i t i s p o s s i b l e to s e e the l o g p e e l i n g - v e n e e r d r y i n g  -  veneer upgrading - panel lay-up - panel p r e s s i n g - panel finishing process.  It i s t h e r e f o r e h o p e d t h a t a c o m p r e h e n s i v e a c c o u n t o f t h e  o p e r a t i o n s o f the C a s e C o m p a n y w i l l s u f f i c e to p r e s e n t a g o o d p i c t u r e of the p r o d u c t i o n p r o c e s s  o f t h e soft w o o d p l y w o o d m a n u f a c t u r i n g  b u s i n e s s.  Process  Flow Chart:  C h a r t I t r a c e s out the r e l a t i o n s h i p o f the m a n u f a c t u r i n g s t e p s in a typical plywood m i l l .  L o g Supply: L o g s f e e d i n g the m i l l a r e a c q u i r e d e i t h e r f r o m the o p e n l o g m a r k e t o r f r o m t i m b e r l a n d o w n e d b y the c o m p a n y .  A c o m p a n y that  p u r c h a s e s l o g s i n the o p e n m a r k e t h a s to d e c i d e o n the c o m b i n a t i o n o f w o o d s p e c i e s a n d l o g g r a d e s that w o u l d b e s t m e e t i t s  requirements.  O n the o t h e r h a n d , a w e l l i n t e g r a t e d c o m p a n y w i t h i t s o w n s o u r c e s l o g s u p p l y h a s to d e c i d e o n the b e s t a l l o c a t i o n of i t s l o g s to i t s  of  various  m a n u f a c t u r i n g o r p r o c e s s i n g a c t i v i t i e s o r e v e n to the o p e n l o g - m a r k e t .  L o g s a r e t r a n s p o r t e d to the m i l l s i t e , u s u a l l y b y w a t e r , i n 24  b o o m s of v a r i o u s s p e c i e - m i x a n d g r a d e - m i x .  B o o m s of a s i n g l e  24 F o r a s a m p l e o f the l o g g r a d i n g s y s t e m u s e d i n B r i t i s h Columbia,  s e e A p p e n d i x I.  CHART I PLYWOOD MANUFACTURING PROCESS FLOW-CHART  Veneer  Production  Veneer  Logs fcefie.(L For Veneer  Processing  Plywood Panel Production  Ven.ee r 2>rie.cL  Pr esse-A. Pro A u c t i o n .  Venctr  AruL Sale, of Bj- Proiuct  Pantt  * 4-  ^ tferueer fatxKed  30 s p e c i e a n d l o g g r a d e a r e the u n u s u a l c a s e .  It i s d e e m e d u n e c o n o m i c a l to  s o r t logs down into b o o m s c o n s i s t i n g of l o g s of a single s p e c i e and a single l o g g r a d e o r a n y p r e d e t e r m i n e d c o m b i n a t i o n s of t h e s e .  A t the p l y w o o d m i l l , length,  the l o g s a r e s a w n i n t o the r e q u i r e d v e n e e r  r e a d y to b e d e b a r k e d a n d p e e l e d .  Log Peeling: The l o g b l o c k s a r e d e b a r k e d and p e e l e d (in a r o t a r y fashion) into v e n e e r  s h e e t s o f the r e q u i r e d t h i c k n e s s .  The veneer thickness  is  s e l e c t e d so as to p e r m i t an e c o n o m i c a l u s a g e of w o o d i n the p a n e l construction.  T h e w a y i n w h i c h the m i l l s a r r i v e at t h e i r c h o i c e of v e n e e r  thickness varies.  S o m e m e r e l y f o l l o w an e x i s t i n g w o r k a b l e p r a c t i c e  d e r i v e d f r o m e x p e r i e n c e w h i l e o t h e r s a r r i v e at t h e i r c h o i c e b y a s c i e n t i f i c a p p r o a c h w i t h the h e l p o f a c o m p u t e r .  In-process  G r e e n Veneer Inventory:  T h e i n - p r o c e s s g r e e n v e n e e r i n v e n t o r y s e r v e s as a b u f f e r a g a i n s t m a c h i n e r y b r e a k d o w n o r the l a c k of c o o r d i n a t i o n b e t w e e n the log peeling process in batches vs.  a n d the v e n e e r d r y i n g p r o c e s s .  T h e v e n e e r is  s o r t e d a c c o r d i n g to s p e c i e , l e n g t h , b r e a d t h ( c o m p l e t e  r a n d o m width),  thickness  and m o i s t u r e content.  dried  sheets  E v e r y r u n o f the  lathes p r o d u c e j o i n t l y a v a r i e d c o m b i n a t i o n of v e n e e r k i n d s .  The presence  of a n i n - p r o c e s s i n v e n t o r y g r e a t l y h e l p s to c o o r d i n a t e the p e e l i n g a n d the d r y i n g  activities.  31  Veneer  Drying:  T h e v e n e e r p i e c e s a r e d r i e d i n 'kilns' before they are l a i d up into p l y w o o d p a n e l s .  It i s as n e c e s s a r y to a v o i d o v e r - d r y i n g the  as i n a d e q u a t e l y d r y i n g the v e n e e r .  It i s a q u e s t i o n o f e c o n o m i c s  veneer and  technical requirements.  In-process  D r y V e n e e r Inventory:  S i m i l a r to the g r e e n v e n e e r i n v e n t o r y , the d r y v e n e e r i n v e n t o r y h e l p s to c o o r d i n a t e t h e d r y i n g a c t i v i t i e s ,  veneer-upgrading activities  and p a n e l - l a y - u p a c t i v i t i e s .  Veneer  Edge-Gluing:  A s p a r t of the v e n e e r u p g r a d i n g p r o c e s s ,  good q u a l i t y v e n e e r  p i e c e s of r a n d o m b r e a d t h ( c a l l e d R a n d o m h e n c e f o r t h ) a r e  edge-glued  i n t o a c o n t i n u o u s s h e e t a n d c l i p p e d i n t o s h e e t s o f the r e q u i r e d f u l l b r e a d t h ( c a l l e d sheets henceforth).  Veneer Patching; T o u p g r a d e the v e n e e r s h e e t s , d e f e c t s l i k e k n o t h o l e s ,  etc.  a r e p u n c h e d off a n d p a t c h e s o f g o o d v e n e e r a r e i n s e r t e d i n t h e i r p l a c e . T h e l i m i t s to t h i s u p - g r a d i n g p r o c e s s of u p - g r a d i n g ( m a r g i n a l r e t u r n v s .  a r e s e t b y e i t h e r the  economics  m a r g i n a l c o s t s ) o r b y the  Canadian  S t a n d a r d s A s s o c i a t i o n w h i c h d e f i n e s the m a x i m u m e x t e n t o f p a t c h i n g a c c e p t a b l e f o r e a c h g r a d e o f p l y w o o d (thus,  -veneer).  32 Glue-Spreading  Panel Lay-up:  P o o r q u a l i t y c o r e - v e n e e r of r a n d o m b r e a d t h is s p r e a d with g l u e o n b o t h s i d e s a n d u s e d as c r o s s - b a n d s i n l a y i n g up p l y w o o d p a n e l s .  T h e p a n e l s a r e a s s e m b l e d a c c o r d i n g to the r e q u i r e d p a n e l s p e c i f i c a t i o n of t h i c k n e s s  and g r a d e s .  The desired panel thickness  i s o b t a i n e d f r o m a c h o i c e o f the c o m b i n a t i o n o f v e n e e r t h i c k n e s s  and  the n u m b e r o f p l i e s i n the p a n e l .  Panel-pressing; T h e a s s e m b l e d p a n e l s a r e p r e s s e d into p l y w o o d p a n e l s u n d e r h i g h p r e s s u r e and intense heat.  T h e y a r e t h e n l e f t to c o o l a n d 'set'  before final finishing.  Panel-Finishing: H i g h grade panels are sanded and graded. g r a d e d into s t a n d a r d sheathings  Sheathings  and select sheathings.  are  Panel reclaim  w o r k i s done o n s o m e o f the p a n e l s .  I n v e n t o r y of F i n i s h e d P ' l y w o o d P a n e l s : M o s t f i r m s a i m to p r o d u c e to o r d e r , p r o v i d e d d e m a n d p r o v i d e s a r e l a t i v e l y stable l e v e l of o p e r a t i o n .  The plywood market however  25 t e n d s to e x p e r i e n c e  a s u m m e r peak followed by a winter low.  Many  f i r m s p a r t l y a d a p t t h e m s e l v e s to the s e a s o n a l c h a n g e b y w o r k i n g t h r e e  25 R e f e r to D o m i n i o n B u r e a u of S t a t i s t i c s ' f i g u r e s i n G r a p h s I-'X, I - Y o n p a g e s 7 8 a n d 7 9 -  shifts  d u r i n g the p e a k s e a s o n a n d o n l y two s h i f t s  season.  d u r i n g the  T h e f l u c t u a t i o n o f the i n v e n t o r y l e v e l i s u s e d to  slack supplement  the a d a p t a t i o n o f the p r o d u c t i o n l e v e l s to the s e a s o n a l p a t t e r n o f the demand.  M a t e r i a l F l o w i n the C a s e C o m p a n y : A n a t t e m p t w i l l now be m a d e to p r e s e n t the s y s t e m o f p r o d u c t i o n f l o w t h r o u g h the C a s e m i l l .  T h e m a i n o b j e c t i v e i s to p i n -  p o i n t the m a j o r d e c i s i o n a r e a s i n the b u s i n e s s ,  s o as to p r e p a r e the  b a c k g r o u n d f r a m e w o r k upon w h i c h a l i n e a r p r o g r a m m i n g m o d e l w i l l be b u i l t to a n a l y s e the c a s e s i t u a t i o n .  It i s h o p e d t h a t this L . P .  model  w i l l b e h e l p f u l f o r m a k i n g m a n a g e m e n t d e c i s i o n s o n the o p e r a t i o n of the business.  T h e m i l l o p e r a t i o n w i l l b e p r e s e n t e d as i t e x i s t s t o d a y .  Chart  II i s u s e d to t r a c e the flow o f a c t i v i t i e s t h r o u g h the m i l l f r o m the b e g i n n i n g o f the c o n v e r s i o n p r o c e s s to the f i n i s h i n g e n d .  Logs: T h e l o g s a r e t o w e d to the m i l l s i t e i n l a r g e b o o m s . b o o m s a r e not e x a c t l y homogenous  These  i n s p e c i e a n d l o g - g r a d e , but e a c h  d o e s i n c l u d e one o r m o r e p r e d o m i n e n t s p e c i e s a n d l o g - g r a d e s .  T h e l o g s a r e s t o r e d i n b o o m s as t h e y c o m e . a n i n v e n t o r y of about t h r e e m o n t h s ' s u p p l y of l o g s .  The m i l l maintains  CHART AN ILLUSTRATION  TI  -  OF T H EMILL  LAY-OUT  10  20.  il  (5 It  (9) P a n e l  • (1) L o g - d e b a r k i n g (2)  Lathe  (3) V e n e e r - C l i p p e r  (5) M o i s t u r e D e t e c t o r  (7) V e n e e r P a t c h i n g  (4) D r y e r I n - F e e d  (6) V e n e e r E d g e - G l u e r  (8)  Glue-Spreader  Pres  (10) P a n e l  Trimming  (11) P a n e l S a n d e r (12) P l a s t i c  Patching  (13)  Davis  Patching  (14)  Panel Grading  35  T h e w a t e r s t o r a g e a r e a i s d i v i d e d i n t o two s e c t i o n s ,  one f o r  k e e p i n g c o m p l e t e b o o m s a n d the o t h e r f o r b o o m s that a r e i n the of b e i n g f e d i n t o the m i l l .  process  F o r l a c k o f b e t t e r t e r m s , l e t us c a l l t h e  f o r m e r the l o g - i n v e n t o r y s t o r a g e p o n d a n d the l a t t e r , the l o g - c o n s u m p t i o n pond.  A t a n y one t i m e ,  the l o g - c o n s u m p t i o n p o n d h o l d s f o u r b o o m s , 26  e v e r y o n e o f w h i c h i s at v a r i o u s s t a g e s o f r u n - d o w n .  One section  holds a b o o m of D o u g l a s F i r p e e l e r l o g s ( p r e d o m i n e n t l y a c o m b i n a t i o n of g r a d e s #1 to #4. )  A n o t h e r s e c t i o n h o l d s one o f I n t e r i o r F i r a n d  yet a n o t h e r one h o l d s a b o o m o f F i r S a w l o g s . for l o g s of s p e c i e s other than D o u g l a s F i r . categories  T h e last section is  used  T h e s e a r e the o n l y f o u r  o f l o g s that the m i l l p r e s e n t l y r e c o g n i z e s i n c o n t r o l l i n g  its l o g peeling  activities.  T h e l o g s u s u a l l y c o m e i n l e n g t h s o f 42 feet, 34 feet, 26 feet, a n d 18 feet,  w h i c h i n fact a r e m u l t i p l e s of 8-foot and 10-foot  p l u s a l l o w a n c e f o r l o s s at the  lengths  saw.  T h e logs a r e m o s t l y sawn into lengths of 8-foot and l O e f o o t , (the s t a n d a r d l e n g t h s o f p l y w o o d p a n e l s . ) a r e a l s o d e v e l o p e d i n the p r o c e s s .  S o m e b l o c k s of o d d lengths  T h e s e b l o c k s of o d d s i z e s a r e u s u a l l y  f o u n d to b e a d e q u a t e f o r m e e t i n g the d e m a n d f o r p l y w o o d p a n e l s o f odd s i z e s .  26  ~~ S e e C h a r t III, p a g e  36  CHART  III  LOG IN-FEED AT  MILL  (BOOM)  Log-Boom  Log-Boom  Storage  Consumption  Pond  Pond  P r e p a r i n g L o g s for peeling  INTERIOR  Log-Reject Storage  37  A t the b e g i n n i n g of e a c h w e e k the s a w y e r i s i n s t r u c t e d as to h o w m u c h of e a c h o f the f o u r c a t e g o r i e s A s one m i g h t e x p e c t , i n the c o u r s e o f the  o f l o g s to p r o c e s s d u r i n g the  week.  r e v i s i o n s to the w o r k o r d e r a r e s o m e t i m e s  made  week.  A f t e r b e i n g cut into the r e q u i r e d l e n g t h , the l o g s (now c a l l e d b l o c k s ) a r e m e c h a n i c a l l y d e b a r k e d a n d f e d s t r a i g h t to the two  lathes.  T h e ' e x c e s s ' b l o c k s go i n t o a n i n v e n t o r y u s e d to c o o r d i n a t e the output o f the s a w y e r a n d the i n t a k e o f the l a t h e s .  The inventory also  keeps  the l a t h e s g o i n g d u r i n g the n i g h t s h i f t w h e n the b u l l - s a w i s not o p e r a t e d .  L o g s to V e n e e r : T h e w o o d - b l o c k s a r e p e e l e d b y a r o t a r y p r o c e s s into a continuous s h e e t and c l i p p e d into v e n e e r p i e c e s of four feet b r o a d o r l e s s where splits o r m a j o r defects d i s a l l o w . to t h r e e t h i c k n e s s e s ,  i . e. 0. 104",  The m i l l peels  0. 130" a n d 0. 171".  veneer  Good quality  l o g s a r e u s u a l l y p e e l e d to 0; 104" so as to d e v e l o p the m a x i m u m a m o u n t of g o o d s u r f a c e v e n e e r .  P o o r e r g r a d e s o f l o g s a r e p e e l e d to 0 . 1 3 0 "  a n d 0. 171" to d e v e l o p m a i n l y c o r e a n d c e n t r e v e n e e r .  Species  other  t h a n D o u g l a s F i r a r e p e e l e d to 0. 171" o n l y to d e v e l o p c o r e a n d c e n t r e v e n e e r o n l y as t h e s e s p e c i e s m a y o n l y b e u s e d as s u c h u n d e r the specifications  of D o u g l a s F i r p l y w o o d .  These specifications  are laid  d o w n b y the 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 , O t t a w a ( # 0 1 2 1 - 1 9 6 1 . )  38 A t the g r e e n e n d , the v e n e e r p r o d u c e d i s s o r t e d out b y d i m e n s i o n a n d m o i s t u r e c o n t e n t , as  - Sap,  27  sheets  - Heart, - Sap,  follows:  sheets  r a n d o m width  - Heart,  r a n d o m width  - F i s h tail  T h e p u r p o s e o f s o r t i n g out the S a p w o o d f r o m the H e a r t w o o d i s to f a c i l i t a t e d r y i n g .  T h e s e p a r a t i o n of s h e e t s f r o m r a n d o m w i d t h  a n d f i s h t a i l i s to f a c i l i t a t e h a n d l i n g f o r e d g e - g l u i n g a n d c o r e  veneer  s a l v a g e f r o m the f i s h t a i l as the c a s e a p p l i e s .  T h e c e n t r e s o f the l o g s a r e cut i n t o h a l f - l e n g t h s a n d f u r t h e r p e e l e d b y the c o r e - l a t h e f o r c o r e v e n e e r u s e d as c r o s s - b a n d s i n the panel lay-up.  G r e e n V e n e e r to D r y V e n e e r ;  The veneer produced moves  the d r y e r s e i t h e r d i r e c t l y f r o m the g r e e n e n d o r t h r o u g h the  to  green  veneer inventory.  T h e v e n e e r i s d r i e d i n b a t c h e s a c c o r d i n g to the g r a d e s i n t o w h i c h i t h a s b e e n s o r t e d at the g r e e n e n d .  E v e r y piece of v e n e e r  27 S a p w o o d i s f r o m the o u t e r p o r t i o n o f the l o g , w e t t e r t h a n H e a r t w o o d f r o m the i n n e r p o r t i o n of the l o g .  generally Sheets  a r e p i e c e s of full length and b r e a d t h while R a n d o m p i e c e s a r e those with a w i d t h l e s s t h a n the f u l l i n t e n d e d w i d t h . F i s h t a i l s u s u a l l y c o m e f r o m S a p wood,  p e e l e d f r o m the l o g b e f o r e i t h a s f u l l y b e e n r o u n d e d . O n l y one e n d  o f t h e s e p i e c e s i s s a l v a g e d f o r c o r e v e n e e r u s e d as a c r o s s - b a n d i n the panel construction.  39 e m e r g i n g f r o m the d r y e r s i s e l e c t r o n i c a l l y t e s t e d f o r m o i s t u r e Inadequately d r i e d v e n e e r is a c c u m u l a t e d for r e - d r y i n g .  It i s  content. believed  t h a t the o p t i m u m d o e s n o t l i e i n s e t t i n g the d r y e r s so as to e n s u r e  that  100% o f the v e n e e r i s a d e q u a t e l y d r i e d at the f i r s t r u n .  After drying,  the v e n e e r  s h e e t s a r e g r a d e d i n t o the  following  . 28 categories:  - A Face - Patch - #1  Back  - #2  Back  -  Core  - Tie c l i p  T h e R a n d o m v e n e e r p i e c e s a r e g r a d e d as  follows:  - Patch - #1 -  Back  Core  - Re clip  T h e p u r p o s e of t h i s g r a d i n g s y s t e m i s a p p a r e n t f r o m an e x a m i n a t i o n o f the a c c o m p a n y i n g f l o w - c h a r t ,  Chart IV.  The chart  t r a c e s the f l o w o f the v a r i o u s g r a d e s o f v e n e e r f r o m the d r y - e n d , the u p - g r a d i n g a n d r e c l a i m i n g p r o c e s s e s to the p a n e l l a y - u p .  28 F o r an a c c o u n t o f the g r a d i n g s y s t e m ,  see page  4 3.  through  4Q The In-process Together,  Green & Dry Veneer  Inventories;  t h e s e two i n v e n t o r i e s h e l p to b a l a n c e the  of the two l a t h e s a n d that of the f o u r d r y e r s .  capacity  T h e two l a t h e s t o g e t h e r  h a v e a h i g h e r output c a p a c i t y t h a n the d r y e r s .  C o n s e q u e n t l y , one o r two  of the d r y e r s a r e o p e r a t e d d u r i n g the w e e k - e n d s w h i l e the r e s t of the m i l l i s shut d o w n . pattern,  T h e l e v e l o f the two i n v e n t o r i e s  assume a weekly  m o v i n g i n d i r e c t o p p o s i t i o n to one a n o t h e r . T h i s  p a t t e r n i s d e p i c t e d b y G r a p h I, o n the f o l l o w i n g  weekly  page.  T h e green veneer inventory g r a d u a l l y i n c r e a s e s f r o m a low l e v e l o n M o n d a y a n d r e a c h e s i t s p e a k at the c l o s e of F r i d a y . week-end,  O v e r the  i t i s b e i n g r u n d o w n b y the o p e r a t i o n of the e x t r a s h i f t s  o n the d r y e r s .  T h e d r y v e n e e r i n v e n t o r y s t a r t s off f r o m a h i g h on  M o n d a y a n d i s r u n d o w n to i t s l o w b y the c l o s e of F r i d a y . up to i t s p e a k a g a i n d u r i n g the  It i s b u i l t  week-end.  S u p e r i m p o s e d o n t h i s p a t t e r n i s the i n f l o w of g r e e n v e n e e r f r o m purchases made. days.  T h e d e l i v e r y i s u s u a l l y m a d e d u r i n g the w e e k  A l s o , i t i s not to be e x p e c t e d that the v e n e e r a l w a y s  t h r o u g h the i n v e n t o r i e s  s t r i c t l y on a f i r s t - i n - f i r s t - o u t  flows  basis.  D r y V e n e e r to P a n e l L a y - u p : T h e flow o f the v a r i o u s g r a d e s of v e n e e r f r o m the d r y - e n d to panel l a y - u p is presented in Chart I V . p a t t e r n of flow,  This represents  the u s u a l  without a l l o w i n g for s o m e o c c a s i o n a l d o w n - g r a d i n g of  41  GRAPH I VENEER  INVENTORIES  42 CHART FLOW GRADES AT  GRP, DES AT  CVREEN - E N D  OF  CTRPIDES  &fU\3ES  A T  AT  ED<5e-GLUER.  IV VENEER CORE. VENEER.  SOURCE • • ftoftPTEb futw CtHftiDI CHURT  CtRASE S A T  PAT CHER.  RECLIPPER  Ui-Op  SPREADER  - CORE -  ->  /  5  ->  U/L  SHLET5-  K  ->  Core,  Core _  feclip  -O-  -X-  -o-  -X-  0 ->  fatck .  -> UfL-  -> -> ->  3• 6/ -  Patch.  Cf U/L. WIDTH  Bfcs# j  —o -X— -X-  -o-o-  Cove Core,^eclib  3 ?atck  8, FISH-Turn. AMD C O P U  e^bore  —>  -> a-  -3> ->  43 the v e n e e r  s u c h as b y s k i p p i n g e d g e - g l u i n g o r p a t c h i n g f o r s o m e  T h e c h a r t d o e s not s h o w the d e l a y at the i n - p r o c e s s  Veneer  veneer.  inventory.  sheets:  A F a c e veneer is defectless.  No u p - g r a d i n g is  a n d i t i s i m m e d i a t e l y r e a d y f o r u s e as S e l e c t f a c e  necessary  veneer.  P a t c h v e n e e r i s p a t c h e d , u p - g r a d e d i n t o f o u r g r a d e s of f a c e veneer.  U n d e r - l a y ( U / L ) i s u s e d as f a c e v e n e e r f o r S e l e c t S h e a t h i n g  p a n e l s w h i l e C e m e n t F o r m ( C / F ) a s u s e d as f a c e f o r C e m e n t panels.  Form  T h e S o l i d a n d the G o o d g r a d e a r e u s e d f o r s a n d e d p a n e l s .  #1 B a c k v e n e e r h a s l i t t l e p o t e n t i a l f o r u p - g r a d i n g a n d i s t h e r e f o r e i m m e d i a t e l y r e a d y to be u s e d f o r the b a c k o f p a n e l s .  #2 B a c k i s p a t c h e d a n d u p - g r a d e d i n t o #1 B a c k . is sawn into h a l f - l e n g t h s  Core grade  a n d u s e d as c r o s s - b a n d i n g i n n e r p l i e s .  R e c l i p g r a d e i n c l u d e s t h o s e t h a t h a v e u n p a t c h a b l e but ' l o c a l i s e d ' d e f e c t s s u c h as s p l i t s  and l a r g e knot-holes,  a r e r e c l i p p e d into R a n d o m p i e c e s ,  etc.  These  w i t h the d e f e c t s r e m o v e d .  They  a r e then e d g e - g l u e d into sheets and p a t c h e d and u p - g r a d e d .  Veneer Random; V e n e e r p i e c e s o f r a n d o m w i d t h a r e g r a d e d s i m i l a r l y to the veneer  sheets.  H o w e v e r , no A  F a c e g r a d e i s d e v e l o p e d as t h i s  d o e s not u s u a l l y i n c l u d e e d g e - g l u e d s h e e t s .  T h e P a t c h grade is  grade edge-  44  glued and then patched.  #1 B a c k i s e d g e - g l u e d a n d t h e n r e a d y f o r  N o #2 B a c k i s d e v e l o p e d as i t m i g h t b e u n e c o n o m i c a l to d e v e l o p #1 by edge-gluing plus patching.  use. Back  It s e e m s to b e m o r e e c o n o m i c a l to u s e  the p o t e n t i a l #2 B a c k s as c o r e v e n e e r .  T h e R e c l i p g r a d e has  its  u n p a t c h a b l e b u t l o c a l i z e d d e f e c t s c l i p p e d off b e f o r e e d g e - g l u i n g . C o r e grade is sawn into h a l f - l e n g t h b e f o r e  The  use.  F i s h t a i l &: C o r e : T h e f i s h t a i l has its defective T h e s e a n d the c o r e v e n e e r  e n d s a w n off b e f o r e b e i n g d r i e d .  d e v e l o p e d f r o m the c o r e of the l o g s b y the  s m a l l C o e l a t h e a r e now r e a d y to b e u s e d f o r l a y i n g u p p a n e l s .  T h e a b o v e g r a d i n g s y s t e m i s b y no m e a n s u n i v e r s a l . internal planning purposes, system. market,  F o r its  a c o m p a n y m a y develop its own g r a d i n g  B u t i n o r d e r to s e l l the f i n i s h e d p r o d u c t i n the o p e n C a n a d i a n the f i n i s h e d p l y w o o d m u s t m e e t the s p e c i f i c a t i o n s  b y the 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 ,  and for a s a m p l e  of the g r a d i n g s y s t e m of the v e n e e r at the P r e s s ,  stipulated explanation  s e e A p p e n d i x III.  It i s a l s o to b e r e m e m b e r e d t h a t a n y p a r t i c u l a r g r a d e o f v e n e e r u s e d at the p a n e l l a y - u p n e e d not a l w a y s g r a d e at the f i n i s h i n g e n d .  e n d up as the  same  T h e r e w i l l b e a c e r t a i n a m o u n t of d o w n -  grading a r i s i n g f r o m handling damage,  etc.  Glue-Spreading: B e f o r e the p a n e l l a y - u p , the c o r e v e n e e r i s s p r e a d w i t h a  45 p h e n o l i c glue on both s i d e s .  T h i s glue, when p r e s s e d u n d e r h i g h heat and  h i g h p r e s s u r e i s s a i d to p r o d u c e a b o n d a g e  s t r o n g e r t h a n the v e n e e r i t s e l f .  Plywood Panel Construction: T h i s i s the p r o c e s s of c o n s t r u c t i n g a p l y w o o d p a n e l . of t h r e e p l i e s ( i . e.  A panel  c o n s t r u c t e d o f t h r e e l a y e r s of v e n e e r ) c o n s i s t s  of,  - a face sheet - a core  layer  - a back sheet The  c o r e l a y e r h a s i t s g r a i n r u n n i n g at r i g h t a n g l e to the f a c e a n d the  back sheets;  see  d i a g r a m I below.  A p a n e l of f i v e p l i e s i s l a i d up w i t h  a face sheet,  followed b y a c r o s s - b a n d i n g c o r e l a y e r , a c e n t r a l sheet,  Diagram I The  S t r u c t u r e of a P l y w o o d P a n e l  BftcK I i  CORE  I  1  i  l  I  CfcNTRE CORE  '  » ' '  ' 1  1  ' i  '  1  i  1  1  I  face  I  1  1  1  i. . , ' ' i J  I  I  (  r  - H  1  i  1  '  M  I  i  i  yet a n o t h e r c r o s s - b a n d i n g c o r e l a y e r p l u s a b a c k s h e e t . of t h e f a c e ,  The grains  c e n t r a l a n d the b a c k s h e e t s r u n p e r p e n d i c u l a r l y to t h o s e  of the two c o r e l a y e r s .  Plywood Panel Pressing: T h e p a n e l s that h a v e b e e n l a i d up a r e t h e n p r e s s e d u n d e r h i g h p r e s s u r e and h i g h t e m p e r a t u r e . process.  T h i s s t e p c o m p l e t e s the g l u i n g  T h e heat intensity applied v a r i e s between 2 8 5 ° F and 3 0 0 ° F ,  a n d the l e n g t h of the p r e s s i n g t i m e v a r i e s f r o m 5 m i n u t e s to 7  1/2  30 minutes.  T h e l e n g t h o f the p r e s s i n g t i m e i s  with t e m p e r a t u r e within certain l i m i t s .  inter-changeable  When a softer  s p e c i e s of wood,  s u c h as H e m l o c k , i s u s e d f o r the i n n e r p l i e s i n s t e a d o f D o u g l a s F i r , the p r e s s u r e u s e d i s l o w e r . Panel  Trimming:  A f t e r the c o m p l e t i o n o f the p r e s s i n g p r o c e s s , the p a n e l s  are  s a w - t r i m m e d i n t o the e x a c t l e n g t h a n d e x a c t b r e a d t h a n d t h e n a l l o w e d to c o o l a n d 'set'  for s o m e t i m e before final face finishing.  Quality Control; S a m p l e s o f the t r i m m e d - o f f e d g e s of the p a n e l s a n d a l s o s a m p l e s o f c o m p l e t e d p a n e l s a r e t e s t e d to k e e p a c o n s t a n t c h e c k o n the q u a l i t i e s o f the p a n e l s .  T h e o b j e c t i v e i s to m e e t the C S A s t a n d a r d s  and t h o s e o f the f o r e i g n m a r k e t s t h a t the c o m p a n y  30  serves.  S e e A p p e n d i x II f o r a s a m p l e o f the p r e s s i n s t r u c t i o n s .  Panel Finishing: Sanding: The good quality panels  31  are sanded to produce  the required smoothness as well as to remove excess thickness when it arises. Plastic-wood Patching:  The sanded grades are checked for  splits on their faces and patched with a glue-like paste called 'plastic wood, ' where possible.  Those face defects that cannot be so patched  are treated by Davis Patching.  By this, the localized defective parts  of the face of the panel are cut off and a plastic patch is glued and pressed into place. Panel Grading: F i n a l l y the panels are graded and sorted out by grade, thickness and dimension.  The grade planned for at the panel lay-up i s not  final as there may be down-grading arising from damages during the process.  Panels that are s t i l l found defective are sent for further  r e c l a i m work where possible.  Some are graded as unsaleable i n the  open market. The finished panels are then packed and ready for shipment. 31  ~  Panels of the Marine Grade, Good/Select, Good-two-Side and Solid-two-Side are sanded equally deeply on both sides. Those of Good-one-Side and Solid-one-Side are sanded more deeply on the better side. Those of the Sheathing grades and Cement F o r m are not sanded.  P u r c h a s e of G r e e n V e n e e r ; A s e c o n d a r y i n f l o w o f v e n e e r to the m i l l c o m e s f r o m the p u r c h a s e s of g r e e n v e n e e r .  T h i s v e n e e r i s p r o c e s s e d i n the  same  w a y as the v e n e e r p r o d u c e d i n t e r n a l l y .  It m a y b e p o s s i b l e f o r the c o m p a n y to e s t a b l i s h a s a l e m a r k e t for s o m e of its v e n e e r .  B u t b y no m e a n s i s t h i s a n a c t i v i t y o f the  c o m p a n y at the p r e s e n t .  N e i t h e r w o u l d i t b e so i n the  foreseeable  future.  A Note on the M a c h i n e r y : T h e C a s e m i l l u s e s two l a t h e s to p e e l l o g s f o r v e n e e r . s m a l l e r lathe,  The  c a l l e d the M e r r i t t L a t h e , c a n p e e l l o g s u p to a m a x i m u m  l e n g t h of eight feet.  It h a s a n a u t o m a t i c c h a r g e r to l o a d a n d to c e n t r e  the l o g s f o r p e e l i n g .  Its s i n g l e l e v e l v e n e e r t r a y i s s e r v e d b y a s i n g l e  veneer clipper.  The other lathe, ten feet.  the P r e m i e r ,  p e e l s l o g s u p to a l e n g t h o f  It d o e s not h a v e an a u t o m a t i c c h a r g e r b u t h a s a s i x - l e v e l  v e n e e r t r a y s e r v e d b y two v e n e e r c l i p p e r s .  T h e c y c l e o f o p e r a t i o n i n p e e l i n g a l o g m a y b e d i v i d e d into two s e c t i o n s .  Firstly,  the l o g i s l o a d e d a n d r o u n d e d , r e a d y to b e  p e e l e d into v e n e e r sheets.  T h e s e c o n d p a r t o f the c y c l e b e g i n s  when  the l a t h e b e g i n s to p r o d u c e v e n e e r , a n d f e e d s i t onto the v e n e e r t r a y for c l i p p i n g into the a p p r o p r i a t e w i d t h .  D u r i n g the s e c o n d p a r t o f t h e  49 cycle,  the l a t h e p r o d u c e s v e n e e r at a r a t e g r e a t e r t h a n that w i t h w h i c h  the c l i p p e r s c a n c o p e .  A n d the l a r g e r the d i a m e t e r of the l o g ,  the  l o n g e r w i l l the s e c o n d p a r t o f the o p e r a t i o n - c y c l e b e c o m p a r e d to the first part.  T h e p o r t i o n of the v e n e e r t r a y b e t w e e n the l a t h e a n d the c l i p p e r h e l p s to b a l a n c e the r a t e o f o p e r a t i o n o f the l a t h e a n d the c l i p p e r . the P r e m i e r l a t h e ,  with its l o n g e r v e n e e r t r a y ( m u l t i p l e level) is  Thus, more  e f f i c i e n t i n p e e l i n g l a r g e r l o g s t h a n the M e r r i t t l a t h e .  The  Dryers: V e n e e r i s b e i n g d r i e d as i t i s p a s s e d t h r o u g h a ' k i l n ' m a i n t a i n e d  at a c e r t a i n t e m p e r a t u r e .  T h e l e n g t h of t i m e that a s h e e t o f v e n e e r  s p e n d s i n d r y i n g i s a r e s u l t of the l e n g t h o f the d r y e r ( m e a s u r e d b y the n u m b e r o f s e c t i o n s ) a n d the s p e e d at w h i c h the v e n e e r i s b e i n g p a s s e d through it.  T h e l e n g t h of d r y i n g t i m e r e q u i r e d b y a p i e c e of v e n e e r d e p e n d s o n the t h i c k n e s s of the v e n e e r , the m o i s t u r e c o n t e n t w h i c h i n t u r n d e p e n d s o n the s p e c i e s o f the w o o d a n d w h e t h e r i t i s S a p w o o d o r H e a r t wood.  It s e e m s w i s e to m o v e the v e n e e r t h r o u g h the d r y e r at a r a t e c o m p a r a b l e to that at w h i c h the v e n e e r c a n be f e d i n t o the d r y e r a n d the r a t e the d r i e d v e n e e r c a n b e g r a d e d a n d s t a c k e d . T h e r e i s a l s o a n  o p t i m u m r a n g e o f t e m p e r a t u r e to s e t i n the d r y e r .  A p a r t f r o m the  q u e s t i o n o f e c o n o m i c s , t h e r e i s a l s o the q u e s t i o n o f d a m a g e b y too r a p i d a d r y i n g o f the v e n e e r at a v e r y h i g h t e m p e r a t u r e .  T h e C a s e m i l l has four d r y e r s . sections i n length,  T w o of t h e m a r e of  sixteen  a n o t h e r o f t w e n t y - f o u r a n d the f o u r t h t w e l v e .  o f the f o u r h a s s i x l i n e s ,  i . e.  s i x l e v e l s of v e n e e r a r e b e i n g d r i e d  simultaneously i n each d r y e r .  T h e d i f f e r e n c e i n the l e n g t h o f the  d r y e r s reflects  Each  a d i f f e r e n c e i n c a p a c i t y as w e l l as r e f l e c t i n g a m e a n s  of a d a p t i n g to the d r y i n g n e e d s o f the d i f f e r e n t c a t e g o r i e s  of v e n e e r .  T h e S y s t e m of P r o d u c t i o n Scheduling; It w i l l not b e too f a r w r o n g to s t a t e that the s t a r t i n g p o i n t f o r d e c i d i n g what to p r o d u c e a n d w h e n to p r o d u c e it i s the s a l e o r d e r a n d the i n v e n t o r y r e q u i r e m e n t s .  O n the a v e r a g e , about 60% o f the m i l l ' s  output i s p r o d u c e d to o r d e r w h i l e the r e s t i s p r o d u c e d f o r i n v e n t o r y , e s p e c i a l l y f o r the p u r p o s e of e a s i n g out the s e a s o n a l f l u c t u a t i o n i n the demand.  B a s e d on a p o l i c y of m a i n t a i n i n g a two-week l e a d t i m e  over  the d e l i v e r y date o f e a c h o f the o r d e r s , the d a i l y p r o d u c t i o n w o r k - o r d e r is d r a w n u p .  T h e p a n e l p r e s s i s u s e d as the c e n t r a l p o i n t f o r the  c o n t r o l o f the d a i l y o p e r a t i o n s .  T h e a m o u n t , the g r a d e a n d o t h e r s p e c i f i c a t i o n s of the p a n e l s to b e l a i d u p a n d p r e s s e d d u r i n g e a c h s h i f t a r e s e t out f o r the  presses.  51 B a s e d on this w o r k o r d e r , d r a w n up d a i l y .  the w o r k o r d e r s to the d r y e r s a r e a l s o  T h e d r y v e n e e r i n - p r o c e s s i n v e n t o r y p l u s the 32  p o s s i b i l i t y o f a l t e r i n g the s t r u c t u r e o f  a panel  or down-grading a  p a r t i c u l a r g r a d e o f v e n e e r h e l p f u r t h e r to c o o r d i n a t e the s u p p l y o f dried,  p r o c e s s e d v e n e e r a n d the c o n s u m p t i o n at the p a n e l l a y - u p . B a s e d o n the p r e s s r e q u i r e m e n t s , the l a t h e s a r e i n s t r u c t e d  for e a c h shift,  as to the l e n g t h of t i m e to s p e n d o n p e e l i n g a n y p a r t i c u l a r 33  c a t e g o r y of l o g s ,  the l e n g t h of the l o g s a n d t h e t h i c k n e s s o f the  v e n e e r to b e p r o d u c e d . T h e i n = p r o c e s s  green veneer inventory helps  to b a l a n c e the o u t - p u t o f the l a t h e s a n d the r e q u i r e m e n t s o f the dryers.  T h i s i s e s p e c i a l l y n e c e s s a r y b e c a u s e o f the d i f f e r e n c e i n the 34  c a p a c i t y o f t h e l a t h e s a n d t h a t o f the d r y e r s .  The particular  c a t e g o r y o f v e n e e r t h a t w i l l go i n t o b u i l d i n g up t h e g r e e n v e n e e r i n v e n t o r y i s m o r e a r e s u l t o f the l e f t o v e r a f t e r m e e t i n g the i m m e d i a t e n e e d s o f the d r y e r s t h a n a c a s e o f s t r i c t p l a n n i n g . T h e r e a p p e a r s a l s o that t h e r e i s no c l o s e r e c o r d k e p t o f the c o m p o n e n t s o f the i n - p r o c e s s v e n e e r i n v e n t o r i e s . T h e f o r e m e n h a v e h a r d l y anything m o r e than a v i s u a l estimate.  T h e r e f o r e , it might be  32 S e e A p p e n d i x I V f o r a s a m p l e of the a l t e r n a t i v e s t r u c t u r e s for plywood p a n e l s . 33 34  S e e p a r a g r a p h two o f p a g e 35 A s has a l r e a d y b e e n m e n t i o n e d i n p a r a g r a p h  one o f p a g e 40  s u s p e c t e d that the e x a c t c o n s t i t u e n t s  o f the g r e e n a n d the d r y v e n e e r  i n v e n t o r i e s a r e n o t f u l l y t a k e n into a c c o u n t i n p l a n n i n g the d a i l y a c t i v i t i e s o f the l a t h e s a n d the d r y e r s .  In s h o r t , the w h o l e  i s not p r e c i s e l y a n d r i g i d l y c o n t r o l l e d .  T h e r e is m u c h r o o m for  f l e x i b i l i t y a n d o n the s p o t d e c i s i o n b a s e d o n j u d g m e n t .  process  CHAPTER  FORMULATING A LINEAR  PROGRAMMING  T O B E U S E D IN A N A L Y S I N G  The  T H E CASE  MODEL COMPANY  a p p l i c a t i o n of O . R . t e c h n i q u e s i n s o l v i n g a p r o b l e m i s  c h a r a c t e r i z e d b y its exception.  V  'scientific'  approach.  L . P . t e c h n i q u e i s no  T h e a p p r o a c h m a y be d i v i d e d i n t o s i x m a j o r p h a s e s : -  35  1) F o r m u l a t i n g the p r o b l e m 2) C o n s t r u c t i n g a m a t h e m a t i c a l  model  to r e p r e s e n t the s y s t e m u n d e r 3) D e r i v i n g a s o l u t i o n f r o m the (plus p o s t - s o l u t i o n  study  model  analysis)  4) T e s t i n g the m o d e l a n d the  solution  d e r i v e d f r o m it. 5) E s t a b l i s h i n g c o n t r o l o v e r the  solution.  6) P u t t i n g the s o l u t i o n to w o r k , (i. e.  implementation.)  C W . C h u r c h m a n , R . L . A c k o f f and E . L . A r n o f f , I n t r o d u c t i o n to O p e r a t i o n s R e s e a r c h , p a g e 13, J o h n W i l e y & S o n s , New Y o r k , 1913.  54 T h i s c h a p t e r s h a l l u n d e r t a k e to p r e s e n t the f o r m u l a t i o n of the p r o b l e m a n d the f r a m e w o r k of the L . P . m o d e l .  It i s a l s o b e l i e v e d  t h a t t h i s m o d e l s h a l l h a v e s o m e g e n e r a l a p p l i c a t i o n to p l y w o o d b u s i n e s s e s o t h e r t h a n the C a s e c o m p a n y as w e l l .  C h a p t e r V I d e v e l o p s the n e c e s s a r y to the C a s e c o m p a n y .  d a t a f o r a p p l y i n g the m o d e l  A n i n t r o d u c t i o n to the c o m p u t e r p r o g r a m u s e d  to c o m p u t e the s o l u t i o n i s t h e n g i v e n i n C h a p t e r V I I .  A n interpretation  of the s o l u t i o n of the m o d e l i s f o u n d i n C h a p t e r VIII f o l l o w e d b y  areas  r e c o m m e n d e d for further r e s e a r c h in Chapter IX.  :  C o n f i g u r a t i o n of the L . P .  M a t r i c e s i n the  Model:  T h e p r o p o s e d L . P . m o d e l a t t e m p t s to c o o r d i n a t e t h r e e m a j o r g r o u p s of a c t i v i t i e s i n the b u s i n e s s ; the m i l l - o p e r a t i o n a c t i v i t i e s (see  d i a g r a m II b e l o w ) .  a f f e c t the d e c i s i o n s  n a m e l y , the l o g s u p p l y  a n d the p l y w o o d m a r k e t i n g  The decisions  activities,  activities  m a d e i n one a r e a w i l l u n d o u b t e d l y  to b e m a d e i n the o t h e r two a r e a s .  The L . P.  a p p r o a c h w i l l i n d i c a t e p o l i c i e s w h i c h c a n h e l p to e n s u r e that the decisions  m a d e i n e a c h a r e a a r e o p t i m u m f o r the b u s i n e s s as a w h o l e .  D i a g r a m II Plywood Business Activity Grouping  Log-supply ( l o g - p u r c h a s i n g and log-alio cation p o l i cies)  <  >  Mill-operation  (log-peeling  panel structure p o l i cies)  <  and p l y w o o d  ->  Panel-marketing sale-effort  concen-  tration policies)  55 A c o n f i g u r a t i o n of the m a t r i c e s i n the r e s u l t i n g m o d e l i s p r e s e n t e d i n F i g u r e I.  T h e m a t r i c e s a r e d i v i d e d into s u b - s e t s ,  r e p r e s e n t i n g v a r i o u s g r o u p s of a c t i v i t i e s business.  i n the o p e r a t i o n of the  S e e a l s o F i g u r e JJ.  Log-supply: T h e log input is defined b y a s e r i e s of inequalities the a m o u n t , the l o g g r a d e a n d the s p e c i e s .  defining  T h e total supply is p a r t l y  m a d e u p of ' u s u a b l e ' l o g s f r o m the t i m b e r - l a n d o w n e d b y the  company  a n d p a r t l y m a d e up o f s u p p l y t h a t the c o m p a n y c a n o b t a i n i n the log market.  T h e l o g s f r o m e i t h e r o f t h e s e two s o u r c e s  are  open  costed  at the o p e n m a r k e t p r i c e s a n t i c i p a t e d f o r the p l a n n i n g p e r i o d .  F o r the  l o g s t h a t a r e g o i n g to be p u r c h a s e d , the m a r k e t p r i c e s r e p r e s e n t actual out-of-pocket  the  c o s t . T h e s e m a r k e t p r i c e s w i l l be c h a r g e d to the  c o m p a n y f o r e v e r y u n i t of log p e e l e d >by the  company.  P e e l i n g L o g s for V e n e e r : F r o m the g i v e n s u p p l y , the m o d e l s e l e c t s the b e s t c o m b i n a t i o n of l o g g r a d e s a n d l o g s p e c i e to p e e l . length and veneer thickness  Specified alternatives  a r e p r o g r a m m e d i n the m o d e l .  for  veneer  M o r e than  one l e v e l of v e n e e r u p - g r a d i n g i s p r o g r a m m e d b y r e c o g n i z i n g d i f f e r e n t l e v e l s of v e n e e r r e c o v e r y a c c o r d i n g to s o m e s p e c i f i c of veneer u p - g r a d i n g . T h u s , log grade,  veneer length,  levels  e a c h d i f f e r e n t c o m b i n a t i o n of l o g s p e c i e s ,  veneer thickness and veneer u p - g r a d i n g is  FIGURE  CONFIGURATION  M f B M )  T H E  OPENING  LOG  (10  OF  pf\neL (car-Loach)  iMueNTOny  IN JEMT^KV ((Oo sheets)  PRODUCTION  I  MATRIX  5 f l L 6 OfPAN 6 1 - 5  OF  T H E  L . P.  CLOilMd GREEN \itnUt. SR)I vstteet.  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CAPACITY ct>n-  - tJET »y-pw*er REVENUE  MP- 6MW%  VARIABLE  CARIA8L&  PR0C6W  fRttfeSi AM> UP-6KA>;N6  <:«T of up-6RAJ/»<«;  fA.H6LPKesjiwCc AN]) 6m e » ; r  gtGHr- HAUb  £*yo panels)  SUMPTIDhJ  PURCHASE PR.I6E + VARIABLE PR&CES5 Of-  Part 3  (Xi'OptDtlS)  CflPflCITJ  VARIABLE Pf.tLi.ii. Ctt~ of rtt-UHH, SRVlNfr, UP-6RAMNSI, + ty Cost  .  CAP Herri  ADJUSTMENT  ON  VMIAftte. CtfST of  AJJUSTWI 0N  VARIABLE CKtlf  SHL6 met  ten COST  OBJECTIVE FiiNcri»w (7°  MiwiMijg)  i  !  i  CJ '; Q  j  •.  I  I - i — - f —  !/>  !  X  *0 H  Q  3  Ui *s  X|  !••  i  H II ; II !  4  Iv  •i  ; ' •  II II  :  1  1  In ;  II i n  o  Cv>  SJl ' M l  D  5•  <V?  ,  Q  CS  . O  j  o  . ..... . j  VI  II  I!  ! « |n  i  3-  5  X  ft, 5  X>  NO  X 1  >< X  •' •- i  i «ai  <i  «*  X m X X »X  M  in  o H |  i^:  X  ^(  I  -i  X  I  — { , -  !2 X  I  !  M  X  I ^ i- °  X i  „i  vu  L  vy |  • 'vT  15  X  r< X  i  "T"  »v*  .01 1 :  0C  X  ' si! s  "0 ; i  I  o  X  o  X  1?  I _;  V *  ><  -I  u X  a:  u>  i  X  *oor>f>u i £ c j  tlNINJJO  > M  " F T  ' T'  • K <^ V-  I  o  vn *>H1N3<I0  a: a.  *  4. r  "H33N3A  H33X9  rs> i <i ,  V .  -J...  I •I I  1  T  J...  1~  3 sv Hound  i  T  o  X In  i  In  —1  ! -4  i  l  l  *C  S i  ! a.  -!"2 : o! u 1  CQ  lo  i i  '  1""  ex.  4_ [  "T  i  j  O  i  *«•"*«  * I  1 *  * i  *  i'v; <T37 J3<t  t><? 7:  4-  kj vB  vr  ; .. .,  j - i/?  ?/V3A\  .1  JLitfjy »33N3fi  fa01N3ANX  H33N3n  ^  m  vl  Oo  OQ  o ^  V. H Wl Vi  v5  ....!  vj 3-  V  V  S*' -  iff*  V33N3A  ...  fir ... 'ft  *>NlV3dO \-:>'  I - - •'• ! ! I  -  I  1  I  "I  f  I  ; !,  L-..U4SO VI  \»  V(  1  <* 1  V/  <5  . V}  Cl ^ ^  w.  O 01  % M  rt _L  <*  v* Cs  UJ vu  i  1  H  N»  S *  kl  .4--. - X i  •4_>  uj  a i - j —  >9 X <5C "  Uj >s UJ -  t  <* ><  W " .  J .  . -  V|  0 '  NJ  UJ . Ul  <o  I  -L.  UJ  >5:  «;  -1  '*4l ~  !  C5, '  N  j  Uj <) C>  •J  §•  .—^  - . t  --i  vn  kj  "i  M vo Si  <*».' m I  3  >»  o 3  -i  "V V/> s  Si  ft.  I  ]"  »< «  r~"  ft-  A.  i  '•o  I  ><  * ; v.vi '  o»  U.  X  15=0  X  5i  l-t  Vvl  d>  6i>0J.t*3nC<rI M  Ul  <*: a. ui  I  •:l  Go  M , K -I-  ! 1"  X  t~  1'  I  *9HIH3J0  c  ~~  o  w ^ 1  o  I i  X NJ  "a  I  "I i -.- -t- >  NO ,  1—  X  -^ i. "» i  0,  It-  *- , vi  s. 0, .;  •-4  o  vs  47  V,  vtJ  U( VS  v^  >i  (-  do  V-  a- , *  3  v.  ^V  V)  V)  vj  VJ  <r  V ' VJ ' VA  s  Ul  v^ o f vj >  5  o w  1—  .1—  I  F I G U R E III A MODIFIED  L . P.  VENEER.  LOCs PEELING  PURCHASING  MODEL  PANEL PRODUCTION ANi> SALE  RI6HT HA Ni> S IJ>E  MARKET  L06S  SuppLy  P£eiE2> VENEER  VENEER.  PANE L  PURCHASES  PRODUCTION'  VENEER  MBRKE.T  PURCHASE  Su  PANEL SALE.  PPLy  MARKET .DEMAND  pANEL  CONTRACTUAL  SALE  COMHITTMEWT  LATHE CAPACITY  TIME  I>«yER  3>RyiN£,  CAPACIjy  Ti»»e  TIME.  PRESS  ?RES5  TJME  CflPficiTy  SAUJINC;  TidE VARIA&LE PROCESS OF  COST  PEELING,  BRyiua, Uf*-<S RA»IW'A, r  .+  COST  LESS MET g.S-PROJUCT  REUElJUG.  PURCHASE  PRICE  PLUS  JARIABL E PROCESS COST  AND  of-  S A L E  CAPAciTy  PRICE  OF P A N E L LESS VARIABLE p«oCESS Coir O F PANEL LAyP A N E L  & L O E -  SANDER  FIWUHIMI  C O S T  obJECT've  FuNCTIOM  t r e a t e d as a s p e c i f i c i n d i v i d u a l l o g p e e l i n g a c t i v i t y i n the m o d e l .  Each  36 of these activities peeling,  i s c h a r g e d w i t h the v a r i a b l e p r o c e s s c o s t  d r y i n g a n d u p - g r a d i n g the  of  veneer.  Veneer utilization; D u r i n g any planning p e r i o d , three s o u r c e s of v e n e e r a v a i l a b l e to the m i l l ;  namely,  are  v e n e e r f r o m the l o g s p e e l e d at the  mill,  v e n e e r f r o m the y e a r - b e g i n n i n g v e n e e r i n v e n t o r y , a n d v e n e e r p u r c h a s e d d i r e c t l y f r o m the m a r k e t .  T h e v e n e e r a v a i l a b l e d u r i n g the p l a n n i n g p e r i o d i s  either  c o n s u m e d at the p a n e l l a y - u p o r g o e s i n t o b u i l d i n g up the p e r i o d - e n d veneer inventory, with an e q u a l i t y  a n d the o p e n i n g i n v e n t o r i e s  m a y also be p r o g r a m m e d  constraint.  A l t e r n a t i v e w a y s of c o n s t r u c t i n g a p a n e l a r e p r o g r a m m e d i n the m o d e l .  T h e d o w n - g r a d i n g of c e r t a i n g r a d e s o f v e n e e r i s  p r o g r a m m e d for.  also  E a c h w a y o f c o n s t r u c t i n g a p a n e l i s p r o g r a m m e d as a  s p e c i f i c i n d i v i d u a l a c t i v i t y f o r the m o d e l to s e l e c t f r o m .  Plywood Panel Production: T h e o p e n i n g p l y w o o d p a n e l i n v e n t o r y a n d the p a n e l s  produced  i n the p e r i o d a r e e i t h e r s o l d i n the p e r i o d o r go i n t o b u i l d i n g up the c l o s i n g p a n e l i n v e n t o r y f o r the p e r i o d .  36 T h e c o n c e p t of v a r i a b l e c o s t w i l l be d e v e l o p e d o n p a g e 64.  T h e m o d e l a s s u m e s that a l l the p a n e l s l a i d u p a n d p r e s s e d i n the p e r i o d go t h r o u g h p a n e l - f i n i s h i n g i n the s a m e p e r i o d . T h i s  is  b e l i e v e d to b e a n a c c e p t a b l e  the  s i m p l i f i c a t i o n a s i t m a y not a f f e c t  a n a l y s i s i n any s i g n i f i c a n t way.  Also,  no p a n e l d o w n - g r a d i n g i s  allowed  f o r i n the m o d e l b e c a u s e i t s e e m s to b e m o r e a p p r o p r i a t e to m a k e allowance for l o s s f r o m  p a n e l d o w n - g r a d i n g o u t s i d e the m o d e l .  Capacity Constraint: A s m e n t i o n e d i n C h a p t e r I V , the p r o c e s s a relatively fixed l a b o u r / m a c h i n e ratio. one y e a r ,  F o r a p l a n n i n g p e r i o d of  i t s h o u l d b e r e a s o n a b l e to t r e a t the s u p p l y o f m a c h i n e r y  as b e i n g f i x e d i n k i n d a n d i n a m o u n t . therefore  of p r o d u c t i o n has  The production capacity is  d e f i n e d b y the m a x i m u m n u m b e r o f w o r k i n g m a c h i n e - h o u r s  a v a i l a b l e i n the p e r i o d .  T h i s m a y i n c l u d e the o v e r t i m e h o u r s p r o v i d e d  f o r i n the l a b o u r c o n t r a c t ( a l l o w a n c e f o r d o w n t i m e i s m a d e i n the t i m e a l l o w e d f o r e a c h u n i t of o p e r a t i o n . )  It m a y b e s e e n f r o m F i g u r e s I a n d II t h a t i n the m o d e l , peeling,  veneer  single operation,  d r y i n g a n d v e n e e r u p - g r a d i n g a r e t r e a t e d as namely,  log-peeling.  The log-peeling  log  one  activities  h a v e b e e n c h a r g e d w i t h the f u l l a m o u n t o f the d r y i n g t i m e .  But,  i n f a c t the c l o s i n g g r e e n v e n e e r i n v e n t o r y h a s n o t y e t b e e n d r i e d .  The  c l o s i n g g r e e n a n d the d r y v e n e e r i n v e n t o r y a l s o u s u a l l y h a v e not y e t b e e n  up-graded.  A d j u s t m e n t i s t h e r e f o r e m a d e to the c o n s u m p t i o n o f d r y e r  t i m e f o r the v e n e e r that g o e s i n t o c l o s i n g i n v e n t o r y f o r the p e r i o d . Likewise,  d r y i n g and u p - g r a d i n g p r o c e s s cost are also adjusted for  the c l o s i n g v e n e e r  inventories.  L i m i t s to C l o s i n g I n v e n t o r i e s : T h e e x p l i c i t m a x i m u m l i m i t to the c l o s i n g v e n e e r a n d p l y w o o d i n v e n t o r i e s is storage space.  T h e l o w e s t l i m i t i s d e f i n e d b y the  s t r a t e g i c m i n i m u m r e q u i r e d to k e e p the o p e r a t i o n r u n n i n g s m o o t h l y i n t o the n e x t p e r i o d .  Objective Function: A s h a s b e e n d e f i n e d , the L . P . m o d e l h a s a n o b j e c t i v e w h i c h is e i t h e r to m a x i m i s e o r to m i n i m i s e a c e r t a i n o b j e c t i v e v a l u e d e f i n e d b y a l i n e a r f u n c t i o n o f the v a r i a b l e s ( a c t i v i t i e s ) i n the s y s t e m .  This  o b j e c t i v e f u n c t i o n i s i n f a c t l i k e a n e r v e - c e n t r e of the s y s t e m .  The  r e s o u r c e c o n s t r a i n t s p r o g r a m m e d i n t h e s y s t e m s e r v e to l i m i t the p o s s i b l e s o l u t i o n to a f i n i t e n u m b e r .  A n a n a l y s i s o f the v a l u e of the  o b j e c t i v e f u n c t i o n f o r e a c h o f the p o s s i b l e s o l u t i o n s l e a d s to f i n d i n g the best solution.  T h e s i n g l e o b j e c t i v e p r o g r a m m e d i n the m o d e l i s p r o f i t maximisation. problem.  T h e p r o b l e m s h a l l b e t r e a t e d as p u r e l y an e c o n o m i c  64 In the o b j e c t i v e f u n c t i o n , the c o e f f i c i e n t o f e a c h o f the v a r i a b l e s i n d i c a t e s the v a l u e c o n t r i b u t e d b y one u n i t o f t h a t a c t i v i t y when u n d e r t a k e n .  A positive coefficient usually indicates a revenue  i t e m while a negative coefficient indicates a cost i t e m .  The cost m a y  b e j u s t a n o p p o r t u n i t y c o s t w h i l e the r e v e n u e m a y b e a c t u a l l y r e a l i z e d o n l y i n the n e x t p e r i o d , s u c h as i n e v a l u a t i o n o f a c l o s i n g i n v e n t o r y . (Of c o u r s e ,  the s i g n s o f the c o e f f i c i e n t s  are completely reversed if a  m a x i m i s i n g o b j e c t i v e f u n c t i o n i s t r e a t e d as a m i n i m i s i n g o n e i n the computation. )  The variable process  c o s t and v a r i a b l e r e v e n u e ;  B e f o r e p r o c e e d i n g to d i s c u s s the m a k e - u p o f the  coefficients  of the o b j e c t i v e f u n c t i o n i t i s n e c e s s a r y to d e f i n e the c o n c e p t o f v a r i a b l e  37 cost (revenue);  used in linear programming.  In t h e L . P .  context,  the v a r i a b l e c o s t o f an a c t i v i t y i s t h o s e c o s t s w h i c h a r i s e o n l y b e c a u s e of u n d e r t a k i n g t h a t a c t i v i t y .  It m a y b e m o n e y t h a t h a s to b e p a i d out as  a r e s u l t of that a c t i v i t y o r it m a y be an o p p o r t u n i t y forgone b e c a u s e u n d e r t a k i n g that a c t i v i t y .  of  It i s a l s o i m p l i c i t l y a s s u m e d t h a t t h e s i z e  of the c o s t b e a r s a l i n e a r r e l a t i o n s h i p to the l e v e l of the  activity  undertaken. Of course,  the v a r i a b i l i t y o f a c o s t i t e m i n r e l a t i o n to the  l e v e l o f an a c t i v i t y u n d e r t a k e n c a n b e d e f i n e d o n l y i n r e l a t i o n to t h e  37 T h e f o l l o w i n g d i s c u s s i o n w i l l r e f e r to the c o s t o n l y . i t i s e q u a l l y a p p l i c a b l e to the r e v e n u e  items.  But  time period concerned.  In o r d e r that the L . P . m o d e l w i l l b e  meaningful,  i t i s n e c e s s a r y to d e f i n e the v a r i a b l e c o s t i n the c o n t e x t of the l e n g t h of the p l a n n i n g p e r i o d u s e d .  F o r example,  a r e d u c t i o n of the l e v e l of d e m a n d  o v e r the w h o l e y e a r m a y m e a n a s w i t c h f r o m a t h r e e - s h i f t a two-shift operation.  o p e r a t i o n to  T h i s m a y p e r m i t the r e d u c t i o n o f one  supervisor.  O n the o t h e r h a n d , i f the d r o p i n the d e m a n d i s o n l y to l a s t a m o n t h , no s u p e r v i s o r y p e r s o n n e l m a y be  retrenched.  38 H.G. L . P.  H a n s e n i n his thesis  on cost data r e q u i r e m e n t f o r  a n a l y s i s has given a v e r y c o m p r e h e n s i v e  d i s c u s s i o n on c o s t  c o n c e p t s i n r e l a t i o n to l i n e a r p r o g r a m m i n g a n a l y s i s  of a b u s i n e s s .  He  d i v i d e s the v a r i a b l e c o s t i n t o t h o s e of the ' f i r s t - o r d e r ' a n d t h o s e of the 'second-order.'  T h e f i r s t - o r d e r v a r i a b l e c o s t v a r i e s s o l e l y w i t h the  l e v e l of the a c t i v i t y t a k e n .  The second-order variable cost varies  with  the l e v e l of the a c t i v i t y u n d e r t a k e n a n d a l s o at a f i x e d r a t e ( s a y x %) w i t h the f i r s t - o r d e r c o s t o f the a c t i v i t y . (same in terms  If the s a m e s e c o n d - o r d e r  of the r a t e of v a r i a t i o n w i t h the f i r s t - o r d e r c o s t ) i s  p r e s e n t i n e v e r y a c t i v i t y i n the p r o g r a m , t h i s c o s t i t e m m a y b e i n the a n a l y s i s  activities  cost  ignored  w i t h o u t c h a n g i n g the r e l a t i v e a t t r a c t i v e n e s s of the 39  a m o n g one  another.  38 H . G . Hansen,  S o m e I m p l i c a t i o n s of the C o s t D a t a R e q u i r e -  m e n t s of L i n e a r P r o g r a m m i n g A n a l y s i s f o r C o s t A c c o u n t i n g , P h . D . Dissertation,  1963,  U n i v e r s i t y of M i n n e s o t a ,  pp.30-35.  39 B u t f o r a n y a c t i v i t y to be u n d e r t a k e n i n the p e r i o d the  resultant  r e v e n u e m u s t b e a b l e to c o v e r a l l the v a r i a b l e c o s t , b o t h the f i r s t - o r d e r a n d the s e c o n d - o r d e r  categories.  66  T h e C o e f f i c i e n t s o f the O b j e c t i v e F u n c t i o n ; A s c a n b e s e e n i n F i g u r e I, e a c h o f the a c t i v i t i e s i n the m o d e l is treated like a cost-centre.  T h e v a r i a b l e cost (revenue)  incurred  (earned) b y that a c t i v i t y i s c h a r g e d o n l y against that p a r t i c u l a r activity. another,  T h o u g h the p r o d u c t m a y go t h r o u g h f r o m one a c t i v i t y to the c o s t i s not c a r r i e d f o r w a r d .  Log Peeling: variable process grading.  A g a i n s t the peeling a c t i v i t i e s  a r e c h a r g e d the  c o s t of l o g p e e l i n g , v e n e e r d r y i n g and v e n e e r u p -  This presupposes  that a l l the v e n e e r p r o d u c e d f r o m the l o g s  go t h r o u g h t h e s e p r o c e s s e s to b e r e a d y f o r p a n e l l a y - u p o r go i n t o closing veneer inventories.  H o w e v e r the v e n e e r t h a t g o e s i n t o the  g r e e n i n v e n t o r y w o u l d b e d r i e d a n d u p - g r a d e d o n l y i n the n e x t p e r i o d . T h e d r y v e n e e r i n v e n t o r y a l s o as a r u l e i s u p - g r a d e d i n the n e x t p e r i o d . T h e m o d e l t h e r e f o r e p r o v i d e s a n a d j u s t m e n t b y d e d u c t i n g the process  c o s t f o r the c l o s i n g v e n e e r i n v e n t o r i e s .  respective  Conceptually, it  i s w r o n g to a p p l y t h i s a d j u s t m e n t to the v e n e e r t h a t c o m e s f r o m the opening veneer inventories.  However,  for reasons  of e c o n o m i c s ,  the  m o d e l w o u l d h a v e c o n s u m e d a l l the o p e n i n g v e n e e r i n v e n t o r i e s (as a f r e e g o o d f o r the c u r r e n t p e r i o d ) b e f o r e p e e l i n g a n y l o g f o r  Veneer Purchasing:  veneer.  The veneer purchasing activities  are  c h a r g e d w i t h the p u r c h a s e p r i c e of the v e n e e r a n d the v a r i a b l e c o s t o f d r y i n g a n d u p - g r a d i n g the  veneer.  67  T h e c o n s u m p t i o n of o p e n i n g g r e e n a n d d r y v e n e e r T h e s e activities  a r e c h a r g e d w i t h the v a r i a b l e p r o c e s s c o s t of p r e p a r i n g  the v e n e e r f o r p a n e l l a y - u p . free,  inventories:  T h e m o d e l a s s u m e s the v e n e e r i t s e l f  as the c o m p a n y h a s not e s t a b l i s h e d  is  a m a r k e t for its v e n e e r .  c o s t o f a c q u i r i n g the v e n e e r i n the p r e v i o u s p e r i o d i s t h e r e f o r e  The  treated  as s u n k i n t h i s c u r r e n t p e r i o d .  Sale of Opening P l y w o o d P a n e l Inventory:  These  panels  a r e t r e a t e d as f r e e f o r the c u r r e n t p e r i o d as i t s c o s t of a c q u i s i t i o n is a l r e a d y sunk.  Panel Construction:  These activities  a r e c h a r g e d w i t h the  v a r i a b l e p r o c e s s c o s t of p a n e l l a y - u p , p a n e l - p r e s s i n g , panel-surface  sanding (where applicable);  panel-trimming,  p a n e l - r e c l a i m , and p a n e l -  grading.  S a l e of P l y w o o d P a n e l s : the s a l e p r i c e of the p a n e l s ,  These activities  are credited with  F.O.B.  P r o d u c t i o n a n d S a l e of C h i p s  and Other B y - P r o d u c t :  net s a l e r e v e n u e f r o m the s a l e o f c h i p s i s c r e d i t e d to the activities.  log-peeling  T h i s i s so b e c a u s e the p r o d u c t i o n of the b y - p r o d u c t i s  a r e s u l t o f the l o g - p e e l i n g  The  largely  activities.  C l o s i n g G r e e n and D r y V e n e e r Inventories: p l a c e d o n the c l o s i n g v e n e e r i n v e n t o r i e s  No value  ( e x c e p t the a d j u s t m e n t s  is made  68 for p r o c e s s i n g  costs,  see  F i g u r e I.)  H o w e v e r , this  treatment  w i l l a f f e c t o n l y the a t t r a c t i v e n e s s o f b u i l d i n g the v e n e e r a b o v e the s t r a t e g i c inventories  T h i s m e t h o d of t r e a t i n g the v e n e e r  i s s e l e c t e d so as to d i s c o u r a g e the b u i l d i n g up of e x c e s s  veneer inventories. Besides,  requirement.  inventories  T h i s i s b e l i e v e d to be s o u n d p l a n n i n g p o l i c y .  i t i s a l m o s t i m p o s s i b l e to p l a c e a r e l i a b l e v a l u e o n the v e n e e r  inventory.  T h e c o m p a n y l a c k s a s a l e s m a r k e t for it.  W h a t the  w i l l be w o r t h to the c o m p a n y w h e n the v e n e e r i n v e n t o r y i s m a d e plywood panels of o t h e r  veneer into  d e p e n d s on the s e l e c t i o n of the p a n e l m i x a n d a h o a r d  factors.  C l o s i n g P l y w o o d P a n e l Inventory:  The plywood panels  v a l u e d at the a n t i c i p a t e d s a l e p r i c e i n the f o l l o w i n g p e r i o d .  are  From  the  s a l e p r i c e i s d e d u c t e d the v a r i a b l e c o s t of c a r r y i n g the i n v e n t o r y f o r an a n t i c i p a t e d l e n g t h of t i m e .  L o g Cost Not Allocated:  L a s t l y , it is thought a p p r o p r i a t e  to c a l l a t t e n t i o n to the f a c t that the m o d e l h a s a v o i d e d the so f a r i n s o l u b l e p r o b l e m of a l l o c a t i n g the l o g c o s t to the v a r i o u s g r a d e s  of  40 veneer jointly produced f r o m each log.  Y e t , the m o d e l i s a b l e to  40 W.E.  M a y h e w ( F o r e s t P r o d u c t s J o u r n a l 8 (4) p p . 2 7 A - 3 1 A .  1957) p r o p o s e d a w a y of a l l o c a t i n g the j o i n t c o s t to the v e n e e r ( p a n e l s ) o n the b a s i s of the r e l a t i v e m a r k e t v a l u e o f the p r o d u c t . T h i s m e t h o d i s M a r k e t p r i c e s of v e n e e r a r e l a c k i n g .  And  the c o n t r i b u t i o n of the v e n e e r to the v a l u e of the p l y w o o d p a n e l s i s  often f o u n d to b e u n r e l i a b l e .  often  f o u n d to d e p e n d o n the p a n e l m i x p r o d u c e d . T h e c o s t p l a c e d on the grades  of v e n e e r (panel) i n t u r n i n f l u e n c e s  a n d that of the p l y w o o d p a n e l s .  various  the m a r k e t p r i c e of the v e n e e r  t a k e i n t o c o n s i d e r a t i o n a l l the r e l e v a n t e c o n o m i c f a c t o r s a n d m a x i m i s e the t o t a l r e t u r n to the l o g s . L. P.  approach.  T h i s i s a r e m a r k a b l e s t r o n g p o i n t of the  70  C H A P T E R VI  DATA PREPARATION FORLINEAR A N A L Y S I S IN T H E C A S E  PROGRAMMING  COMPANY  T h e I m p o r t a n c e of R e l i a b l e Data: It c a n n o t b e o v e r e m p h a s i z e d that the s u c c e s s o f the L . P . a n a l y s i s d e p e n d s l a r g e l y o n the r e l i a b i l i t y o f the d a t a u s e d . d a t a m o r e t h a n d e s t r o y s the u s e f u l n e s s o f the a n a l y s i s . l e a d to c o s t l y e r r o n e o u s  Unreliable  It m a y e v e n  decisions.  C o l l e c t i n g the n e c e s s a r y d a t a i s u s u a l l y the m o s t t i m e c o n s u m ing  a n d the m o s t e x p e n s i v e p a r t of the p r o c e s s o f a p p l y i n g L . P .  to a p l y w o o d b u s i n e s s .  analysis  T h e data c o l l e c t i o n p r o c e s s i s u s u a l l y on a  c o n t i n u o u s b a s i s b e c a u s e m u c h o f t h e d a t a h a s to b e c o n s t a n t l y u p - d a t e d . Besides,  i t m i g h t t a k e y e a r s b e f o r e a c o m p a n y c a n r u n an L . P .  with s u f f i c i e n t l y adequate and sufficiently r e l i a b l e data.  analysis  Fortunately,  we n e e d not a l w a y s w a i t u n t i l the d a t a c o l l e c t i o n p r o c e s s i s f u l l y c o m p l e t e d b e f o r e the L . P . Benefits,  analysis can p r o v i d e some benefits  to the c o m p a n y .  w h i c h often cannot be m e a s u r e d , a c c r u e i n v a r i o u s ways,  such  71  as i n the c o l l e c t i o n o f u s e f u l i n f o r m a t i o n a n d i n m a n a g e m e n t - t r a i n i n g d u r i n g the w h o l e p r o c e s s t o w a r d s an O . R .  of d a t a c o l l e c t i o n a n d i n m a n a g e m e n t  approach.  The L . P .  orientation  m o d e l could also be a p p l i e d with  v a r i o u s d e g r e e s of s o p h i s t i c a t i o n .  T h e d a t a u s e d f o r the C a s e C o m p a n y i s c o l l e c t e d o n as 'scientific'  a b a s i s as p o s s i b l e ,  w i t h i n the l i m i t s o f the  u n d e r w h i c h t h i s p i e c e o f r e s e a r c h i s c a r r i e d out. i n f o r m a t i o n i s not p o s s i b l e ,  circumstances  Where  complete  i n t e l l i g e n t g u e s s e s b a s e d on e x p e r i e n c e  are  u s e d a n d w a y s a r e i n d i c a t e d r e g a r d i n g h o w the m i s s i n g d a t a m i g h t b e c o l l e c t e d i n the n e a r f u t u r e . m u c h to b e d e s i r e d .  W i t h o u t a doubt, t h i s a p p r o a c h s t i l l l e a v e s  B u t i t i s to b e b o r n e i n m i n d that to b u i l d a n i d e a l  m o d e l for a b u s i n e s s is a long p r o c e s s .  T h e r e i s a l m o s t no o t h e r  choice  b u t to b r i n g the m o d e l to the d e s i r e d l e v e l of p r e c i s i o n a n d s o p h i s t i c a t i o n by a gradual process  of i m p r o v e m e n t .  In the i n t e r i m , the m o d e l i s  still  u s e f u l p r o v i d e d i t i s u s e d w i t h the r i g h t u n d e r s t a n d i n g a n d w i t h s o u n d judgment.  It i s w i t h t h i s t h o u g h t i n m i n d t h a t the a n a l y s i s of the C a s e  Company is undertaken.  S e l e c t i n g the P l a n n i n g P e r i o d : T h e i m p o r t a n c e of d e f i n i n g the p l a n n i n g p e r i o d h a s been emphasized.  However,  already  w h e n c h o o s i n g the l e n g t h of the p e r i o d to  b e c o v e r e d b y the a n a l y s i s , one s h o u l d r e m e m b e r s o m e of the cations of this  decision.  impli-  In a n  P.  analysis,  the u n d e r l y i n g e c o n o m i c a n d o p e r a t i n g  c o n d i t i o n s a r e a s s u m e d c o n s t a n t t h r o u g h o u t the p e r i o d .  In a m u l t i p l e -  p e r i o d a p p r o a c h , the t o t a l p e r i o d c o v e r e d b y the a n a l y s i s c a n b e  sub-  d i v i d e d i n t o s u b - p e r i o d s so that the u n d e r l y i n g e c o n o m i c a n d o p e r a t i n g conditions i n each s u b - p e r i o d a r e constant.  T h i s approach enables  the a n a l y s i s to c o v e r a l o n g p e r i o d a n d at the s a m e t i m e t a k e c a r e o f the c h a n g e s i n the u n d e r l y i n g c o n d i t i o n s i n the c o u r s e of the l o n g p e r i o d . In t h i s w a y ,  the s o l u t i o n d e r i v e d w i l l b e c l o s e r to the o p t i m u m t a k e n  e v e n i n the s e n s e o f the l o n g - r u n .  In the p r e s e n t s t u d y , The fiscal year is selected.  a single-period approach is  adopted.  T h i s s e e m s the m o s t p r a c t i c a l c h o i c e  as m a n y of the c o m p a n y p l a n s a r e o n a y e a r l y b a s i s ,  especially  the  detailed ones.  P l y w o o d Sale Opportunities: In o r d e r t h a t the m o d e l c a n s e l e c t the o p t i m u m p r o d u c t m i x , i t i s n e c e s s a r y to p r o g r a m i n t o the m o d e l a l l t h o s e p r o d u c t l i n e s t h e i r s a l e s p o t e n t i a l t h a t a r e a v a i l a b l e to the c o m p a n y .  and  These product  l i n e s n e e d n o t b e l i m i t e d to t h o s e t h a t a r e c u r r e n t l y b e i n g p r o d u c e d b y the c o m p a n y .  T h e y s h o u l d i n c l u d e a l l t h o s e that the c o m p a n y c a n  p r o d u c e a n d s e l l u s i n g the e x i s t i n g f i x e d r e s o u r c e s .  N e i t h e r m u s t the  s a l e s p o t e n t i a l be l i m i t e d to the c o m p a n y ' s e x i s t i n g s a l e f o r e c a s t s f o r the p l a n n i n g p e r i o d ,  as t h e s e a r e b a s e d o n a n a l r e a d y s e t p r o d u c t - l i n e  p o l i c y , and sales p o l i c y .  T h e i d e a l a p p r o a c h i s to i n c l u d e i n the m o d e l a l l  the p o t e n t i a l p r o d u c t l i n e s a n d the m a r k e t o p p o r t u n i t i e s t h a t a r e o p e n to the c h o i c e of the C o m p a n y i n the p l a n n i n g p e r i o d .  The C a s e C o m p a n y operates four m i l l s whose sales centrally managed.  are  T h e h e a d o f f i c e r e c e i v e s the s a l e o r d e r s a n d t h e n  a l l o c a t e s t h e m to e a c h o f the f o u r m i l l s .  C i r c u m s t a n c e s l i m i t the p r e s e n t L . P . the f o u r m i l l s (the l a r g e s t ) .  a n a l y s i s to o n l y one of  T h i s c r e a t e s the i n s o l u b l e p r o b l e m of  d e c i d i n g w h i c h p a r t o f the C o m p a n y ' s s a l e s o p p o r t u n i t i e s to a l l o c a t e  to  the one m i l l w i t h o u t e n d i n g up i n s u b - o p t i m i s a t i o n f o r the C o m p a n y as a whole.  Two alternatives  are available.  We m a y either use  judgment  a n d a l l o c a t e a s h a r e o f the C o m p a n y ' s m a r k e t o p p o r t u n i t i e s to the m i l l concerned.  A l t e r n a t i v e l y , we m a y a l l o w the c h o s e n m i l l  (the  l a r g e s t of the f o u r m i l l s ) to s e l e c t f r o m the m a r k e t o p e n to the Company.  whole  It c a n n o t b e d e n i e d t h a t e i t h e r one of t h e s e a p p r o a c h e s  l e a d to s u b - o p t i m i s a t i o n f o r the C o m p a n y as a w h o l e .  one  may  B u t it i s  b e l i e v e d that w i t h the p o s t - o p t i m a l a n a l y s i s that c a n be p e r f o r m e d i n a d d i t i o n to f i n d i n g p o s s i b l y j u s t an o p t i m u m s o l u t i o n , the L . P .  analysis  as a w h o l e c a n s t i l l b e v e r y u s e f u l f o r t h r o w i n g l i g h t o n c o m p a n y policies  and for guiding future  decisions.  T h e o n l y s u r e w a y of a r r i v i n g at a p e r f e c t o p t i m i s a t i o n f o r the C o m p a n y as a w h o l e i s to a n a l y s e the f o u r m i l l s t o g e t h e r ,  taking  74 i n t o c o n s i d e r a t i o n the c h a r a c t e r i s t i c s of e a c h of the f o u r m i l l s . outline of an L . P .  The  m o d e l a d o p t i n g s u c h an a p p r o a c h i s p r e s e n t e d i n  C h a p t e r I X as one o f the s u g g e s t i o n s f o r f u r t h e r r e s e a r c h .  F o r the p r e s e n t a n a l y s i s ,  a c e r t a i n s h a r e o f the C o m p a n y ' s  p r o j e c t e d s a l e s i s u s e d to a n a l y s e the one m i l l .  In a d d i t i o n ,  a number  of p r o d u c t s a r e a d d e d o n as a t e s t c a s e f o r the m o d e l to s h o w the r e l a t i v e p r e f e r e n c e f o r the p r o d u c t . a r e p r e s e n t e d i n T a b l e I.  The sales opportunities  used  O n l y Douglas F i r plywaod is included.  the s t a n d a r d s i z e p l u s one o d d - s i z e p a n e l s a r e i n c l u d e d .  Only  The demand  for other odd s i z e s is r e l a t i v e l y insignificant.  T h e s a l e f o r e c a s t p r e s e n t e d i n 1967 i s b a s e d o n 1966 and anticipated changes. industry in North A m e r i c a .  experience  1966 was not a g o o d y e a r f o r the p l y w o o d In fact, the i n d u s t r y s u f f e r e d i t s f i r s t s e t -  b a c k i n a s i x - y e a r p e r i o d of a c o n t i n u o u s r e c o r d s e t t i n g p a c e .  B u t the  i n d u s t r y s t i l l m a n a g e d to p u l l t h r o u g h 1966 w i t h a n i n c r e a s e of 5% i n p r o d u c t i o n r e l a t i v e to 1965.  P r o d u c t i o n o f the B r i t i s h C o l u m b i a p l a n t s  f a r e d b e t t e r w i t h a 12% i n c r e a s e .  In 1967, the B . C . p l y w o o d i n d u s t r y  s t i l l f a c e s a s h o r t t e r m p e r i o d of a d j u s t m e n t to a l l o w the d e m a n d f o r p l y w o o d to c a t c h up w i t h p r o d u c t i o n a g a i n .  A n d little i m p r o v e m e n t i n  the p l y w o o d m a r k e t i s e x p e c t e d d u r i n g 19 67, e x c e p t t h a t a s l o w e r  stream  4 of p r o d u c t i o n m a y b a l a n c e w i t h the r e d u c e d d e m a n d f o r h o u s e c o n s t r u c t i o n . S e e 36th A n n u a l P l y w o o d R e v i e w , F o r e s t I n d u s t r i e s , J a n , See also G r a p h s I - X and I - Y for i n d u s t r i a l figures p a t t e r n of the m a r k e t of the p l y w o o d i n d u s t r y .  a n d the  seasonal  1967.  TABLE I PLYWOOD SALE OPPORTUNITIES  F O R 1967  ( i n u n i t s o f 250 p a n e l s each)  1/4"  4' x 8'  3/8"  5/8"  11/16"  3/4 c"  0. 90  0. 08  0. 84 33. 20  7. 69  9. 25 2 1 . 34  0. 40  86. 42  Marine Grade (MG) Good-Select (G/Sel)  1. 77  1.72  20. 72  5. 75  G o o d - T w o - S i d e (G2S)i  32. 66 67. 26  37. 11  G o o d - O n e - S i d e (G1S)|  2013.88  717.02  S o l i d - T w o - S i d e (S2S)  58. 48  S o l i d - O n e - S i d e (SIS)  966. 85  Good-Solid (G/Sol)  1/2"  7/8"  1"  1 1 /8"  ;0. 22)  ; 0.22)  6. 58  61. 98  2. 64  49. 01 80. 34 3 6 5 . 8 4  204. 74  0. 22  2. 20 8. 80  i.  io  t  1 1/4"  1. 10  1055. 24  8. 80  13. 20  2.20  2. 20  61.41  293. 41  4. 40  13. 20  2. 20  2. 20  2 6 9 . 4 4 259. 69 1 2 1 . 8 4  522. 89  2.20  2. 20  2. 20  2. 20  24. 24 502. 18  0. 22 0. 22  0. 22 0. 22  0. 22  325. 54  0. 22  0. 22 0. 22  4 7 . 74 1 2 4 . 3 5  Cement-Form-One53. 57  Side ( C F 1 ) Cement-Form-TwoSide ( C F 2 )  33. 32  S e l e c t Sheathing (Sel-Sh) 1243.62 S t a n d a r d Sheating (Std-Sh) 1538.84  553.48 1472.01  516. 73 493. 33 724.53 451.23  372.12 52. 86  50. 87  4' x 10' Marine Grade (MG)  2. 00  0.97  0. 40  G o o d - T w o - S i d e (G2S)  0. 62  0. 79  0 . 70  0. 58  2. 30  0. 22  1. 14  0. 22  0. 22  Good Solid (G/Sol)  1. 32  1. 20  3. 70  0.98  14. 75  0. 22  1.90.  0. 22  0. 22  14. 12  75. 12 28. 77 26. 48  0. 22  2. 96  0. 22  0. 22  1. 32  2. 00  1.3 2  1. 32  0. 66  0. 88  0. 66  0. 66  G o o d - O n e - S i d e (G1S)  9 6 . 28  S o l i d - T w o - S i d e (S2S)  3. 70  44. 00 8. 17  47. 30 18. 14  S o l i d - O n e - S i d e (SIS)  16. 57  7.98  10. 29  7. 09 5.92  Select Sheating  28. 10  34. 37  27. 95  28. 14  34. 23  0. 22  0. 22  0. 22  0. 22  72. 61  183.75  50. 00  27. 03  33. 90  0. 22  0. 22  0. 22  0. 22  (Sel-Sh):  Standard Sheating  (Std-Sh)  F o r p a n e l p r i c e s , see A p p e n d i x L X .  Minimum Market Commitment: In a n y b u s i n e s s f o r the s a k e o f g o o d c u s t o m e r  services,  o f t e n n e c e s s a r y to m a i n t a i n a c o m p l e t e l i n e of p r o d u c t .  it is  Some products  m a y not be p r o f i t a b l e b y t h e m s e l v e s , yet, i t i s n e c e s s a r y to p r o v i d e t h e m , i n o r d e r to p u l l the s a l e s o f the m o r e p r o f i t a b l e l i n e s a l o n g . m a r k e t i s no e x c e p t i o n .  The larger customers  The plywood  sometimes order in  b a t c h e s c o n s i s t i n g of a c o m b i n a t i o n o f v a r i o u s p r o d u c t k i n d s .  Failure  to m e e t s o m e of the p r o d u c t o r d e r e d m a y l e a d to a l o s s of the w h o l e order.  Also,  t h e r e i s a n e e d to m e e t e x i s t i n g c o n t r a c t u a l m a r k e t  commitments.  The L . P .  m o d e l i s t h e r e f o r e p r o g r a m m e d to e n s u r e that the  c o m p a n y w i l l f i l l at l e a s t a c e r t a i n m i n i m u m f o r s o m e of the p r o d u c t lines.  S e e T a b l e II.  A n analysis  of the p a s t c o n s u m e r o r d e r s  r e v e a l the n a t u r e o f s u c h ' j o i n t ' d e m a n d , a n d the n e e d f o r certain market  will  meeting  commitments.  L o g Supplies: Species and grade: Standards and Specifications (#0121-1961),  D o u g l a s F i r p l y w o o d , as d e f i n e d i n the set b y the C a n a d i a n S t a n d a r d s  are manufactured f r o m Douglas F i r .  Association  H o w e v e r , the i n n e r  p l i e s of the p l y w o o d p a n e l s m a y be o f D o u g l a s F i r o r a n y o t h e r s o f t w o o d s p e c i e s as l i s t e d i n C S A S t a n d a r d s ( # 0 1 5 1 - 1 9 6 1 ) .  western  The only  T A B L E II MINIMUM M A R K E T COMMITMENT (in units of 2 50 panels each)  4! x 8' Good-Two-Side Good-Solid Good-One-Side Solid-Two-Side Solid-One-Side  1 /4" 4.0 4.0 20.0 4.0  Select Sheathing Standard Sheathing  4' x 10' Good-One-Side Standard Sheathing  20.0  3/8"  1/2" 4. 0  20.0 20.0  4.0  4.0 20.0  4.0 20.0  78  '79 GRAPH zis ,  D O U G L A S FIR P L Y W O O D (BRITISH  Zoo  I-Y SHIPMENT  COLUMBIA)  e x c e p t i o n i s M a r i n e G r a d e p l y w o o d p a n e l s w h i c h h a v e to b e t o t a l l y m a d e of Douglas F i r .  F r o m each species of logs,  the m a n u f a c t u r e r a l s o h a s a n u m b e r  of g r a d e s to c h o o s e f r o m i n o r d e r to m e e t h i s v e n e e r  requirement.  T a b l e III s h o w s the w o o d s p e c i e s a n d the l o g g r a d e s a v a i l a b l e to a manufacturer in British Columbia.  The Case Company, in North America, Douglas F i r .  j u s t l i k e m o s t of the o t h e r m a n u f a c t u r e r s  h a d not p a i d m u c h a t t e n t i o n to s p e c i e s o t h e r t h a n  H i g h grade Douglas F i r logs were plentiful and r e l a t i v e l y  c h e a p c o m p a r e d to the p r i c e s o f p l y w o o d .  But profit-squeeze  and a  t h r e a t o f an e v e n t u a l s h o r t a g e i n the s u p p l y o f D o u g l a s F i r l o g s h a v e to a g r e a t e x t e n t m o d i f i e d the o u t l o o k of-the p l y w o o d m a n u f a c t u r e r s .  F o r the a n a l y s i s of the C a s e C o m p a n y ,  o n l y a s a m p l e o f the  a v a i l a b l e s p e c i e s and the a v a i l a b l e g r a d e s of l o g s i s u s e d . Table IV.  See  T h e s e l e c t i o n i s m a d e o n the b a s i s o f the a v a i l a b i l i t y o f  d a t a o n the r e c o v e r y o f v e n e e r f r o m the l o g s .  The choice is  also  i n f l u e n c e d b y the f a m i l i a r i t y o f the C a s e C o m p a n y w i t h the p a r t i c u l a r categories  of logs  selected.  Sources of Supply:  D u r i n g the p a s t d e c a d e o r so the w o o d  i n d u s t r i e s i n N o r t h A m e r i c a h a v e f o u n d i t a d v a n t a g e o u s to i n t e g r a t e v e r t i c a l l y f r o m t h e s o u r c e of s u p p l y o f l o g s ( t i m b e r l a n d ) to the v a r i o u s wood conversion p r o c e s s e s .  T h e advantage of owning one's own l o g  81  T A B L E UJ L O G SPECIES A V A I L A B L E T O BRITISH PLYWOOD SPECIES  COLUMBIA  MANUFACTURERS GRADES  Douglas F i r P e e l e r s  #1 #2 #3 #4  Douglas F i r P e e l e r s  S F P (suitable f o r p e e l i n g ) .  Douglas F i r Sawlogs  #1 #2 #3  Douglas F i r P e e l e r s Douglas F i r P e e l e r s Douglas F i r P e e l e r s  Douglas F i r Sawlogs Douglas F i r Sawlogs Interior F i r  * Cottonwood Kennedy * Cottonwood P e e l e r * Cottonwood Peelable v  Cottonwood P u l p Spruce  W h i t e Spot  Spruce  B l u e Spot  Spruce Spruce  #1 #2 #3  Balsam  Peelers  Spruce  Balsam Cedar  Peelers  Cedar  #1 #3  Cedar Hemlock H e m l o ck Hemlock Pine Pine Pine  #1 #2 #3 #1 #2 #3  T h i s i s a v a i l a b l e as o d d s p e c i e s t h r o w n i n w i t h b o o m s o f o t h e r m a j o r s p e c i e s .  T A B L E IV  LOG SUPPLY  TO CASE MILL  ( i n u n i t s o f 10, 000 feet b o a r d m e a s u r e e a c h )  SPECIES  & GRADES  AMOUNT  COST /UNIT  Units  $  FIR-Peeler  #1  515, 085  1,400. 00  FIR-Peeler  #2  364, 205  1, 300. 00  FIR-Peeler  #3  1, 318, 590  1,200. 00  FIR-Peeler  #4  364, 205  1,100.00  FIR-SFP  1,000. 00  1,120,097  FIR-Sawlogs  #2  FIR-Sawlogs  #3  793, 960  825. 00  371, 565  700.00  Interior F i r  977,615  685. 00  H e m l o c k - B a l s a m Mix'''  263, 000  664. 00  Spruce M i x  700,600  730. 00  H e m l o c k - B a l s a m M i x consists of:-  Balsam Peeler  52.2  Balsam  10. 6  H e m l o c k #2  31.6  H e m l o c k #3  5. 6 100%  Spruce M i x consists of:-  S p r u c e #2  80  S p r u c e #3  20 100%  83 s u p p l i e s a r e m a n y , i n c l u d i n g a l o n g - t e r m p l a n n e d s u p p l y o f l o g s to the m i l l s a n d a n o p t i m u m u s e o f the f o r e s t l a n d a n d the t i m b e r . E v e n w h e n c e r t a i n c o m p a n i e s h a v e f a i l e d to a c h i e v e a c o m p l e t e l e v e l of i n t e g r a t i o n t h e y h a v e t e n d e d to b e c o m e s o m e w h a t c o - o p e r a t i v e i n t h e i r s u p p l y o f l o g s a n d b y - p r o d u c t s to one a n o t h e r .  T h e C a s e C o m p a n y p u r c h a s e s about 60% o f i t s l o g r e q u i r e m e n t s . T h i s h a s r e s u l t e d i n a t r a d i t i o n o f k e e n c o n c e r n o v e r the e f f i c i e n t u s a g e of the l o g s ,  the p r i c e s o f the l o g s a n d s o u n d p u r c h a s i n g p o l i c i e s .  l o g s u p p l i e s u s e d f o r the p r e s e n t a n a l y s i s a n d t h e i r p r i c e s ( s e e  The  T a b l e IV)  a r e b a s e d o n the 1966 e x p e r i e n c e a n d a n t i c i p a t e d c h a n g e s .  Opening Veneer & Plywood Panels  Inventories:  T h e o p e n i n g i n v e n t o r i e s a r e i n h e r i t e d f r o m the p r e c e e d i n g period.  T h e s e c a n b e e x a c t l y d e t e r m i n e d at the c l o s e o f the p r e c e e d i n g  period.  H o w e v e r , i f the a n a l y s i s i s to b e m a d e s o m e t i m e b e f o r e the  b e g i n n i n g o f the p e r i o d ( i . e. period),  s h o r t l y b e f o r e the e n d o f the p r e c e e d i n g  t h e n i t m i g h t not b e p r a c t i c a b l e to w a i t u n t i l the c l o s e o f the  p r e c e e d i n g p e r i o d to t a k e a p r e c i s e s t o c k o f the i n v e n t o r i e s .  Past  e x p e r i e n c e w i l l h a v e to b e r e l i e d o n u n l e s s a v e r y s t r o n g c o n t r o l o r a c o n t i n u o u s r e c o r d i s m a i n t a i n e d o v e r the i n v e n t o r i e s .  B u t i t i s not  e x p e c t e d t h a t the o p e n i n g i n v e n t o r i e s w i l l s i g n i f i c a n t l y affect the  choice  o f the b e s t p r o g r a m o f a c t i v i t i e s f o r the p e r i o d .  T h e o p e n i n g i n v e n t o r i e s u s e d i n the p r e s e n t a n a l y s i s a r e b a s e d o n the 1966 e x p e r i e n c e .  See T a b l e s V - A , V - B and V I  TABLE V - A  Y E A R BEGINNING G R E E N V E N E E R  INVENTORY  ( i n u n i t s o f 100 s h e e t s o r s h e e t - e q u i v a l e n t each)  G o o d (B) .104"  4" x 8'  4' x 10'  234. 1  8.9  -ISO"  Solid (Bi), .104" .130'  U/L .104" .130"  60. 7  33.0  3.2  9.5  1.7  3.4  1.7  7. 1  41.9  B a c k s #1 .104" -130"  C e n t r e s #1 .104" .130" .171'  Core - X C .104" .130" .171"  297.8  81.2  37.8  140.9  101.1  391.9  36.8  1.7  2.5  5.1  1.3  31.8  110.7  179.1  19.3  oo  TABLE V-B  Y E A R BEGINNING  DRY VENEER  INVENTORY  ( i n u n i t s o f 100 s h e e t s o r s h e e t - e q u i v a l e n t  G o o d (B) .104"  4' x 8'  4' x 10'  .130"  S o l i d (Brf .104" .130"  U/L .104"  69. 4  18. 0  9.8  0.9  28.0  2.6  0.5  1.0  0.5  2. 1  .130"  12.4  B a c k s #1 104" .130"  each )  C e n t r e s #1 .104" .130" .171"  88.2  24.0  11.2  41.7  10.9  0.5  0.8  1.5  Core - X C •104" .130" .171"  30.0  116.0  3.8  9.9  32.8  53.0  5. 7  oo Ul  T A B L E VI  Y E A R BEGINNING  FINISHED P L Y W O O D P A N E L  INVENTORY  ( i n u n i t s o f 250 p a n e l s e a c h )  1/4  M  3/8"  1/2"  5/8"  3/4'  5.80  2 1 . 32  4' x 8' G2S G/Sol  9. 81  5.47  6.32  7. 67  8.39  18.93  10.56  40.65  G1S  238.82  108.09  121.44  60.03  115.26  SIS  0. 48  0,10  0.90  1.76  11.51  Sh-Sel  135.85  68.73  60.74  59.61  58.05  Sh-Std  1.81  5.38  1. 43  0.79  1.43  G1S  9.57  4.48  4.04  8.16  8. 26  Sh-Sel  6.37  6.32  4.04  7.22  5.16  Sh-Std  5.28  11. 13  2.65  0.90  2.08  4' x 10'  87  Closing V e n e e r Inventories Constraints: T h e g r e e n v e n e e r i n v e n t o r y i s k e p t l a r g e l y for the p u r p o s e o f 42 c o o r d i n a t i n g the flow o f m a t e r i a l t h r o u g h the l a t h e s a n d t h e d r y e r s a n d a l s o to s a f e g u a r d a g a i n s t the b r e a k d o w n o f e i t h e r o f the l a t h e s the d r y e r s .  or  It i s not p o s s i b l e to k e e p the g r e e n v e n e e r i n v e n t o r i e s i n  the o p e n f o r l o n g w i t h o u t d a m a g i n g the v e n e e r .  N o r i s i t a d v i s a b l e to  m o v e t h e s e i n - p r o c e s s i n v e n t o r i e s a g r e a t d i s t a n c e a w a y f r o m the operating centres w h i c h they feed.  T h e u l t i m a t e p h y s i c a l l i m i t to  the l e v e l o f g r e e n v e n e e r i n v e n t o r y l e v e l i s s t o r a g e  space.  A l s o f o r the p u r p o s e o f c o o r d i n a t i n g o p e r a t i o n s , the m i l l a dry inventory.  keeps  B e c a u s e the g r e e n a n d the d r y v e n e e r i n v e n t o r i e s  the s a m e s t o r a g e a r e a , the s t o r a g e s p a c e the d r y v e n e e r i n v e n t o r i e s c o m b i n e d .  share  l i m i t i s s e t f o r the g r e e n a n d  See T a b l e V I I .  Strategic M i n i m u m Veneer Inventory L e v e l :  T o e n s u r e that  the m i l l i s k e p t r u n n i n g a l l the t i m e a s t r a t e g i c m i n i m u m  veneer  i n v e n t o r y l e v e l i s m a i n t a i n e d a l l the t i m e .  F o r the p r e s e n t a n a l y s i s the m o d e l p r o v i d e s f o r m a i n t a i n i n g at l e a s t a c e r t a i n c l o s i n g l e v e l o f v e n e e r i n v e n t o r i e s .  This  m i n i m u m f o r the c l o s i n g i n v e n t o r i e s i n c l u d e s o n l y s o m e o f the grades.  I d e a l l y i n a o n e - p e r i o d a n a l y s i s , as t h e p r e s e n t o n e ,  42  See p a g e 40.  strategic veneer the  88 veneer grades to include i n the strategic minimum are those expected to be required i n the early part of the following period. Table VIII-A presents the strategic minimum requirement called for each of the closing green and dry inventories.  In this case  the two inventories should be treated separately as each serves a different set of needs. The strategic minimum i s here computed to keep the m i l l operating for half a shift, producing a plywood m i x representative of that i n the 1966 sales, (see Table VIII-B) Closing Plywood Panel Inventory Constraint:  The maximum  l i m i t to the closing plywood panel inventory is again storage space.  A  strategic minimum equivalent to 4 days' production i n volume and representing the 1966 product m i x is called for i n the model, (see Table VIII-C)  Ideally, this strategic m i n i m u m should consist of  the anticipated requirement i n the early part of the next period. Veneer Purchasing:  The Case Company has the option of  purchasing up to a weekly average of 2. 5 car-loads (50, 000 sq. ft. 3/8" each) of A B M i x grade of green veneer from the United States. The Company pretty well has the choice of thickness of . 104" or . 130" and 4' x 8' or 4' x 10'. Table I X A presents the veneer recovery (at the press) from the purchased veneer.  This i s based on company experience. It i s also  estimated that 1. 3 to 1.5 units of chips are recovered from each car-load  89  TABLE  Vn  INVENTORY STORAGE (in u n i t s of 10, 000 s q . f t .  Inventory Type  G r e e n plus d r y veneer  CAPACITY  3 / 8 " e q u i v a l e n t each)  Amount  400  Estimated Equivalent  4.5 d a y s m i l l c o n s u m p t i o n  inventories  Finished plywood panel inventory  1, 500  1. 2 m o n t h s m i l l p r o d u c t i o n at an a v e r a g e o f 13,000 s q u a r e feet 3 / 8 " / m o n t h  TABLE  VIII-A  STRATEGIC MINIMUM Y E A R - E N D G R E E N A N D DRYINVENTORIES, (VENEER) E A C H AS B E L O W ( i n u n i t s o f 100 s h e e t s o r s h e e t - e q u i v a l e n t each)  G o o d (B) .104"  4' x 8'  4' x 10'  13. 92  0. 63  .130"  3. 61  0. 1  Solid (Bi) .104"  1.96  .130"  0.19  U/L  Backs  .104"  .130"  5.63  2.49  0. 62  .104"  17.71  2.19  #1 .130"  C e n t r e s #1 >  Core - X C  .104"  .130"  .171"  4.83  2.25  8.38  6.02  23.30  0.1  0. 15  0.3  0. 77  1. 89  .104?  .130  n  6.58  .171"  10.65  1. 15  vO  o  91  TABLE  VIII-B  A N A V E R A G E O N EH A L F SHIFT PRODUCTION O F A P R O D U C T - M I X R E P R E S E N T A T I V E O F 1966 (in units of panels)'  1 /4"  3/8"  21  12  1/2"  5/8"  3/4"  4' x 8' G2S G/Sol G1S SIS  16 506  18 229  13  12  45  41  22  86  258  127  244  1  1  2  4  24  Sh-Sel  288  146  129  126  123  Sh-Std  4  11  3  2  3  G1S Sh-Sel  20  10  17  14  13  15  17 11  Sh-Std  11  24  9 9 6  2  4  4' x 10'  92  TABLE  STRATEGIC  VIII-C  MINIMUM  YEAR-END  FINISHED P L Y W O O D P A N E L ( i n u n i t s o f 250 p a n e l s  1/4 .II  3/8  I'  INVENTORY each)  1/2  II  5/8  11  3/4"  4' x 8' 2. 17  1. 21  1. 70 52. 84  1. 86 23. 92  26. 87  0. 11  0. 03  0. 20  Sh-Sel  30. 06  15. 21  Sh-Std  0. 40  1. 19  13. 44 0. 32  G1S  2. 12  Sh-Sel  1. 41 1. 17  0. 99 1. 40 2. 46  G2S G/Sol G1S SIS  1. 40 4. 24  1. 28 2. 34 13. 28 0. 39 13. 19 0. 18  4. 72 8. 99 25. 50 2. 54 12. 84 0. 32  4' x 10'  Sh-Std  0. 90 0. 90  1. 80 1. 60  1. 80 1. 14  0. 60  0. 20  0. 46  93  TABLE IX-A  VENEER RECOVERY FROM A/B  PURCHASED  M I X V E N E E R ( A T PRESS)'  Veneer Grade  % R e c o v e r y at P r e s s  A  4.4  B  32. 2  B  36.8  C/F  15.0  U/L  7.9  B a c k s #1  1.4  Loss  2. 3 100  SOURCE:  Company Experience  TABLE IX-B  V E N E E R RECOVERY F R O M PURCHASED A / B MIX VENEER (AT PRESS,  A T '02' L E V E L O F U P - G R A D I N G )  .(in u n i t s o f 100 s h e e t s o r s h e e t - e q u i v a l e n t , p e r 50, 000 s q . ' 3 / 8 " v e n e e r p u r c h a s e d )  A  B  £ l  C/F  U/L  B a c k s #1  • 1 0 4 " x 4" x 8'  2.4770  17.6692  20.2563  8.2566  4.3485  0. 7706  . 1 3 0 " x 4' x 8'  1.9816  14.1354  16.2050  6.6053  3.4788  0. 6165  . 1 0 4 " x 4' x 10'  1. 9816  14.1354  16.2050  6.6053  3.4788  0.6165  . 1 3 0 " x 4' x 10'  1.5853  11.3083  12.9640  5.2842  2.7830  0. 4932  of v e n e e r p u r c h a s e d .  F o r t h i s s t u d y the p u r c h a s e d v e n e e r i s p r i c e d  at $ 8 3 / - p e r 1000 s q . ft.  3/8".  Veneer Recovery from Log-peeling: T h e d a t a f o r v e n e e r r e c o v e r y f r o m the v a r i o u s g r a d e s a n d the v a r i o u s s p e c i e s o f l o g s p e e l e d a r e o b t a i n e d f r o m a t e s t r u n at the case m i l l .  A r a n d o m s a m p l e o f a s i z e o f about 10% o f a n a v e r a g e  month's c o n s u m p t i o n of logs is u s e d .  T h e t e s t r u n was  necessary  b e c a u s e o f a l a c k o f p u b l i s h e d r e l i a b l e v e n e e r r e c o v e r y d a t a i n the industry.  Besides,  the g r a d i n g s y s t e m u s e d a n d the l e v e l of v e n e e r  u p - g r a d i n g c a r r i e d out o f t e n d i f f e r f r o m one C o m p a n y to a n o t h e r . q u a l i t y o f t h e l a t h e o p e r a t i o n a n d the c o n d i t i o n o f the l a t h e a l s o a f f e c t the v e n e e r  The  can  recovery.  In the v e n e e r r e c o v e r y t e s t s t u d y , the C o m p a n y ' s u s u a l t h r e e v e n e e r t h i c k n e s s o f . 104",  . 130" a n d . 171" w e r e u s e d .  The  u s u a l p o l i c y o f a s s i g n i n g the v a r i o u s g r a d e s o f l o g s to e i t h e r o f the two l a t h e s w a s f o l l o w e d .  T h e t e s t was o n 8-ft v e n e e r o n l y .  The  r e c o v e r y f o r t h e 10-ft v e n e e r i s d e r i v e d f r o m the r e s u l t s o b t a i n e d o n the 8 - f t  veneer.  T h e u s u a l l e v e l o f v e n e e r - u p g r a d i n g was p e r f o r m e d o n t h e v e n e e r d u r i n g the t e s t r u n .  B u t i n the L . P .  analysis (see  l e v e l s o f v e n e e r u p - g r a d i n g (01 a n d 02) a r e u s e d . following ways.  T a b l e X), two  T h e y differ i n the  TABLE X  (per  VENEER RECOVERY 10, 000 F B M o f l o g s p e e l e d )  V E N E E R GRADES UP-GRADE  DIM. 4'x8'  LOG - TYPE Species Grade  01  . 104"  D.  02 01  . 104" . 130"  02  . 130"  01  . 104"  02  . 104"  01  . 130"  02  . 130"  LEVEL  D. D.  D.  . 130"  02  . 130" . 104" . 104"  P  FIR  P  #3  " FIR  P  FIR FIR II  D. FIR II  #3 11  P  11  D.  #2 11  II  . 104"  01 02  FIR  n  D.  #2 II  #4 11  P  #4 II  S. F . P . 11  r  t  1  A T P R E S S ( u n i t s i n 100 s h e e t s o r s h e e t -  B  B  l  C/F  U/L  8.1990  2.7526  2. 8953  2.3148  6.4360 5.5431  2.7526 3.5861  2. 8953  2.3148  2.5960  0.8490  1. 4710 • -  4.0721  3.5861  2. 5960  0. 8490  6.5752  2.2711  1.8960  1.6892  4.8859 3.2582  2.2711  1. 8960  0.8888 0.8888  2.5044  0.6670  4.8002  2.5499  2.5044  0.6670 0.8248  1. 7633 #1  it  a  equivalent) A  #1  P  II  . 130"  01  FIR  D.  01  . 104"  P  n  D.  . 130"  FIR II  . 104" . 104"  01 02  P II  01 02 02  FIR  P  -  0.7083  -  4.9109 3.8806  -  3.8220 3.0202  1. 0302 0.8018  _  5.0555 5.0555 0.6458  5. 0013  0.8248  4.7502 4. 7502  1. 6281  3.0084  0.6458  1. 6281  3. 0084  1.3818 1.3818  2.0068 2.0068  2.0085 2.0085  0.8099 2. 6938  0.7210  2.3078  0.8827  1. 8492  0.7210  2.3078  0.8827  1.9767  1.2050  0.2384  2.4778  1.2050  0.2384  2.4778  1. 1401 1. 7586  TABLE X  •VENEER RECOVERY ( p e r 10, 000 F B M of l o g s peeled)) V E N E E R GRADES UP-GRADE LEVEL  DIM. 4'x8'  01 02  . 104"  01 02  . 130"  . 104" . 130"  A T P R E S S ( u n i t s i n 100 s h e e t s o r s h e e t -  LOG-TYPE  Backs  Solid  -Species G r a d e  #1  Centres  D. F I R  P  D. F I R  P  . 104"  D. F I R  . 104"  11  01 02  . 130" . 130"  D. F I R  01 02  . 104"  D. F I R  . 104"  11  01  . 130"  D. F I R  02  . 130"  01 02  . 104"  D. F I R  . 104"  11  01 02  . 130" . 130"  D. F I R  01  . 104"  D. F I R  02  . 104"  #1  P P  3.5919  #2  3. 5919 3.6101 5.3180  11  P  #3 11  P  11  9.2369 4.5673  #4  8.5049 11.9181  11  II  P  8.6965  #3 II  P  3.2273 4.5263  #2 II  11  3. 4316 4.8303  11  II  01 02  #1 II  II  14. 2253 #4  11  S. F . P . 11  9.2462 12. 2874 14. 2216 20.9040  Part 1  -  -  0.0039  •  XB  XC  1.5793  -  8.2283  0.1805  0.4114  7. 8169  -  7. 4080  #1  1.2989  -  0.3704  7.0376  4.5792  0.6885 0.3324 0.4396 0.4581 -  10. 0895  0.3803  0.5045  9.5850  0.1988  0.0044 -  0.1949 2.1301 0.2167 1.0396  0.0010  0.4982  0.0078 -  3. 9376  -  equivalent)'  Centres  -  3.1687  -  0.4300 7.3007  -  13. 7699 13. 0814 6.6479 6.3155 8.7922 8.3526 9. 1626 8.7045  8. 6006 8. 1706  -  11. 3468  0.5673  10. 7794  TABLE X  VENEER  RECOVERY  ( p e r 10, 000 F B M o f l o g s p e e l e d )  VENEER -GRADE ^EVEL 01 02  DIM. 4'x8' . 130" . 130"  LOG-TYPE Species Grade D. F I R II  D. F I R  01  . 104"  02  . 104"  01 02  . 130"  01 02  . 171"  01 02  . 171"  D. F I R  . 171"  11  . 130" . 171"  II  D. F I R  A  S. F . P . II  „  S - l o g #2 II  _  S - l o g #2  II  D. F I R II  D. F I R  S - l o g #2  tt S - l o g #3 Interior  . 130"  02 01  . 130" . 171"  02  . 171"  01  . 171"  Hemlock B a l s a m Mix  01  . 171"  Spruce M i x  D. F I R  G R A D E S A T P R E S S (units i n 100 s h e e t s o r s h e e t equivalent) B  'i  Interior  II  B  l  C/F  U/L  0.9067 0.9067 0.5362  0.6554  1.2097  1. 6596  0.6554 0.6967  1.6865 4.2527  2.2411  0. 5362  0.6967  4. 2527  0.3445  0.4105  2.6084  0.3445  0.4105  2.6084  -  M  m  -  *•  -  -  01  II  „  Part 2  -  --  3. 7241 2.7239 1. 5196 1.8701  **  0.12  0.24  0.49  1. 86  0.12  0.24  0.49  1.86  -  -  -  -•  -  -  -  -  -  -  *•  -  v£>  oo  TABLE X VENEER (tper  RECOVERY  VENEER -GRADE  DIM.  J  4'x8'  Species  Grade  01  . 130"  D. F I R  S. F . P .  02  . 130"  E  V  E  L  01  . 104"  02  . 104"  01  . 130"  02  . 130" .171"  LOGOTYPE  *  It  D. F I R  ti  S - l o g #2  11  D. F I R  II  S - l o g #2 it  II  S - l o g #2  02  . 171"  D. F I R n  01  . 171"  D. F I R  02  . 171"  ti  S - l o g #3 n  01  < 130"  D. F I R  Interior  02  . 130"  11  01  . 171"  D. F I R  02  . 171"  11  01  . 171"  Hemlock-Balsam Mix  01  . 171"  Spruce Mix  01  Part 2  10, 000 F B M o f l o g s p e e l e d )  11  11  Interior 11  Backs #1  G R A D E S A T P R E S S ( u n i t s i n 100 s h e e t s o r s h e e t equivalent)) Solid Centres XB -XC Centres • #1  8.5082  7.0184  12 . 9 8 5 4 6. 0730  0.6632  12. 1986  0.0547  3. 5990 8.5372  5.2886  m — -  0.4808  M  tm *•  *•  0.5413 •*  1.0982  11.9356 11.00 10.45 6. 19  0.05  2.43 10.37 9. 88 11.37  10. 2854 9. 7096 9.2241  0.7703  5. 8149 5. 0446  *•  7. 64  0. 76  6. 88  0. 54  10. 35  0. 79  7.91 7. 12  -  10.92 0.55  9.1354 10. 8267  0.4855 13. 0338  0.55 4.95 8. 67  9.6163  10.89  8.76 M  7. 27  vO vD  TABLE X  VENEER RECOVERY (vper 10, 000 F B M o f l o g s p e e l e d )  Part 3  - V E N E E R G R A D E S A T P R E S S ( u n i t s i n 100 s h e e t s o r UP-GRADE  DIM.  LOG-TYPE  LEVEL  4'xl'O'  Species Grade  01 02 01 02 01 02 01 02 01 02 01 02 01 02 01 02 01 02  . 104" . 104" . 130" . 130" . 104" . 104" . 130" . 130" . 104" . 104" . 130" . 130" . 104" . 104" . 130" . 130" . 104" . 104"  D. F I R D. F I R D. F I R  ci  P P  ti  P  11  D. F I R II  0.6414  #4 II  P  0.8242  #3  ii t  P  11  D. F I R  0.5666  P@  II  D. F I R  1.3514  #2 11  II  D. F I R  _  1.1768  #2 11  II  D. F I R  #1  P  II  D. F I R  1.4107  II  II  V  #1  P  •II  B  A  #4 it  _  S. F . P . it  **  6.5596 5.1489 4.4345 3.2577 5.6664 3.9088 2.6065 2.0399 3.9287 3.1045 3.0576 2.4162 1.1054 1.1054 0.5768 0.5768 0.9640 0.9640  B  l  equivalent) C/F  2.2021 2.2021 2.8689 2.8689 1.8169 1,8;169 2.0035 2.0035 4.0444 4.0444 0.5167 0.5167 1.6055 1. 6055 1.8463 1.8463 0.1907 0.1907  2.3163 2.3163 2.0768 2.0768 1.5168 1.5168 0.5336 0.5336 0.6598 0.6598 1. 3025 1. 3025 1. 6068 1.6068 0. 7061 0.7061 1.9823 1.9823  sheetU/L  1.8519 1.8519 0.6792 0. 6792 0. 7110 0.7110 3.8402 4.0011 3.8002 3.8002 2.4067 2.4067 0.6479 0.6479 1. 4794 1.5814 0. 9121 1.4067  TABLE X  (per  -GRADE J  E  V  01 02 01 02 01 02 01 02 01 02 01 02  E  L  DIM. 4'xlO'  LOG- TYPE Species Grade  . 104"  D. F I R n  . 104" . 130" . 130" . 104" . . . .  104" 130" 130" 104"  . 104" . 130"  D. F I R  P#l  D. F I R D. F I R  P  #3 n  P  #3 ri  D. F I R tt  P  01 02  . 130"  D. F I R  P  . 130"  11  01 02  . 104" . 104"  D. F I R  II  II  #2 II  . 130" . 104" . 104"  01 02  #2  P  11  D. F I R  II  n  II  D. F I R  3. 8643  P  11  2.7452 2.5819 3.6210 2.8735  #1  #4 II  #4 II  S. F . P . S. F . P .  Part 3  V E N E E R G R A D E S A T P R E S S ( u n i t s i n 100 s h e e t s o r s h e e t e q u i v a l entjl Solid Centres * Backs XB Centres XC #1 #1  II  P  II  VENEER RECOVERY 10, 000 F B M o f l o g s p e e l e d )  2.8735 2.8880 4.2544 6. 9572 7. 3895 3. 6538 6. 8039 9.5345 11. 3803 7. 3969 9.8300 11. 3773 16. 7232  6.5827  1.2634  -  _  0.0032  0.0035 0.0080 0.0062 _  0.1444 1.0391  -  0.3291  6. 2535 5. 9264  -  0.2963  0.1590  -  5.6301 11. 0160  0. 1558  0.5508  10.4652  1.7041 0.1734  -  0.8317 0.3985 3.1501  -  3.6634 0.3042 2.5350  -  5. 8406  -  0. 2659  0. 3665 0.4036 0. 3440 0.3517  0.4539  5.3183 5.0524 7.0338 6.6821 7.3301 6.9631 8.0716 7.6680 6. 8805 6.5365 9.0774 8.6235  TABLE X  •VENEER RECOVERY (.per 10, 000 F B M o f l o g s p e e l e d )  V E N E E R GRADES -GRADE  DIM.  _iEVEL  4'xlO' . 130"  01  . 104"  D. F I R  02  . 104"  11  S - l o g #2 ii  01  . 130"  D. F I R  S - l o g #2  02  . 130"  01  . 171"  02  . 171"  01  . 171"  D. F I R  S»log  02  . 171"  11  11  01  S. F . P . II  11  II  D. F I R  S - l o g #2  II  II  #3  Interior  01  . 130" . 171"  11  02  . 171"  01  . 171"  Hemlock-Balsam Mix  01  . 171"  Spruce Mix  II  „  II  -  Interior II  „  -  B  l  C/F  U/L  0.7253  0.5243  0.9678  1.3277  0.7253  0. 5243 0.5573  1.3492 3.4021  2.9793 1.7928  0.5573  3. 4021  0.3284  2.0867  2. 1791 1. 2157  0.3284  2.0867  1. 2157  0.4289 0.4289 0.2756 0.2756 •*  _  D. F I R D. F I R  „  —  . 130"  02  B  A  01 02  . 130"  A T P R E S S ( u n i t s i n 100 s h e e t s o r s h e e t equivalent)'  LOG-TYPE - Species Grade D. F I R  Part 4  --  -  **  -  -  -  **  0.096  0.192  0. 392  1.488  0.096  0.192  0. 392  1. 488  -  -  •*  -  -  o ro  TABLE X  VENEER (per  RECOVERY  10, 000 F B M o f l o g s p e e l e d )  Part 4  V E N E E R G R A D E S A T P R E S S -(units i n 100 s h e e t s o r  sheet-  equivalent) -GRADE  iEVEL 01 02 01 02 01 02 01 02 01 02 01 02 01 02 01 01  DIM. 4'xlO'  LOG-TYPE Species Grade  . 130" . 130" . 104" . 104" . 130" . 130" . 171" . 171" . 171" . 171" . 130" . 130" . 171" . 171" . 171" . 171"  D. F I R  t> D. F I R  Backs  •#1  S. F . P .  it S - l o g #2  is D. F I R mi  D. F I R  S - l o g #2  n S - l o g #2  n  tt  D. F I R  S«log  ti  #3  11  D. F I R n  Interior  D. F I R  Interior  it  ri  6. 8065 10. 3883 4. 8583 9.7589 2.8792 6.8297  „  -  «#  -  3.96 6.94  -  Spruce M i x  •a  0. 8786 0. 02 0. 048  -  0. 176 m  -  Centres  #1  XB  5.6148 0.3846  m  it  Hemlock - B a l s a m Mix  Solid Centres  «* M  5.3058 0.0438 4.2309 M  10.4270 9.5484 8. 80 8. 78 6.19 2. 432 8.736 8. 56 7. 904 9. 096  0.4331 0.3884 0.6162 0. 31 0. 544 0. 35  -  -xc 7.6930 7.3084 8.6614 8.2283 7.7677 7.3793 4.6519 4. 0357 6. 11 5. 80 10. 89 10. 346 6. 328 5.98 7. 008 5. 816  104  A t the 02 l e v e l , i n a d d i t i o n to a l l t h a t a r e done at t h e 01 l e v e l , the f o l l o w i n g i s a l s o c a r r i e d out: 1)  S e l e c t F a c e v e n e e r i s d e v e l o p e d f r o m the B v e n e e r ,  2)  S o l i d C e n t r e s a r e d e v e l o p e d f r o m the C e n t r e #1,  3)  Solid Core,  4)  A t 01 t h e d r y e r - g r a d e , B a c k #2 i s u p - g r a d e d to C e n t r e s #1.  to B a c k  X B , i s d e v e l o p e d f r o m the C c o r e , X C ,  only.  A t 02,  B a c k #2 i s u p - g r a d e d  #1.  T a b l e X I p r e s e n t s the b y - p r o d u c t p r o d u c e d at l o g p e e l i n g . The figures reflect Company experience.  Manufacturing Process  Cost:  T h e w a y to t r e a t the m a n u f a c t u r i n g p r o c e s s a n a l y s i s i s as f o l l o w s : the v a r i a b l e p r o c e s s variable process  h a v i n g d e f i n e d the l e n g t h o f the p l a n n i n g p e r i o d ,  cost items are then identified.  N e x t , the  c o s t s of o p e r a t i n g e a c h o f the p r o c e s s  unit of t i m e i s c o m p u t e d .  c o s t i n the L . P .  centres per  T h e l e n g t h o f t i m e that e a c h o f the p r o g r a m m e d  a c t i v i t i e s o c c u p i e s e a c h o f the p r o c e s s  centres is also m e a s u r e d .  t h e s e d a t a i t b e c o m e s p o s s i b l e to c o m p u t e the v a r i a b l e p r o c e s s a s s o c i a t e d w i t h e a c h o f the p r o g r a m m e d a c t i v i t i e s . e a c h of the p r o c e s s  centres  With  cost  T h e c a p a c i t y of  c a n a l s o b e d e f i n e d i n t e r m s o f the l e n g t h  of w o r k i n g t i m e a v a i l a b l e d u r i n g the p l a n n i n g p e r i o d .  T A B L E XI  BY-PRODUCT (NET  RECOVERY  (CHIPS)  V A L U E R E T U R N P E R 10, 000 F B M O F L O G S  PEELED)  TOTAL UNITS O F CHIPS  NET REVENUE  D. F I R P E E L E R S  6.0  114. 40  D. F I R S A W L O G S  6. 5  124. 00  8.0  152.50  HEMLOCK,  BALSAM,  SPRUCE  PURCHASED VENEER A B M I X , ( p e r 50, 000 s q . ft.  SOURCE:  3/8");  C o m p a n y a v e r a g e f i g u r e s a n d 1966  25.00  xinet r e t u r n f i g u r e s .  106 Identifying the Variable Process Cost Items: E v e r y significant cost item of each of the process centres in the Case Company i s examined visually on graphs to see how the cost items behave i n relation to past levels of activity of the process centres. More sophisticated methods, such as statistical correlation methods may be used to study the behavior of the cost items.  However, i n the  circumstance of the present case, it i s believed that such methods w i l l not improve the accuracy of the graphical and judgment approach to the extent that the extra effort is justified. The source of data for the cost behavior analysis i s the internal monthly cost statements of the m i l l .  It should be emphasized  that the unit of measure (sq. ft. 3 / 8 " equivalent) used i n the cost state*, ;  ments i s an imperfect measure of the volume of production, especially when used to analyse the behavior of the process cost. F o r example, a 1" plywood panel does not take exactly twice as much machine time to produce as a 1/2" panel.  Likewise, it is expected that a 4' x 8'  panel does not take exactly twice as long as a 4' x 4' panel. (Of course for perfection's sake, the multiple correlation method may be used to overcome the inadequacy of the measurement unit by identifying the part of the change i n the process cost that i s associated with the physical volume of production. Such approach requires data with a breakdown of production by each specification group.  107 Though the planning period used is the year, monthly cost data i s here used because of practical considerations.  Using yearly  figures w i l l require the analysis to used data collected over a long period of time.  During such a long period of time, very significant  changes might have taken place, and i t is very difficult to isolate the effect of these changes i n order to make the data homogeneous. Besides, it i s difficult to expect the Company to have kept a complete set of its detailed cost statements covering at least 8 to 10 years, a number that is believed to be the minimum required for the sample to be of much use. It i s fully realized that some cost items are not variable in the monthly period but are so i n the 'longer run, ' such as a year. We  can quite safely conclude that a cost item that varies with the  production f r o m month to month w i l l also be variable over a year. F o r those cost items that do not vary significantly with production over the months, judgment w i l l be used to analyse company policy and company experience to deduce the variability of the cost items over the year. Direct Production Labour Cost; The plywood m i l l i s organized on a process centre basis, each centre with a definite man  assigned to each work station.  daily operation i s organized into three shifts.  The  The two day-shifts have  108  a w o r k i n g t i m e o f 7 h o u r s 'i'O m i n u t e s e a c h .  T h e night shift is  compen-  s a t e d b y a s h o r t e r p e r i o d of w o r k i n g h o u r s (6 h o u r s 10 m i n u t e s )  rather 43  than b y a p a y d i f f e r e n t i a l .  E a c h shift has a b r e a k o f 50  minutes.  W o r k on Sundays and S a t u r d a y s i s p a i d a t i m e - a n d - a - h a l f , In t h i s Li. P .  analysis,  divisible for every p r o c e s s  b a s i s of a 3-shift e x c e p t two.  over-time.  the w o r k i n g t i m e i s t r e a t e d as  centre and e v e r y activity.  that a s s u m i n g t h i s f o r a p l a n n i n g p e r i o d o f a y e a r i s  In the a n a l y s i s ,  as  It i s  perfectly  believed  reasonable.  the d i r e c t l a b o u r c o s t i s c o m p u t e d o n the  d a y a n d a 5 - d a y w e e k f o r a l l the p r o c e s s  centres  T h e B o o m o p e r a t i o n ( b r e a k i n g up b o o m s of l o g s a n d s a w i n g  t h e m i n t o v e n e e r l e n g t h a n d l o g - d e b a r k i n g ) i s c a r r i e d out o n l y i n the two d a y s h i f t s .  O n the o t h e r h a n d , two of the d r y e r s a r e o p e r a t e d o v e r  the w e e k e n d s ( s e e  Chapter IV).  T h i s i s s t r i c t l y a r e s u l t of f a c i l i t y -  capacity balancing practices.  A g r a p h i c a n a l y s i s of a s a m p l e o f the d i r e c t p r o d u c t i o n l a b o u r c o s t i n d i c a t e s t h a t t h i s c o s t i t e m v a r i e s v e r y c l o s e l y w i t h the p h y s i c a l v o l u m e of p r o d u c t i o n . See G r a p h s I I - A and I I - B . be c l o s e r  The relationship may  s t i l l i f the d a t a p e r t a i n s to the y e a r l y b e h a v i o r  relationship  r a t h e r t h a n to the m o n t h l y o n e .  43 With a s m a l l exception;  u s u a l l y the d r y e r s a r e o p e r a t e d  t h r o u g h o u t the l u n c h a n d the c o f f e e - b r e a k s .  W o r k e r s f r o m other  centres  s t a n d i n f o r the u s u a l d r y e r o p e r a t o r s w h i l e t h e y h a v e the b r e a k s .  109 i  3 / t  (,100  ".  isooo  GRAPH  AT  II-A  PRESS  sm  5J»0  Moo  rS>0  Iflto  3100  3500  PK0J>UCTI0N  S I RE6T PRODUCTION  21oo  LABOUR  <W» woo Xl'd  TJ*'*t  JW«  FU.T  *f»7  "•»**  COST  ***  GRAPH AT BOOM  II-B  PROCESSING  Ill It i s t h o u g h t r e a s o n a b l e to t r e a t t h e d i r e c t p r o d u c t i o n l a b o u r c o s t as a c o m p l e t e l y v a r i a b l e p r o c e s s  cost  i t e m i n the L . P .  analysis.  D i r e c t Maintenance L a b o u r and D i r e c t Maintenance M a t e r i a l Cost: M a i n t e n a n c e l a b o u r cost and maintenance m a t e r i a l costs a r e c h a r g e d d i r e c t l y to the p r o c e s s  c e n t r e s as t h e y a r e i n c u r r e d .  The term  ' m a i n t e n a n c e ' i s h e r e u s e d to i n c l u d e r e p a i r w o r k ( c a r r i e d out w h e n the m a c h i n e b r e a k s down) a n d p r e v e n t i v e m a i n t e n a n c e .  The major preventive  w o r k i s done d u r i n g t h e a n n u a l v a c a t i o n i n the m i l l .  The Case Company  k e e p s a v e r y d e t a i l e d r e c o r d o f the m a i n t e n a n c e c o s t s i n c u r r e d b y e v e r y m a j o r p a r t o f e a c h o f the m a c h i n e s .  T h i s i s p r e s u m a b l y done f o r the  p u r p o s e of guiding m a c h i n e r y r e p l a c e m e n t and for g e n e r a l c o n t r o l purposes.  A g r a p h i c a n a l y s i s o f the m a i n t e n a n c e c o s t s i n G r a p h s L U - A to G r a p h I I I - D , i n d i c a t e s that the b e h a v i o r o f t h e s e c o s t i t e m s b e a r a n y s t r o n g r e l a t i o n s h i p to that o f the v o l u m e o f output.  d o e s not  The major  p r e v e n t i v e m a i n t e n a n c e w o r k done d u r i n g the J u l y v a c a t i o n i s o u t s t a n d i n g . A t best,  we c a n o n l y c o n c l u d e that t h e m a i n t e n a n c e c o s t s do not v a r y  d i r e c t l y with the l e v e l of p r o d u c t i o n .  T h e r e i s s o m e i n d i c a t i o n that  the s i z e o f the m a i n t e n a n c e i n one m o n t h i s a f f e c t e d b y the a m o u n t o f m a i n t e n a n c e done i n the p r e c e e d i n g one o r two m o n t h s . a two o r t h r e e - m o n t h p e r i o d w i l l b e q u i t e  T h e average of  even.  It i s g u e s s e d that 90% o f the m a i n t e n a n c e c o s t s i n c u r r e d i n were incurred irrespective  o f t h e l e n g t h of the t i m e o f o p e r a t i o n .  1966  The  GRAPH AT BOOM  III-A  PROCESSING  113 G R A P H III-B ill , AT  ISMS  DRYERS  iOOO  St't  X'to  J  PRODUCTION LEVEL  Bl«6CT *00  J  too o  l J  I  I I  Co I T  J looo S N I U :  WM,  iecU  J«K«  J»»i7  F.b'n  /if'w  CoMfKMV  iV'tf  K sTATEMtlOTt,  Fl&URM  J>l»Suii6.J>  «»»'«  114 GRAPH  "31? | 4  III-C  AT GREEN  END  %01>Q  PROuOTIftf LEVEL TJIR6CT MAINTENANCE LASOue CMI  S"ooo  T«ru  ta'H  «'o  «f'  H  *»'«*  PW  ''  1  *  , u  r h , u  s  *  f U  *»  u  GRAPH MILL,  III-D  TOTAL  \looo  j j; 4 n  fib'..Mtril  SpW  M^U  Jurv'a  JulU S O U R C E :  Auj'M  conrfiN))  t«p'tt K  ixfittnwrs  fctit fttnta  rin'ii  itcil  »u&ms£J>  116 o t h e r 10% w a s t h o u g h t to b e v a r i a b l e w i t h the t i m e o f o p e r a t i o n . i s t a k e n as the b a s i s f o r c a l c u l a t i n g v a r i a b l e d i r e c t m a i n t e n a n c e  This cost  f o r the L . P . a n a l y s i s .  Indirect Production Cost: Electrical Power Cost:  One would quite n a t u r a l l y expect  that the c o n s u m p t i o n o f e l e c t r i c a l p o w e r w i l l v a r y to a l a r g e e x t e n t w i t h the l e v e l o f p r o d u c t i o n .  G r a p h I V i n d i c a t e s that b y no m e a n s  c a n we  s a y f o r s u r e t h a t the e l e c t r i c a l p o w e r c o n s u m p t i o n i n t h e m i l l  varies  d i r e c t l y w i t h the l e v e l o f output.  It i s the p o l i c y o f the m i l l to k e e p the m i l l w e l l l i g h t e d e v e n d u r i n g the v a c a t i o n .  M o s t o f the e q u i p m e n t i n the m i l l i s l e f t w i t h the  p o w e r on o v e r the w e e k - e n d s . course,  A l o n g e r p e r i o d of s h u t - d o w n w i l l , of  r e d u c e t h e c o n s u m p t i o n of e l e c t r i c a l p o w e r  substantially.  It i s b e l i e v e d r e a s o n a b l e to t r e a t 10% o f the e l e c t r i c p o w e r c o n s u m p t i o n c o s t i n 1966 as c o n s t i t u t i n g the v a r i a b l e p o r t i o n o f e l e c t r i c power consumption.  A n d t h i s i s u s e d as the b a s i s f o r c a l c u l a t i n g  v a r i a b l e e l e c t r i c p o w e r c o s t f o r the L . P . a n a l y s i s . for the r e l a t i v e s i g n i f i c a n c e of this c o s t i t e m . p o w e r c o s t i s p r o r a t e d to e a c h o f the p r o c e s s u s e d b y the a c c o u n t i n g d e p a r t m e n t .  See  Table XII  A n d t h i s p o r t i o n o f the centre,  u s i n g the  basis  T h i s b a s i s has been d e r i v e d f r o m  a n e s t i m a t e o f the p o w e r c o n s u m p t i o n c a p a c i t y o f the m a c h i n e r y i n e a c h o f the p r o c e s s  centre.  GRAPH MILL  IV  TOTAL  >/«" "•VPFINISHED PANEL  Hyulseb 0UTPI*  ELECTRICAL  CONSun»TION vUATER  T  POWER  t04T  CONSUrtPTIOAl  COiT I toot  »»0  too  If 00  » e « W  "*  U  ^  ^  118  T A B L E XI1  "THE  P R O P O R T I O N OF  THE  C O S T I T E M S OF T R E A T E D AS  VARIOUS  1966  VARIABLE  A s % of total production c o s t (I960)  Direct Production Labour  21. 86  A s % of total direct production labor cost (1966) 100  Portion treated as variable  100%  D i r e c t Maintenance - labour -material  1. 88 2.54  8. 6 11.7  10% 10%  E l e c t r i c a l - power  1. 22  5. 6  10%  f 12. 3  100% 100%  F o r k l i f t - labour - fuel  (2.69 *•  Water O i l & Grease - labour - material Direct Production material - Total - Plastic Patch - Davis Patch - Sander - Raiman - Others  Source:  i  0.96  4.4  5%  i 0. 37 '  jl. 7 *"  5% 5%  1. 50  6. 8  K statements of C a s e C o m p a n y  100% 100% 100% 100% 20%  119  T h e Cost of Water Consumption: G r a p h I V a l s o i n d i c a t e s that the b e h a v i o r o f the o f w a t e r i n the m i l l i s v e r y s i m i l a r to t h a t o f p o w e r c o s t . for cleaning and for p r o v i d i n g s t e a m for p o w e r .  consumption Water is  used  In 1966, the  c o n s u m p t i o n a p p e a r s to b e c y c l i n g up a n d d o w n f r o m m o n t h to m o n t h , w i t h o u t a n y o b v i o u s r e l a t i o n s h i p to the l e v e l o f p r o d u c t i o n .  A g a i n i t i s t h o u g h t r e a s o n a b l e to t r e a t 5 % o f the c o s t o f w a t e r c o n s u m p t i o n i n 1 9 6 6 as the v a r i a b l e p o r t i o n o f t h i s c o s t i t e m . i s p r o r a t e d to the p r o c e s s accounting department.  This  cost  c o s t c e n t r e o n the b a s i s u s e d b y the c o s t  A l s o see  T a b l e X I I f o r the s i g n i f i c a n c e o f t h i s  cost item.  P l a n t S e r v i c e Cost and O i l and G r e a s e Cost: P l a n t s e r v i c e c o s t appears to b e a l m o s t a f i x e d c o s t i t e m o n G r a p h V , a n d i t i s t r e a t e d as a f i x e d c o s t i t e m i n the a n a l y s i s .  The oil  and g r e a s e cost (labour and m a t e r i a l ) on G r a p h V I appearsto be  slightly  m o r e v a r i a b l e w i t h the p r o d u c t i o n . number of purposes  T h e o i l and g r e a s e a r e u s e d for a  a m o n g w h i c h i s to l u b r i c a t e the m a c h i n e s .  It i s  j u d g e d t h a t 5 % o f t h i s c o s t i t e m i n 1 9 6 6 c o n s t i t u t e d the v a r i a b l e p o r t i o n . Again,  t h i s c o s t i s c h a r g e d to the p r o c e s s  c e n t r e as b y the  accounting  department.  C o s t of F o r k l i f t  Truck  Service:  F o r k l i f t c o s t ( l a b o u r a n d p o w e r ) a p p e a r s q u i t e c l e a r l y as a variable cost i t e m i n G r a p h VII.  T h e A p r i l figures  a p p e a r to b e q u i t e  120  GRAPH V 3/6 "  MILL  TOTAL  /Ji'OO  FINISHES PLywoot PANEL  OUTPUT  fl-flNT SERMICE COST  l/ooo  tooo  Sooo  Jooo 3000  Julifc  /  » i7 r  J4»'.7  JU'U  fct'M  "W7 seoitcE:  */*!'« COMMIT  K  SmtMsiiT*, FituKEs J>is&uise» .  fl^'M  G R A P H VI it* MILL TOTAL  (3000  1*000 J  FINISHES PAHEL  ?H^DOI> 6UTPUT  OIL ^ 4REASE. 6PST  fOOB J  goto  If 000  iooo 3000  S o u R c e : C o n p n w g K ST*T6ME<ITJ, F i s u R e s »IS»UI«£I> JiUfc  Jin'w  J«t'«  F«fc'<7  flp'tT  I*''*/  ftt^  rJ«v'^  Mw)i<  fUjit  123  out o f l i n e .  T h i s i s l i k e l y to h a v e b e e n c a u s e d b y u n u s u a l  circumstances.  F o r k l i f t t r u c k s a r e u s e d to c a r r y v e n e e r a n d p l y w o o d p a n e l s f r o m one p r o c e s s forklift service  s t a t i o n to a n o t h e r .  It i s t h e r e f o r e e x p e c t e d  that  c o s t w i l l v a r y w i t h the v o l u m e o f p r o d u c t i o n .  F o r k l i f t c o s t i s t h e r e f o r e t r e a t e d as a v a r i a b l e c o s t i t e m i n the L . P .  analysis.  It i s p r o r a t e d to the p r o c e s s  the f o r k l i f t t r u c k s a r e a s s i g n e d to the w o r k s t a t i o n s .  c e n t r e s i n the See  way  Tables  XII a n d X I I I .  Direct Production Material Cost: T h e s e c o s t i t e m s i n c l u d e the v a r i o u s k i n d s o f m a t e r i a l ( o t h e r t h a n the wood) u s e d at v a r i o u s s t a g e s of the p r o d u c t i o n p r o c e s s . i m p o r t a n t i t e m s a r e the ' p l a s t i c w o o d ' ( a k i n d o f p a t c h i n g g l u e  The  used  to p a t c h s p l i t s o n the s u r f a c e of the p a n e l s at the P l a s t i c P a t c h i n g p r o c e s s ) . t h e D a v i s P a t c h e s u s e d f o r D a v i s P a n e l r e c l a i m , the R a i m a n p a t c h i n g m a t e r i a l u s e d f o r v e n e e r p a t c h i n g a n d a l s o the s a n d i n g m a t e r i a l .  A g r a p h i c a n a l y s i s of the b e h a v i o r of t h e s e d i r e c t m a t e r i a l i t e m s as a g r o u p r e v e a l s no c l o s e r e l a t i o n s h i p b e t w e e n t h e s e c o s t i t e m s and p r o d u c t i o n . S e e G r a p h s V I L T - A a n d V L U - B .  T h e v a r i a b l e na t ure of  the a b o v e d i r e c t m a t e r i a l i t e m s w a s n o t r e v e a l e d i n the a n a l y s i s p a r t l y b e c a u s e of the i n a d e q u a t e m e a s u r e o f the l e v e l o f a c t i v i t y . different grades of panels and v e n e e r As  a result,  F o r example,  r e q u i r e different amount of p a t c h i n g .  the c o n s u m p t i o n o f p a t c h i n g m a t e r i a l i s a f f e c t e d b y the  volume  124  T A B L E XI11  T H E R E L A T I V E SIGNIFICANCE VARIOUS COST (BY C O S T  O FT H E  ITEMS  CENTRES)  A s % of D i r e c t P r o d u c t i o n L a b o u r C o s t  Direct  G r e e n Dry-  Veneer P r e s s  Panel  End  Pro-  Finish-  cess-  cess-  ing  ing  ing  End  Production  Labour Direct  Boom Pro-  100  100  100  100  100  100  Maintenance  - Labour  35.70  0.90  7.50  4.80  5.60  8.0  - Material  53.20  0.60  2.90  1.70  8.90  10.8  E l e c t r i c a l - power  12.60  0.52  7.90  3.70  4.10  4.4  F o r k l i f t ( l a b o u r & fuel)  27.53  7.40  8.80  10.40  11.50  32.0  Water  -  0.035  0.110  0.037  0.042  0.012  O i l & G r e a s e (labour & material)  3.75  2.91  2.58  0.18  1.32  0.33  25.13  4.80  0.42  5.30  6.44  18.20  Direct Production Material  125 GRAPH  AT  VIII-A  DRYERS  PRODUCTION UUE-L >IRetT PRODUCTION M l r e R i f l L COST  \ZODO  1060  -Soo  SOURCE:  J u l U  let'u  W M  J u n ' t ;  F < b ' 4 7  CfiM'M*)  flp'"  K STATEMENTS,  H a r i /  FI<kU,r?6S  N o v ' * * " 6 c t < 4  DIS6UIS6J>  MR^'W S*fn> flujifc  126 GRAPH  AT  VIII-B  PRESS  Hi llfooe  PRODUCTION  Ijmo  Uu£L DIRECT  PROiUCTmM  PI ATEftfftL  COST  izooo  I [too  31700  10000  2110  ftoo  two  -f090 J  S o u r c e : Conrttui k irftrtMsufi,  booo J « l M '  Hac'u  J u » «  JV.T  F * b ' * 7  ff'<T  M w ' < 7  f m u R C r Jis«uit«.»  A**'* 1  ^  of output as w e l l as the m i x o f the output.  In f a c t ,  s o m e of t h e s e  d i r e c t m a t e r i a l i t e m s m a y b e t r a c e d d i r e c t l y to the i n d i v i d u a l p r o d u c t a n d so t h e y m a y v a r y d i r e c t l y w i t h the v o l u m e o f output o f the p r o d u c t .  However,  f o r the p u r p o s e o f the L . P .  analysis,  it m a y  b e c o n v e n i e n t a n d q u i t e r e a s o n a b l e to a s s u m e that the s i z e o f t h e s e c o s t i t e m s v a r i e s w i t h the l e n g t h o f t i m e f o r w h i c h the p r o c e s s  centres  a r e o p e r a t e d a n d t h a t the c o s t m a y b e a l l o c a t e d to the i n d i v i d u a l p r o d u c t o n the b a s i s o f the m a c h i n e t i m e u s e d .  In the L . P .  analysis,  i t i s c o n s i d e r e d r e a s o n a b l e to t r e a t the  above mentioned four d i r e c t m a t e r i a l items  as v a r i a b l e c o s t i t e m s  a n d to t r e a t o n l y 20% o f the c o s t o f a l l o t h e r r e m a i n i n g i t e m s i n as v a r i a b l e .  1966  S e e T a b l e s X I I a n d XLII.  S u m m a r y of P r o c e s s  Costs  T a b l e X1TI p r e s e n t s t h e r e l a t i v e s i g n i f i c a n c e o f the v a r i o u s categories 1966.  o f c o s t as e x p e r i e n c e d at the d i f f e r e n t p r o c e s s  centres  in  T h i s p a t t e r n o f r e l a t i o n s h i p m i g h t b e d e t e r m i n e d b y the m a n u -  f a c t u r i n g p r o c e s s i t s e l f a n d a l s o b y the p e r u n i t c o s t o f the v a r i o u s f a c t o r s of p r o d u c t i o n .  In the L . P .  b o t h the m a n u f a c t u r i n g p r o c e s s  analysis,  the m o d e l a s s u m e d t h a t  a n d the p e r u n i t c o s t o f t h e  factors  of p r o d u c t i o n r e l a t i v e to o n e a n o t h e r as e x p e r i e n c e d i n 1966 a r e a p p l i c a b l e i n 1967.  F r o m T a b l e s X I I a n d XIII,  T a b l e X I V was  d e v e l o p e d to e x p r e s s the r e l a t i o n s h i p s a m o n g the d i f f e r e n t of v a r i a b l e p r o c e s s  costs.  also  categories  128 TABLE XIV  T H E RELATIONSHIP A M O N G VARIOUS PROCESS COST (BY P R O C E S S  VARIABLE  ITEMS  CENTRES)  A s % of D i r e c t P r o d u c t i o n L a b o u r C o s t  Direct  Boom  G r e e n Dry-  Veneer Press  Panel  Pro-  End  Pro-  Finish-  cess-  cess-  ing  ing  ing  Production  Labour Direct  End  100  100  100  100  100  100  Maintenance 3.57  0.09  0.75  0.48  0.56  0.>80  5.32  0.06  0.29  0.17  0.89  1.08  1.26  0.05  0.79  0.37  0.41  0.44  F o r k l i f t - L a b o u r tk F u e l 27. 53  7.40  8.80  10.40  11.50  32.00  Water  0.002  0.005  0.002  0.002  0.001  145  129  009  .066  .016  - Labour - Material E l e c t r i c a l - power  O i l and G r e a s e -Labour & Material  187  Direct Production M a t e r i a l (excluding logs a n d glue)  5.03  0.96  0.08  3.19  1.28  18.01  129  T a b l e X V p r e s e n t s the c o m p u t e d v a r i a b l e p r o d u c t i o n p r o c e s s c o s t u s e d i n the L . P .  analysis.  f o r e a c h o f the p r o c e s s  T h e direct production labour cost  c e n t r e s i s c o m p u t e d b y the n u m b e r of m e n  e n g a g e d a n d the c o n t r a c t e d w a g e r a t e s .  T h e r e s t of the c o s t i t e m s  a r e c o m p u t e d a c c o r d i n g to the r e l a t i o n s h i p t h e y b e a r w i t h the d i r e c t p r o d u c t i o n l a b o u r c o s t as s h o w n i n T a b l e X I V . on T a b l e X V are working time  c o m p u t e d f o r the ' a v e r a g e '  T h e c o s t s as.,  shown  shift o f 7:10 h o u r s of  each.  Other Production Costs O t h e r p r o d u c t i o n c o s t i t e m s not p r o g r a m m e d f o r i n the L . P . analysis  are listed in Table X V I .  T h e y a r e e x c l u d e d b e c a u s e t h e y do  n o t v a r y w i t h the l e v e l of p r o d u c t i o n o r b e c a u s e o f t h e i r In t o t a l ,  insignificance.  t h e y c o n s t i t u t e d 9- 6% o f the t o t a l p r o d u c t i o n c o s t o r 44% o f  the d i r e c t p r o d u c t i o n l a b o u r c o s t i n  1966.  Other Operating Costs O t h e r o p e r a t i n g c o s t s not p r o g r a m m e d f o r i n the include g e n e r a l a d m i n i s t r a t i o n cost,  analysis  s e l l i n g c o s t a n d the c o s t o f  o p e r a t i n g the s h i p p i n g d e p a r t m e n t . T h e y a r e e x c l u d e d f o r v a r i o u s reasons.  The administrative cost is essentially  fixed i n nature.  The  c o s t of s e l l i n g i s d e e m e d to be the s a m e f o r e v e r y t y p e o f p l y w o o d p a n e l a n d the c u s t o m e r s  a r e c h a r g e d at F . O . B .  The activities  the s h i p p i n g d e p a r t m e n t i s l a r g e l y a d m i n i s t r a t i v e i n n a t u r e .  of  Of course  a l l t h e s e c o s t s h a v e a l s o to b e c o v e r e d i f the m i l l i s to s t a y i n p r o d u c t i o n  TABLE XV VARIABLE PRODUCTION PROCESS (per  ' a v e r a g e shift  1  of 7 h o u r s  COSTS  10 m i n u t e s w o r k i n g t i m e each)  Green End  Veneer  Boom Pro-  Direct Production Labour F o r k - l i f t L a b o u r &c F u e l Direct  Part 1  Processing  DryPremier  Merritt  cessing  Lathe  Lathe  198. 68  470.52  268. 79  54. 71  34. 82  19. 89  0. 42  End  Edge-  Raiman  Glue 85  496. 23  4 1 . 41  26. 50  51. 61  0. 25  3. 53  1. 22  2. 38  0. 28  0. 16  1. 36  0. 43  0. 84  0. 24  0. 14  3. 71  0. 84  1. 83  0. 68  0. 39  0. 61  0. 02  0. 06  470.  63  254.  Maintenance  - Labour  7. 09  - Material  10. 57  Electric Power  2. 50  Oil & Grease - Labour & Material  0. 37 . 008  Water  . 004  . 026  . 004  .010  Direct Production Material ( e x c l u d i n g l o g s & glue) TOTAL C o s t p e r 10 m a c h i n e  o  7. 77 281.70  hour  0. 39  1. 33  7. 01  292.53  511. 74  284.29  561.07  408.18  178. 51  198. 35  48.93  4. 51  2.91  511.48 713.66  TABLE XV VARIABLE PRODUCTION PROCESS (per  'average  1  s h i f t of 7 h o u r s  Trim-  Part 2  10 m i n u t e s w o r k i n g t i m e e a c h ) Panel  Presses  COSTS  Sandei  Saw  Finishing  Plastic  Davis  Patch  Patch  Grading  Direct Production Labour  897.  83  47. 23  99. 62  95. 59  95.99  142.88  Fork-lift Labour h Fuel  103. 25  15. 11  31. 88  30. 59  30. 72  45. 72  5. 03  0. 38  0. 80  0. 76  0. 77  7.99  0. 51  1. 08  1. 03  1. 04  1. 14 1. 54  3. 68  0. 21  0. 43  0. 42  0. 63  Direct  Maintenance  -  Labour  -  Material  Electric  Power  0. 42  O i l and G r e a s e s - Labour & Material  0. 09  Water  018  008  016  000  001  . 015 . 001  .015  .023  .001  .001  Direct Production Material ( e x c l u d i n g l o g s & glue) TOTAL C o s t per 10-machine hour  04  2. 94  1. 84  1. 20  0. 13  44  63.48  136.77  130. 25  132.07  191.68  478. 81  88. 58  190. 84  90. 81  61.43  267.46  11.55 1029.  NOTE  TO T A B L E X V  T h e c o s t of o p e r a t i n g the C o e L a t h e i n p e e l i n g c o r e b l o c k s f o r c o r e v e n e e r is i n c l u d e d i n the c o s t c h a r g e d to the o t h e r two l a t h e s .  T h e c o s t of o p e r a t i n g the S t r i p a n d P a t c h . Icutter,  a n d S t o c k R u s t l i n g i s t r e a t e d as p a r t of  the c o s t of o p e r a t i n g the R a i m a n P a t c h e r s .  V e n e e r Salvage (Reclip) is included i n veneer  edge-glueing.  T h e c o s t of o p e r a t i n g the D r u m S a n d e r a n d the B e l t S a n d e r - H y d r a s t r o k e is i n c l u d e d i n the c o s t of o p e r a t i n g the S m i t h w a y S a n d e r .  T h e c o s t of o p e r a t i n g the J e n k i n S a w i s  i n c l u d e d as a p a r t of the c o s t of p r o d u c i n g p l y w o o d p a n e l s .  not  133  T A B L E XVI  O T H E R P R O D U C T I O N C O S T I T E M S (1966)  Production  Overhead  Supervision  -  labour  -  (L)  others  XX  - M a t e r i a l (M)  XX  - (M)  XX  Safety - (L)  XX  (M)  Plant Service Maintenance  XX XX  F i r s t A i d - (L)  -  XX XX  B o i l e r House - (L)  - (M)  XX  Overhead  S u p e r v i s i o n - (L)  XX  E l e c t r i c a l - (L)  XX  - (M)  XX  W a t e r - (L)  XX  - (M)  XX  B o i l e r House - (L)  XX  - (M)  XX  B a r k Hog S y s t e m - (L)  XX  - (M)  XX  A i r E q u i p m e n t - (L)  XX  - (M) Building,  (Part  XX  r o a d s & grounds - (L) - (M)  XX XX  Dust B l o w e r - (L)  XX  - (M)  XX  Machine-Shop Equipment R e p a i r s & T o o l s - (L)  XX  - (M)  XX  Miscellaneous  Materials &  Supplies - (L)  XX  - (M)  XX  XXX  134 TABLE XVI O T H E R P R O D U C T I O N C O S T I T E M S (1966)  F o r k l i f t - (L)  XX  - (M)  XX  C l e a n e r s & S w e e p e r s - (L)  XX  - (M)  XX  P l a n t S e r v i c e s - (L)  ( P a r t 2)  XX  - (M)  XX  S p e c i a l M a i n t e n a n c e - (L) - (M)  XX XX  XXX  Other Overhead C a r t a g e In - (M)  XX  Taxes Other Than Income  XX  Plant Insurance  XX  Plant Depreciation  XX  S h i p p i n g - (L)  XX  GRAND TOTAL As  % of T o t a l P r o d u c t i o n C o s t s  As  % of T o t a l D i r e c t P r o d u c t i o n Labour Costs  XXX XXXX 9. 65  44.3  135  at a l l i n the l o n g r u n .  Inputed C o s t The veneer  a n d the p a n e l i n v e n t o r i e s  do not n e e d a n y s p e c i a l  t y p e of s t o r a g e o t h e r t h a n s h e l t e r f r o m the r a i n a n d f r o m u n a u t h o r i z e d removal.  It i s t h o u g h t that o n l y the f i n a n c i a l c o s t a n d the l o s s  d a m a g e i n s t o r a g e n e e d b e c o n s i d e r e d i n the a n a l y s i s . panel inventory  from  The closing  i s c h a r g e d t h i s c a r r y i n g c o s t as a p e r c e n t a g e of the  c o s t o f the p a n e l s f o r the a n t i c i p a t e d l e n g t h of t i m e i n i n v e n t o r y .  M a c h i n e - t i m e Consumption Studies: A s has been m e n t i o n e d on page  104  the p u r p o s e o f  m e a s u r i n g the l e n g t h o f m a c h i n e - t i m e that e a c h o p e r a t i o n t a k e s i s two-fold.  Firstly,  i t i s u s e d f o r c a l c u l a t i n g the p r o c e s s  c o s t to b e  a l l o c a t e d to e a c h o p e r a t i o n i n the m a n u f a c t u r i n g p r o c e s s .  Secondly,  i t i s f o r m e a s u r i n g the c a p a c i t y o f the p r o c e s s  centres.  L o g P e e l i n g - T i m e Study: T h e two l a t h e s o p e r a t e d b y the c o m p a n y a r e t r e a t e d as a s i n g l e o p e r a t i n g u n i t i n the L . P . a n a l y s i s .  H o w e v e r , t h i s d o e s not m e a n  t h a t no r e c o g n i t i o n i s g i v e n to s o m e of the d i s t i n c t d i f f e r e n c e s the two  between  lathes.  T h e P r e m i e r l a t h e c a n p e e l l o g s up to a l e n g t h o f 10 f e e t e a c h . With its m u l t i p l e - t r a y s y s t e m ,  the P r e m i e r l a t h e c a n p e e l l a r g e  136  d i a m e t e r logs (thus,  u s u a l l y high grade logs) faster  t h a n the s m a l l e r  M e r r i t t lathe.  F o r the L . P .  a n a l y s i s , the p e e l i n g o f l o g s f o r 10 foot v e n e e r  l i m i t e d to the P r e m i e r l a t h e . the l o g s ,  is  F o r c o m p u t i n g the l a t h e t i m e f o r p e e l i n g  the u s u a l a s s i g n m e n t o f the two l a t h e s to the v a r i o u s g r a d e s  and s p e c i e s of logs i s a s s u m e d .  Douglas F i r P e e l e r s  a s s u m e d to b e p e e l e d b y the P r e m i e r l a t h e o n l y .  #1,  2, 3 a r e  P e e l e r #4 a n d l o w e r  a n d the o t h e r s p e c i e s a r e a s s u m e d to b e p e e l e d b y b o t h l a t h e s , i n the v o l u m e r a t i o o f 1 : 2. 5, P r e m i e r to M e r r i t t .  Table X V I I is computed p a r t l y f r o m actual t i m e - r e a d i n g s taken d u r i n g the v e n e e r - r e c o v e r y study test r u n s ,  and p a r t l y from deduction  and p a r t l y f r o m c o m p a n y e x p e r i e n c e .  A m o r e a c c u r a t e a p p r o a c h i n t r e a t i n g the c o n s u m p t i o n o f the l a t h e - t i m e i s to m e a s u r e the t i m e t a k e n b y e a c h o f the two i n p e e l i n g e a c h of the g r a d e s a n d s p e c i e s o f l o g s .  T h e n , the L . . P .  m o d e l i t s e l f c a n b e u s e d to s e l e c t the b e s t l a t h e a s s i g n m e n t , into account lathe capacities and v e n e e r r e q u i r e m e n t s . t h o u g h t not w o r t h w h i l e to do so at t h i s  lathes  taking  H o w e v e r , it i s  stage.  V e n e e r D r y i n g - T i m e Study: F o r s i m i l a r r e a s o n s , the f o u r d r y e r s i n the m i l l a r e t r e a t e d as a s i n g l e o p e r a t i n g u n i t i n the a n a l y s i s .  F r o m e x p e r i e n c e , c e r t a i n o f the  d r y e r s i s f o u n d to b e m o r e e f f i c i e n t f o r d r y i n g one c a t e g o r y o f v e n e e r  137 T A B L E XV11  LOG-PEELING  TIME  ( p e r 10 000 F B M of l o g s ) 3  T i m e i n u n i t s of 10 - h o u r - l a t h e - t i m e 8 Thickness  . 104'  Using  Species  Premier L a t h e Only  Fir  10 -  FOOT  Grade &  each  FOOT  Using  Premier  or M e r r -  Premier  or  itt(l:25)  L a t h e O n l y itt( 1:2-5)  Premier  0.15207  0.13382  Merr-  Peeler#l . 130  11  0. 13512  . 104  Fir  0. 17500  0.11891 0.15400  Peeler#2 . 130  11  0.14120  0.12426  . 104  Fir  0.15290  0.13454  0. 13145  0.11568  Peeler#3 . 130  11  . 104'  Fir  0.21799  0.17580  0.18205  0.14341  o.23991  0.20262  0.20591  0.17394  0. 19945  0.15729  0.17491 0.09964 0.11813  0.14341 0.07402 0.09252  0.21419  0.18319  0.13317  0.11473  0.09883  0.07402  0.09664  0.07217  Peeler#4 . 130 . 104  F i r S. F . P . -  . 130'  II  F i r Sawl o g #2  . 104 . 130  II  . 171  II  . 171  F i r Saw-  . 130  Interior  l o g #3 Fir 11  . 171  Hemlock  . 171  Balsam Mix Spruce M i x -  . 171" NOTE:  1)  Downtime allowe:  P r e m i e r L a t h e , 4.9% U 9 6 6 , Merritt Lathe,  2)  9. 7%  A u g & Sept.  )experience  T i m e f o r 10-ft l o g s c o m p u t e d f r o m that f o r 8 - f t l o g s . m a t e d for 10-ft,  Esti-  1. 25 t i m e s l e s s c u t t i n g - l e n g t h to c u t t h r o u g h  but at a l o w e r e f f i c i e n c e of 0. 9 t i m e that f o r 8 - f t l o g s .  138  t h a n a n o t h e r , b e c a u s e o f the d i f f e r e n c e i n the s e t - u p a n d the l e n g t h o f the d r y e r s .  A p a t t e r n o f a l l o c a t i n g the v a r i o u s c l a s s e s o f v e n e e r to  the d r y e r s h a s b e e n e s t a b l i s h e d i n the c o m p a n y .  A n d t h i s p a t t e r n of  a l l o c a t i o n i s c o n s i d e r e d v e r y c l o s e to the o p t i m u m .  T h i s p a t t e r n of  a l l o c a t i o n i s a s s u m e d i n c o m p u t i n g the d r y i n g t i m e o f the  veneer.  The t i m e r e q u i r e d for drying veneer is computed f r o m a sample study of actual d r y i n g t i m e o v e r a p e r i o d of t i m e . b y the c o m p a n y .  T h i s study was  A n a d j u s t m e n t i s m a d e to a c c o m m o d a t e the  c h a n g e o f e f f i c i e n c y e f f e c t e d a f t e r the t i m e s t u d y w a s m a d e .  made  slight Table XVIII  i s c o m p u t e d f r o m t h i s t i m e s t u d y a n d the v e n e e r r e c o v e r y d a t a f r o m Table X .  T a b l e X I X i s a l s o c o m p u t e d f r o m the t i m e s t u d y a n d a n  e s t i m a t e o f the v e n e e r k i n d ( s h e e t o r r a n d o m w i d t h , s a p w o o d o r h e a r t wood) t h a t m a k e u p the v a r i o u s v e n e e r g r a d e s r e c o v e r e d at the p r e s s . T h e r e i s s i m p l y no e x a c t w a y to d e t e r m i n e the c o m p o s i t i o n o f the  veneer  g r a d e s at the p r e s s u n l e s s the k i n d s o f l o g s p e e l e d h a v e a l r e a d y b e e n determined.  F o r the L . P .  analysis,  the e s t i m a t e o f the  veneer  c o m p o s i t i o n i s b a s e d o n the r e s u l t s o f the v e n e e r - r e c o v e r y t e s t r u n a n d a n a s s u m p t i o n t h a t the v e n e e r i n v e n t o r i e s a r e d e r i v e d f r o m p e e l i n g a l o g - g r a d e c o m b i n a t i o n e q u a l to that of the l o g s u p p l i e s f o r the p e r i o d .  "Veneer P a t c h i n g - T i m e S t u d y : T h e a v e r a g e r a t e of p a t c h i n g v e n e e r p e r p a t c h e r - h o u r i s e s t i m a t e d at 2, 100 s q . f t . f o r '#2'  grade veneer.  f o r " P a t c h ' g r a d e v e n e e r a n d 2,000 s q .  ft.  T h e s e r a t e s a r e j u d g e d to b e r e p r e s e n t a t i v e  from  139 T A B L E XVI11 V E N E E R DRYING  (per  TIME  10,000 F B M of l o g s )  T i m e i n u n i t s of 1 0 - h o u r - d r y e r - t i m e  Thickness Species  Grade  104" 130" 104" 130" 104" 130" 104" 130 " 104" 130" 104" 130" 171" 171" 130" 171" 171" 171" 104"  Peeler#l  D.  FIR  11  II  D.  FIR II  D.  II  FIR II  D.  FIR FIR FIR  S a w l o g #2 11  it FIR FIR  ti  S.F.P.  ti  ti it D. D.  P e e l e r #4 11  ti D.  Peeler#3 II  it D.  Peeler#2  S a w l o g #3 Interior F i r  ti  Hemlock- Balsam M i x Spr u c e Mix D. FIR Purchased  each  8-foot Veneer Drying time  10-foot Veneer Drying time  0. 47187 0. 42569 0. 48836 0. 40843 0. 56553 0. 46435 0. 53358 0. 46635 0. 59996 0. 57046 0. 50332 0. 40609 0. 32581 0. 32432 0. 44073 0. 33181 0. 36130 0. 35861 0. 74552  0. 45300 0. 40866 0. 46883 0. 39210 0. 54291 0. 44578 0. 51224 0. 44770 0. 57596 0. 54764 0. 48319 0. 38984 0. 31277 0. 31134 0. 34427 0. 31854 0. 34684 0. 42310 0. 71570  Veneer-AB Mix  130" NOTE:  it  11  0. 66713  0. 64044  1) T i m e f o r 10 ft. v e n e e r i s c o m p u t e d f r o m t h a t of 8-ft v e n e e r . E s t i m a t e d t h a t a 4' x 10' s h e e t t a k e s o n l y 1. 2 t i m e s l o n g e r t h a n a 4' x 8' s h e e t . 2) T i m e i n c l u d e s a l l o w a n c e f o r a v e r a g e d o w n - t i m e .  3) T i m e f o r p u r c h a s e d v e n e e r i s p e r c a r l o a d (50,000 s q . ft. 3/8").  140  TABLE X I X  V E N E E R DRYING (per  TIME  100 s h e e t s o r s h e e t - e q u i v a l e n t )  T i m e i n u n i t s of 1 0 - h o u r - d r y e r - t i m e 8 - FOOT  each 10 -  FOOT  Veneer Kind  104'  130"  171'  . 104'  130'  . 171"  0.01295  0.01510  0.01554  0.01812  B  0.01327  0.01530  0.;,01592  0.01835  B  0.01522  0.01653  0.01826  0.01984  C/F  0.01568  0.01684  0.01882  0.02021  U/L  0.01481  0.01625  0.01777  0.01950  B a c k s #1  0.01510  0.01650  0.01812  0.01980  Centres  0.01996  0.01998  0.01890  0.02395  0.02398  0.02269  C e n t r e s #1  0.01996  0.01998  0.01890  0.02395  0.02398  0.02269  Solid  141  experience  a n d f r o m a n e x a m i n a t i o n o f p a s t r e c o r d s o f the P a t c h e r s .  T a b l e X X i s c o m p u t e d f r o m the a v e r a g e r a t e s o f p a t c h i n g a n d the a m o u n t o f v e n e e r p a t c h e d f o r e a c h g r a d e o f l o g s as f r o m the v e n e e r - r e c o v e r y t e s t r u n . d i f f e r e n t l e v e l s of p a t c h i n g , o f '#2'  at '01'  determined  R e c o g n i t i o n i s g i v e n to the two a n d '02' l e v e l s .  The patching  v e n e e r g r a d e at '01' l e v e l i s a s s u m e d to t a k e h a l f as m u c h  t i m e as that at '02' l e v e l .  T a b l e X X I is c o m p u t e d with an a p p r o a c h  s i m i l a r to that u s e d f o r T a b l e X I X .  T h e p r o p o r t i o n o f the  g r a d e s r e c o v e r e d at the p r e s s t h a t r e q u i r e d patching i s f o r e a c h k i n d o f l o g s at the t e s t r u n .  Then,  veneer  determined  i t i s a s s u m e d t h a t the  v e n e e r i n v e n t o r i e s a r e d e r i v e d f r o m p e e l i n g a c o m b i n a t i o n of l o g g r a d e s e q u i v a l e n t to the l o g s u p p l i e s f o r the p e r i o d .  V e n e e r E d g e - g l u i n g - T i m e Study: V e n e e r e d g e - g l u i n g t i m e i s c o m p u t e d o n a n output r a t e o f 12,700 sq.  ft.  p e r h o u r w i t h b o t h the two e d g e - g l u i n g m a c h i n e s w o r k i n g  together.  It i s b e l i e v e d that the r a t e o f output d o e s not c h a n g e w i t h the  g r a d e o f the v e n e e r ,  the s p e c i e s a n d the t h i c k n e s s o f the  T a b l e X X I I i s b a s e d cn the a c t u a l a m o u n t o f v e n e e r  veneer.  edge-glued  as d e t e r m i n e d i n the t e s t r u n .  T a b l e X X I I I i s a g a i n c o m p u t e d b y the s a m e a p p r o a c h as that u s e d f o r T a b l e X I X a n d T a b l e X X I . T h e p r o p o r t i o n o f e a c h o f the g r a d e s at the p r e s s t h a t h a s to go t h r o u g h e d g e - g l u i n g i s  veneer  determined  TABLE XX VENEER PATCHING  (per  TIME  10,000 F B M o f l o g s p e e l e d ) ;  Part 1  T i m e i n units of 1 0 - p a t c h e r - h o u r s each  8-ft V e n e e r Patching  Up-grading Level  01 02 01 02 01 02 01 02 01 02 01 02 01 02 01 02 01 02 01 02  Thickness  . 104" it . 130" II  . 104" II  . 130" II  . 104" .  II  . 130" ti . 104" 11  . 130" II  . 104" 11  . 130" II  Species  Grades  D. F I R  P e e l e r #1  II  D. F I R II  D. F I R II  D. F I R  n D. F I R 11  D. F I R  ti D. F I R II  D. F I R 11  D. F I R II  D. F I R II  II  P e e l e r #1 II  P e e l e r #2  ti P e e l e r #2 II  P e e l e r #3 II  P e e l e r #3 11  P e e l e r #4  n P e e l e r #4 II  S. F . P . II  S. F . P . 11  Time  2. 683 2. 803 1,-987 2. 098 2. 428 2. 485 2. 136 2. 300 2. 976 3. 326 1. 709 2.201 1. 397 1.742 1. 221 1. 489 1. 510 2. 113 1. 352 1.924  10-ft  Veneer  Patching Time  2. 469 2. 578 1. 828 1. 930 2. 050 2. 213 1. 965 2. 116 2. 738 3. 060 1. 572 2. 025 1. 286 1. 603 1. 123 1. 370 1. 389 1. 944 1. 244 1. 771  TABLE XX VENEER PATCHING TIME ( p e r 10, 000 F B M o f l o g s p e e l e d )  Part 2  T i m e i n units of 1 0 ~ p a t c h e r - h o u r s e a c h  Up-grading Level  Thickness  01 02  . 104"  01 02  . 130"  ti  II  Species  Grades  D. F I R  Sawlogs  it  D. F I R  Sawlogs  10-ft V e n e e r  Patching  Patching  Time  Time  #2  1. 819 2.425  1.674 2. 231  #2  1. 296  1. 193  1. 785  1. 642  it  tt  it  8-ft V e n e e r  01 o r 02  . 171"  D. F I R  Sawlogs  #2  0. 719  0. 662  02  . 171"  D. F I R  Sawlogs  #3  0. 700  0. 644  01 02  . 130"  Interior F i r  1. 200  1. 104  1. 601  1.473  0. 710 0. 508  0.653  0. 603  0. 555  01 o r  01 o r 02  it  II  . 171"  Interior F i r  01 01  . 171"  Hemlock-Balsam  .171"  Spruce  02  . 104"  Veneer  A / B Mix  5. 062  4. 657  02  . 130"  Veneer  A  4. 125  3.795  Note:  1) F o r the d e f i n i t i o n o f u p - g r a d i n g l e v e l , s e e p a g e  Mix Mix / B Mix  0. 467  104.  2) T i m e i n c l u d e s a l l o w a n c e f o r d o w n - t i m e 3) T h e t i m e f o r 10-ft v e n e e r i s d e r i v e d f r o m t h a t f o r the 8-ft v e n e e r . E s t i m a t e d t h a t i t t a k e s 1. 15 t i m e s l o n g e r f o r the 10-ft v e n e e r p e r s h e e t . 4) P u r c h a s e d A / B M i x v e n e e r i n u n i t s o f c a r - l o a d s ( 5 0 , 0 0 0 s q . f t . 3 / 8 " e a c h ) .  OJ  144  T A B L E XXI V E N E E R PATCHING TIME (per ICO sheets or sheet-equivalent) 8-foot Veneer . 104" . 130"  171"  10-foot Veneer 104" 130" .171"  0. 0524  0.0524  0.0602  0.0602  0.1524  0.1524  0.1752  0.1752  0.1524  0.1524  0.1752  0.1752  C/F  0.1524  0. 1524  0.1752  0.1752  U/L  0.1537  0.1523  0. 1763  0. 1752  Bks #1  0. 0697  0.-754  0.0801  0.8669  Solid .': . Centres 0.0320  0.0330  0.0360  0.0368  0.0379  0.0414  Centres #1 0. 0349  0.0377  0.0195  0.0401  0.0433  0.0224  XB  0.0266  0. 0160  0.0306  0.0184  0  X C  0.0266  0.0160  0.0306  0.0184  0  B  l  0  Centres Hembal  0. 0%  0. 103  XC-Hembal -  0  0  CentresSpruce  0. 095  0. 109  X C-Spruce-  0  0  Note:  1) Time includes allowance for down-time.  145  TABLE XXn VENEER EDGE-GLUING  TIME Part 1  ( p e r 10, 000 F B M o f l o g s p e e l e d ) T i m e i n units of 1 0 - m a c h i n e - h o u r  Thickness  Species  Grade  104  D. F I R  Peeler  130  it  104  D. F I R  130  II  104  D. F I R  130  II  #1  it Peeler  #2  11  Peeler  #3  n  each  8-ft V e n e e r  10-ft  Veneer  Edge-gluing  Edge-gluing  Time  Time  0.2172  0. 1911  0.1825  0. 1606  0.1259  0.1108  0.1779  0. 1566  0. 1947  0. 1713  0. 1939  0. 1708  0.1325  0.1166  104  D. F I R  130  it  it  0.1544  0. 1358  104  D. F I R  S. F . P .  0.1019  0. 0896  130  II  ii  0. 0761  0. 0670  104  D. F I R  0.0543  0. 0478  0. 0984  0.0866  Peeler  #4  S a w l o g #2 n  130 171  D. F I R  S a w l o g #2  0  0  171  D. F I R  S a w l o g #3  0  0  146  TABLE  XXII  VENEER EDGE-GLUING TIME ( p e r 10, 000 F B M o f l o g s p e e l e d ) T i m e i n units of 1 0 - m a c h i n e - h o u r  Part 2  each  8-ft V e n e e r Edge-gluing Thickness  Species  130"  Interior  10-ft V e n e e r Edge-gluing  Grade  Time  Time  Fir  0.0446  0. 0392  0  0  171" 171"  Hemlock-Balsam Mix  0  0  171"  Spruce  0  0  Mix  . 104"  Purchased  & , 130"  Veneer  Note:  T h e edge-gluing t i m e i s c a l c u l a t e d f r o m a rate of  A  / B Mix  output o f 12, 700 s q . f t . / m a c h i n e h o u r .  It i s  a s s u m e d t h a t the g r a d e a n d the d i m e n s i o n o f the v e n e e r do not c h a n g e t h i s r a t e o f output. The  amount glued for each g r a d e of l o g i s  o b t a i n e d f r o m the t e s t r u n to g a t h e r d a t a o n veneer  recovery.  147  TABLE  XXHI  VENEER EDGE-GLUING TIME ( p e r 100 s h e e t s o r s h e e t - e q u i v a l e n t ) T i m e i n units of 1 0 - h o u r - m a c h i n e - t i m e each  8-foot V e n e e r  10-foot V e n e e r 130'  171'  0.0032  0.0028  0.0027  0.0035  0.0025  0.0040  0.0038  0. 0043  0.0096  0.0049  0.0110  0.0105  0.0009  0.0021  0.0010  0.0025  0.0023  0. 0027:  0.0027  0.0031  0.0031  0.0030  0.0036  0.0009  0  . 104"  . 130"  0.0028  0.0024  0.0022  C/F U/L  . 171"  ,104'  A B B  1  Bks  #1  Solid Centre  -  0  C e n t r e s #1  0  0 0  X B X C  0. 0032  0.0008  0  Hembal  0  Spruce  0  Note:  T i m e includes allowance for down-time.  at the t e s t r u n .  T h e v e n e e r i n v e n t o r i e s a r e a g a i n a s s u m e d to b e  d e r i v e d f r o m p e e l i n g a l o g - g r a d e c o m b i n a t i o n e q u i v a l e n t to the l o g s u p p l i e s a v a i l a b l e f o r the p e r i o d .  P a n e l L a y - u p and P a n e l - P r e s s i n g - T i m e Study: T h e p a n e l l a y - u p a n d the p a n e l - p r e s s i n g o p e r a t i o n s a r e t r e a t e d as a s i n g l e s t e p i n the p r o c e s s .  F o r the L . P . s t u d y , the t h r e e p r e s s e s  d i f f e r o n l y i n the n u m b e r o f p a n e l s e a c h o f t h e m c a n p r e s s at one r u n . T h e p r e s s t i m e i s c o m p u t e d as an a v e r a g e r a t e , w i t h the t h r e e p r e s s e s operating  together.  T a b l e X X I V i s b a s e d o n p r e s s i n s t r u c t i o n s i s s u e d to the p r e s s operators,  p l u s an a l l o w a n c e f o r d o w n - t i m e .  by technical considerations. t h i c k n e s s o f the p a n e l , w h e t h e r i t i s 8 ft.  and is  T h e time r e q u i r e d is  set  A s c a n b e s e e n , the t i m e v a r i e s w i t h the not a f f e c t e d b y the l e n g t h o f the p a n e l ,  o r 10 ft.  P a n e l F i n i s h i n g - T i m e Study: T h e t i m e r e q u i r e d f o r the v a r i o u s p a n e l f i n i s h i n g o p e r a t i o n s o n the 4'..x 8' p a n e l s a r e m e a s u r e d w i t h a s t o p - w a t c h .  It i s  estimated  f r o m c o m p a n y e x p e r i e n c e t h a t o n l y 40% o f t h e G 1 S a n d S I S p a n e l s t h r o u g h the P l a s t i c P a t c h i n g o p e r a t i o n ;  5. 6 % o f a l l the s a n d e d g r a d e s  go t h r o u g h D a v i s R e c l a i m a n d o n l y 5 % o f the s h e a t h i n g s f o r m g r a d e s do s o .  See T a b l e X X V .  go  and C e m e n t -  149  T A B L E XXIV P A N E L PRESS T I M E (per 250 panels) *  Part 1  Time i n units of 10-machine-hour each Panel Grade  Sanded  Final Panel Thickness 1/4" 3/8" 1/2" 5/8" 5/8" 3/4" 7/8" 7/8" 1" 1 1/8" 1 1/8" 1 1/4"  Number of plies per panel 3 3 5 5 7 7 7 9 9 9 11 11  Panels /load (3 presses working together) 136 136 68 68 68 68 68 68 68 68 68 68  Press Time per 250 panels 0.05643 0.08062 0.12255 0.14189 0. 15641 0. 17092 0. 19994 0. 19994 0.25800 0. 29669 0. 29669 0.34506  .150  T A B L E XXIV P A N E L PRESS T I M E (per 250 panels)  Panel •Grade  Unsanded  Note:  Final Panel Thickness  5/16" 3/8" 7/16" 1/2" 5/8" 11/16" 11/16" 3/4" 3/4" 7/8" 1" 1" 1 1/8" 1 1/4" 1 1/4" 1 5/16"  Part 2  Number of plies per panel  Panels /load (3 presses working together  Press Time per 250 panels  3 3 3 5 5 5 7 5 7 7 7 9 9 9 11 11  136 136 136 68 68 68 68 68 68 68 68 68 68 68 68 68  0.05643 0.06853 0.08304 0. 11287 0. 13222 0.14321 0.16124 0.15641 0.16124 0.18059 0.20962 0. 21929 0.26766 0.30636 0.30636 0. 32571  A charge time of 1 minute 20 seconds is allowed for each lead. A slack time of 5% of effective working time i s also allowed.  151  TABLE XXV  P A N E L FINISHING T I M E ( p e r 250 p a n e l s ) T i m e i n units of 1 0 - h o u r - m a c h i n e - t i m e  MG,  G2S  G/Sol,  G/Sel  each  GIS,  Sh-Sel  SIS  C/F  Sh-Std  S2S x 8' Panel  Trimming  0.02242  0.02242  0.04751  0.02830  0.04430  0.02639  0. 07891  0.03613  0.02816 0.04361  0. 02242  0.02242  0.02816  0.02400  0.00480  0.02600  0.02749  0. 02749  0.02447  0.02447  0.02447  0.02447  Rough Sanding  0.05227  0.03113  F i n a l Sanding  0.04873  0.02548  Rough Sanding ( S m i t h way) F i n a l Sanding ( S m i t h way) Plastic Davis  Patching Patching  Grading  4' x 10' Panel  Trimming  Plastic Davis  Patching Patching  Grading  Note:  1)  Down-time  0;11810  0.05408  0.04035  0.04035  0.03600  0.00720  0.04797  0.02858  0.03024  0.03024  a l l o w e d as f o l l o w s : % o f e f f e c t i v e w o r k i n g t i m e P a n e l T r i m m i n g - 3.5%  2)  Sander  - 5%  Plastic Patching  -5%  Davis Patching  - 4. 5%  Grading  - 3. 5%  T i m e f o r 4' x 10' p a n e l s i s m o s t l y e s t i m a t e d f r o m t h a t o f 4' x 8' p a n e l s .  152  Panel Structure Alternatives: W i t h the t h r e e g i v e n t h i c k n e s s o f the v e n e e r o f . 104", and  .171",  . 130"  t h e r e a r e m a n y a l t e r n a t i v e ways of c o n s t r u c t i n g a p l y w o o d  p a n e l t h a t w i l l m e e t the s p e c i f i c a t i o n r e q u i r e m e n t s o f the p a n e l . example,  s o m e s t r u c t u r e s involve a t r a d i n g of m o r e c o r e or  For  centre  veneer for l e s s of high quality face v e n e e r , others i n v o l v e a t r a d i n g of m o r e g l u e f o r the u s e o f a c h e a p e r s p e c i e s o f w o o d f o r i n n e r p l i e s . Yet  s o m e o t h e r s i n v o l v e a t r a d i n g o f an a d d i t i o n a l p l y ( w h i c h m e a n s  m o r e handling cost, As  m o r e g l u e c o s t , etc.) f o r a saving i n f a c e  veneer.  i t i s not p o s s i b l e to a s s i g n the j o i n t w o o d c o s t to the v a r i o u s  of v e n e e r , structure.  i t i s d e c i d e d to l e t the L . P .  grades  m o d e l s e l e c t the b e s t p a n e l  T h e i m p o r t a n t a l t e r n a t i v e s t r u c t u r e s as l i s t e d b y the  c o m p a n y a r e p r o g r a m m e d i n t o the m o d e l .  See T a b l e X X V I a n d a l s o  Appendix IV.  P r o v i s i o n f o r the d o w n - g r a d i n g o f s o m e g r a d e s o f v e n e e r i n t h e p a n e l c o n s t r u c t i o n i s a l s o m a d e b y p r o g r a m m i n g i t as p a n e l s t r u c t u r e s i n the m o d e l .  alternative  T h i s i s f o r the p u r p o s e o f m e e t i n g  s i t u a t i o n s w h e r e the l o g - g r a d e c o m b i n a t i o n at the l a t h e c a n n o t b e s u f f i c i e n t l y a d j u s t e d to p r o v i d e the r e q u i r e d v e n e e r g r a d e s o r w h e r e i t may  b e c h e a p e r to d o w n - g r a d e s o m e o f the v e n e e r t h a n to s w i t c h to  p e e l i n g another g r a d e of l o g s .  T a b l e X X V I a l s o p r e s e n t s the c o s t o f the g l u e u s e d i n c o n s t r u c t i n g the p a n e l s .  T h e g l u e c o s t i s c o m p u t e d f r o m the a m o u n t o f  153  TABLE  XXVI  PANEL STRUCTURE AND GLUE  ALTERNATIVES  ( p e r 250 p a n e l s ) No:  Veneer  Sanded  of  Grades  Plies  1/4" II  3/8" II  1/2"  3  ti  Part 1  COST. x 8'  Veneer  Veneer  for Face  for  for  & Back  Core  Centre  Glue  Cost  4' x 10' Glue  Cost  p e r 250  p e r 250  panels  panels  $  $  104  104  22.672  28.340  104  130  2 3 . 108  28.885 31. 610  3  130  171  25.288  tt  130  171  2 6 . 160  32.700  46. 216  57.770  5  104  104  . 171  II  it  104  104  59.950  II  104  130  , 171 B . 130  47. 960  ii  46.216  57.770  II  II  130  104  . 130  46. 216  57.770  5  104  171  . 171  48.832  61.040  II  II  104  171  64.310  I!  104  171  52.320  65.400  II  II  104  171  . 171 B . 171 B . 171  51.448  11  51.448  64.310  II  II  130  171  . 130  51.448  64.310 88. 290  5/8"  n 3/4"  II  7/8"  7  104  104  . 104  70.632  7  130  130  . 104  7 3 . 248  9 1 . 560  II  104  130  . 130  73.248  9 1 . 560  ti  104  104  . 171  73.248  9 1 . 560 94. 830 94.830  II  104  104  . 171 B  7 5 . 864  7  104  171  . 130  7 5 . 864  98.100  II  II  104  171  . 130  78.480  II  II  130  171  . 104  7 5 . 864  94. 830  II  II  130  171  . 104  78.480  98. 100  154  TABLE  XXVI  •PANEL STRUCTURE AND GLUE  ALTERNATIVES Part 2  COST  ( p e r 250 p a n e l s ) No: Sanded  of  Grades  -Plies  7/8" it  Veneer for  Face  & Back  Veneer for Core  4' x 8' Veneer for Centre  7  . 130"  . 130"  . 171'  II  . 130"  .130"  il71»  •B  Glue  Cost  4' x 10' Glue  Cost  p e r 250  p e r 250  panels  panels  $  $  78. 480  98.100  78. 480  98. 100 135.160 141.700  1"  9  . 104"  . 104"  . 171'  108.128  ti  it  . 104"  . 104"  . 171' 'B  . 130"  9  . 104"  . 171'  113.360 108. 128  it  II  . 104"  . 130"  . 171' 'B  113.360  135. 160 141.700  1 1/8" ti  it  . 130"  .. 171"  . 104'  108.128  135. 160  11  it  11  .171"B . 104"  . 104' . 130'  113.360  II  . 130" . 104"  141.700  141.700 177.125  1 1/4" II  1 1/4"  11  . 104"  . 104"  . 171'  II  , 104"  . 104"  . 171' »B  141.700 148.240  185.300  177.125  11  . 130"  . 130"  . 130»  148.240  185.300  155  XXVI  T A B L E  P A N E L  STRUCTURE AND  GLUE  (per 2 5 0 No: Unsanded Grades  of Plies  Veneer for  Face  & Back  ALTERNATIVES  panels)  Veneer for Core  5/16"  3  .  104"  . 104»  3/8" it  3 ti  .  104"  . 171'  .  104"  . 1 7 1 '' B  II  . 130"  . 130'  1/2"  5  .  104"  . 104'  5/8" ii  5  . 130"  II  .  II  .  5 n  11  n  n  II  7  .  104"  5 •  . 104"  it  11  3/4" it  ti 11/16 11  Part 3  COST  8' Veneer  Glue  for Centre  -  -  4' Cost  x 10'  Glue  Cost  per 2 5 0  per 2 5 0  panels  panels  $  $  22.672  28. 340  24.416  30.520  25.288  26. 332  23.544  29.430  . 104'  45.344  56.680  . 130'  . 130'  47.088  56.860  104"  . 171'  . 104'  48. 832  104"  . 1 7 1 '' B  . 104'  50.576  63. 220  . 130"  . 171»  . 171'  50.  576  63.220  . 130"  . 1 7 1 '' B  . 171'  52. 320  65.400  . 130"  . 1 7 1 '' B  . 1 7 1 '' B  52.320  65.400  . 130"  , 171'  . 1 7 1 '' B  52.320  63.220  . 104'  . 130'  70.632  88.290  . 171'  . 171'  48.832  61.040  .  61. 040  7  . 104"  . 104'  . 130'  70. 632  88.290  7  . 130"  . 130'  . 130'  73. 248  91. 560  II  II  . 104"  . 171'  . 104'  75.  94.830  II  11  : 104"  . 1 7 1 '' B  . 104'  78. 480  7/8"  1"  864  98.  100  7  . 130"  . 1 7 1 '' B  . 130'  86. 096  II  II  . 130"  . 171'  . 130'  78.480  II  11  . 104"  . 1 7 1 '' B  . 171» ' B  9  . 130"  . 130'  . 104'  113.360  141.700  9  . 130"  . 130'  . 130'  113.360  141.700  n 1 1/8"  81. 096  101.370 98.  100  101.370  156  TABLE  XXVI  PANEL STRUCTURE AND GLUE  ALTERNATIVES Part 4  COST  ( p e r 250 p a n e l s ) No:  Veneer  of  for  Grades  Plies  & Back  1 1/8"  9 ti  Unsanded  II  1 1/4" II  1 1/4"  Note:  Face  Veneer for  4' x 8' Veneer for  Glue Cost per  250  panels  4' x 10' Glue Cost per  250  panels  Core  Centre  . 104"  . 171"  . 104"  113.360  141.700  . 104"  .171"B  . 104"  118.592  148.240  9  . 130"  .171"B  . 130"  118.592  148.240  it  . 130"  . 171"  . 130"  113.360  141.700  11  . 130"  . 130"  . 104"  141. 700  177.125  $  " B " r e p r e s e n t s veneer of wood other than Douglas F i r .  $  -•157 g l u e r e q u i r e m e n t t e c h n i c a l l y s p e c i f i e d a n d the c o s t o f the g l u e to the company.  C o e f f i c i e n t s o f the O b j e c t i v e F u n c t i o n : Appendix V presents  a s a m p l e of the c o e f f i c i e n t s  o f the  f u n c t i o n a n d the c o m p o n e n t p a r t s o f e a c h o f the c o e f f i c i e n t s f o r the L . P .  analysis.  The process  computed  c o s t o f e a c h o f the a c t i v i t i e s  a r r i v e d at f r o m the c o s t o f o p e r a t i n g the p r o c e s s (see  objective  c e n t r e p e r unit of t i m e  T a b l e X V ) a n d the l e n g t h o f t i m e that e a c h o f the a c t i v i t i e s  take (see  T a b l e X V I I to T a b l e X X V . )  The b o o m process  is  H o w e v e r , t h e r e i s one  will  exception.  c o s t i s not a r r i v e d at w i t h the s a m e a p p r o a c h .  L a c k i n g a r e l i a b l e t i m e - s t u d y o f the b o o m - o p e r a t i o n ( i . e. p r e p a r i n g the l o g s f o r p e e l i n g ) the 1966 a v e r a g e v a r i a b l e p r o c e s s  cost per unit  v o l u m e o f output i s u s e d .  Process-Centre  Capacity:  T h e e s t i m a t e d n u m b e r o f w o r k i n g d a y s f o r the y e a r u n d e r p l a n n i n g i s 240,  b a s e d on a 5-day week.  The working hours available are  c o m p u t e d o n the b a s i s o f 21 1/2 w o r k i n g h o u r s p e r w o r k i n g d a y .  In the L . P .  a n a l y s i s the two l a t h e s , the f o u r d r y e r s , the t h r e e  p a n e l p r e s s e s a n d the p a n e l s a n d e r i n d i v i d u a l l y s e t the p r o d u c t i o n capacity limits.  T h e s e r e p r e s e n t the m a j o r p r o c e s s  Table XXVII capacity,  c e n t r e s i n the m i l l .  p r e s e n t s the c a p a c i t y c o n s t r a i n t s .  The dryer  as a n e x c e p t i o n , i s c o m p u t e d o n a 5 - d a y w e e k b a s i s p l u s h a v i n g  158  TABLE  PLANT  XXVII  CAPACITY  1967 ( i n u n i t s of 10 m a c h i n e - h o u r e a c h )  LATHE  1,032  DRYERS  2,136  PRESS  1,548  SANDER  516  Please Note: Error i n numbering the pages: Skipped from #158 to #163.  C H A P T E R VII  AN INTRODUCTION  T O T H E L P - H I I B M 7040/7044  COMPUTER  PROGRAM  T h i s b r i e f note a t t e m p t s to s u m m a r i z e s o m e of the outstanding features  of the p r o g r a m i n a s o m e w h a t n o n - t e c h n i c a l  44 language.  It a l s o a i m s to p o i n t out t h o s e c o m p u t a t i o n s w h i c h i n  the w r i t e r ' s o p i n i o n , a r e o f p a r t i c u l a r i n t e r e s t to the p l y w o o d industry. G e n e r a l F e a t u r e s of the  Program:  It i s a g e n e r a l p u r p o s e L . P . p r o g r a m , 7040 o r 7044 m a c h i n e .  r u n o n the I B M  O n a computer with a core storage  capacity  o f 32, 768 w o r d s ,  t h e p r o g r a m w i l l s o l v e p r o b l e m s w i t h as m a n y as  1, 024 r o w s ( i . e.  r e s o u r c e c o n s t r a i n t s p l u s the o b j e c t i v e f i n c t i o n row)  A c o r e s t o r a g e c a p a c i t y o f 16, 384 w o r d s w i l l a c c e p t p r o b l e m s w i t h a m a x i m u m o f 200 r o w s .  T h e n u m b e r of v a r i a b l e s  (representing  i n d i v i d u a l a c t i v i t i e s ) i n the p r o b l e m i s l i m i t e d b y the n u m b e r o f 44 I B M C o . h a s p r o v i d e d a u s e r m a n u a l o n the p r o g r a m .  n o n - z e r o e l e m e n t s that c a n b e s t o r e d o n a s i n g l e r e e l o f m a g n e t i c ( i . e.  a m a x i m u m o f 200, 000, d e p e n d i n g o n the m a t r i x d e n s i t y ) .  tape And  the r o w s a n d the c o l u m n s i n the m a t r i x o f the p r o b l e m a r e i d e n t i f i e d  b y n a m e s to b e s e t up b y the p r o g r a m u s e r .  The  45  p r o g r a m is c o m p o s e d of a n u m b e r of s u b - r o u t i n e s  s t o r e d i n b i n a r y f o r m o n u n i t S. S L B l .  E a c h sub-routine is called i n  o n l y w h e n i t i s d e s i r e d to b e e x e c u t e d .  T h e p r o g r a m u s e r h a s to  prepare Agendum cards,  one f o r e a c h s u b - r o u t i n e ,  s u b - r o u t i n e s he w a n t s e x e c u t e d .  to c a l l i n t h o s e  It i s the p o s s i b l e c h o i c e o f s u b -  r o u t i n e s that p r o v i d e s m u c h f l e x i b i l i t y f o r the p r o g r a m u s e r .  S e l e c t e d S u b - r o u t i n e s f r o m the L P - H I  System:  NORMAL T h i s s u b - r o u t i n e c o m p u t e s the o p t i m a l s o l u t i o n to the problem.  In t h e p l y w o o d p r o d u c t i o n p r o b l e m , i t  computes  - the one set o f p a n e l s to p r o d u c e - the one s e t o f l o g s to p e e l - a n d the one set o f p a n e l c o n s t r u c t i o n a l t e r n a t i v e s use,  so t h a t t o g e t h e r t h e y w i l l g i v e the g r e a t e s t p r o f i t to the  o p e r a t i n g w i t h the g i v e n r e s o u r c e s  to  business  and m a r k e t opportunities.  R e f e r to A p p e n d i x V I to s e e h o w the c h o i c e o f n a m e s w a s u s e d to i d e n t i f y the v a r i o u s a c t i v i t i e s i n the  business.  165  In a d d i t i o n , t h i s s u b - r o u t i n e a l s o c o m p u t e s ,  as a ' b y -  46 product',  the m a r g i n a l p r o f i t c o n t r i b u t i o n  market opportunities.  of e a c h o f the  resources/  T h e m a r g i n a l p r o f i t c o n t r i b u t i o n of a r e s o u r c e  i s the c h a n g e i n the v a l u e o f the t o t a l n e t p r o f i t ( o b j e c t i v e  function)  b r o u g h t about b y one u n i t i n c r e a s e o r d e c r e a s e i n the p r e s e n t of the r e s o u r c e ( w h i l e a l l o t h e r t h i n g s a r e b e s t a d a p t e d to for  the  size  accommodate  change). The  N O R M A L sub-routine represents,  c o m p u t a t i o n a l w o r k of the whole L . P . a n a l y s i s .  i n fact,  the m a j o r  T o a r r i v e at the  o p t i m a l s o l u t i o n m a y t a k e up as m u c h as 7 5% o f the t o t a l c o m p u t i n g time.  T h e r e s t o f the t i m e m a y b e s p e n t c o m p u t i n g a  sensitivity  a n a l y s i s on the o p t i m a l s o l u t i o n .  RHS.  RANGING T h i s p o s t - o p t i m a l a n a l y s i s a g a i n l i s t s out the m a r g i n a l  p r o f i t c o n t r i b u t i o n o f e a c h of the r e s o u r c e s / m a r k e t o p p o r t u n i t i e s ( r e p r e s e n t e d b y the r o w s i n the m a t r i x of the p r o b l e m ) as by N O R M A L .  computed  It a l s o c o m p u t e s the u p p e r l i m i t a n d the l o w e r l i m i t  of the s i z e o f e a c h o f the r e s o u r c e s / m a r k e t o p p o r t u n i t i e s w i t h i n w h i c h the g i v e n m e a s u r e o f the m a r g i n a l p r o f i t c o n t r i b u t i o n i s  S o m e p e o p l e c a l l it 'shadow p r i c e s ' o r 'shadow  cost'.  correct.  The analysis  s h o w s w h i c h of the v a r i a b l e s w i l l l e a v e the o p t i m a l  47 basis  w h e n the s i z e o f a n y one o f the r e s o u r c e s / m a r k e t  opportunities  a s s u m e s a v a l u e b e y o n d the c o m p u t e d l i m i t s . F o r example,  i t m a y t e l l u s that the t o t a l n e t p r o f i t o f  the b u s i n e s s w i l l c h a n g e b y $x f o r e v e r y u n i t c h a n g e i n the o f F i r P e e l e r #2 l o g s , 400 u n i t s .  as l o n g as the s u p p l y i s b e t w e e n 375 u n i t s a n d  A n d t h a t w h e n the s u p p l y e x c e e d s 400 u n i t s ,  b e s t to s t o p p e e l i n g P e e l e r #4, f a l l s b e l o w 37 5 u n i t s ,  supply  it w i l l be  a n d w h e n the s u p p l y of P e e l e r  #2  i t w i l l b e b e s t to s t o p p r o d u c i n g p a n e l A .  DO. D J This post optimal analysis  c o m p u t e s the d e c r e a s e i n  t o t a l n e t p r o f i t b y i n t r o d u c i n g one u n i t of a n o n - o p t i m a l v a r i a b l e into the b a s i s .  F o r example,  i t i s f o u n d o p t i m a l to u s e p a n e l c o n s t r u c t i o n  a l t e r n a t i v e X to l a y up p a n e l A , b u t not c o n s t r u c t i o n Y .  J  D O . DJ will  c o m p u t e the l o s s i n t o t a l net p r o f i t i f the c o m p a n y p r o d u c e s one u n i t of p a n e l A u s i n g Y .  However,  the s i z e of the l o s s of p r o f i t f r o m  p r o d u c i n g y e t a n o t h e r u n i t of p a n e l A u s i n g Y m i g h t b e  In L . P .  terminology,  different.  the o p t i m a l b a s i s r e f e r s to a s e l e c t e d set of  v a r i a b l e s ( w i t h a s s i g n e d p o s i t i v e v a l u e s ) w h i c h c o n s t i t u t e the p r o f i t a b l e p r o g r a m of a c t i v i t i e s  f o r the b u s i n e s s .  o p t i m a l b a s i s d o e s n o t m e r e l y m e a n a c h a n g e i n the v a l u e s to s o m e of t h e s e s e l e c t e d v a r i a b l e s .  It m e a n s the t o t a l  of one o f t h e s e v a r i a b l e s b y a n e w v a r i a b l e .  most  A c h a n g e i n the assigned  replacement  167  DO. P L P During this post-optimal analysis, the size of the resources/ market opportunities are progressively changed together at a defined rate relatively to one another, until a change i n the previous optimal basis i s necessary. A t this point, the new optimal basis and the new set of values of the resources/market opportunities may be printed out as desired.  Then the size of the resources and the  market opportunities are changed further until yet another new optimal basis is necessary. The relative rate at which the size of the individual resources/market opportunities are changed i s defined by the program user.  Some of the resources/market opportunities might be increased  while others might be decreased, while yet some others might be kept constant. The maximum (minimum) values to which the resources/market opportunities are changed to are also defined by the program user.  The maximum frequency i n printing out the  solutions is likewise defined. This sub-routine i n fact enables the user to obtain a series of optimal solution for various sets of values i n the resources /market 47 opportunities available to a business.  This i s achieved not by  47 If the change i n the resources/market opportunities situation constitutes a change i n the kind of resources /market opportunities rather new rows thanand just new a change variables) i n their has to size, be solved then aby new the problem N O R M A(with L routine.  168  s o l v i n g a w h o l e s e r i e s o f new p r o b l e m s b u t r a t h e r b y b u i l d i n g o n the s o l u t i o n to the o r i g i n a l p r o b l e m .  F o r example,  the  resources/  m a r k e t o p p o r t u n i t i e s s i t u a t i o n h a s c h a n g e d f r o m s i t u a t i o n (1) to s i t u a t i o n (2) as s h o w n b e l o w :  s i t u a t i o n (1)  s i t u a t i o n (2)  supply of logs: Peeler  #2  25 u n i t s  50 u n i t s  Peeler  #3  40 u n i t s  10 u n i t s  Panel A  30 u n i t s  60 u n i t s  Panel B  40 u n i t s  40 u n i t s  panel demand:  T h e D O . P L P r o u t i n e d o e s not j u s t c o m p u t e the o p t i m a l s o l u t i o n f o r the l o g s u p p l y / p a n e l d e m a n d at s i t u a t i o n (2).  The  p r o g r a m s t a r t s off w i t h the o p t i m a l s o l u t i o n f o r the l o g s u p p l y / p a n e l d e m a n d at s i t u a t i o n (1) a n d g r a d u a l l y i n c r e a s e s the a m o u n t s o f P e e l e r #2 a n d P a n e l A w h i l e d e c r e a s i n g the a m o u n t o f P e e l e r #3 a n d 48 k e e p i n g that of P a n e l B constant,  u n t i l a new o p t i m a l b a s i s h a s to  b e f o u n d to m a i n t a i n the o p t i m a l i t y o f t h e s o l u t i o n .  T h e n i t p r i n t s out  the n e w o p t i m a l s o l u t i o n a n d the v a l u e s o f t h e l o g s u p p l y a n d the p a n e l 48 T h e c h a n g e i n the l o g s u p p l y / p a n e l d e m a n d s i t u a t i o n h e r e i s  defined  a s : T h e s u p p l y o f P e e l e r #3 i s d e c r e a s e d t w i c e as f a s t as the i n c r e a s e i n the s u p p l y o f P e e l e r #2 a n d t h a t i n the d e m a n d f o r P a n e l A . A n d the demand for P a n e l B remains  constant.  169  demand.  T h r o u g h t h i s p r o c e s s the p r o g r a m c o m p u t e s a l l the  d i f f e r e n t o p t i m a l b a s i s as the l o g s u p p l y / p a n e l d e m a n d  situation  c h a n g e s f r o m t h a t at s i t u a t i o n (1) to t h a t at s i t u a t i o n ( 2 ) .  This series  of o p t i m a l s o l u t i o n t h e r e f o r e p r o v i d e s a s o m e w h a t ' c o n t i n u o u s ' o f the r e s p o n d o f the o p t i m a l s o l u t i o n to s u c h c h a n g e s i n the supply/panel demand  log  situation.  A n d f o r e a c h o f the o p t i m a l s o l u t i o n s c o m p u t e d ,  the  m a r g i n a l p r o f i t c o n t r i b u t i o n o f the l o g s u p p l i e s a n d the p a n e l are also  picture  demand  computed.  DO. P C R O p e r a t i n g l i k e the D O . P L P r o u t i n e ,  t h i s c o m p u t e s the  r e s p o n d o f the o p t i m a l s o l u t i o n to c h a n g e s i n the v a l u e o f t h e c o e f f i c i e n t s i n the o b j e c t i v e f u n c t i o n .  F o r example,  it w i l l  compute  a s e r i e s o f o p t i m a l s o l u t i o n f o r v a r i o u s c h a n g e s i n the l o g p r i c e and/or panel price and/or processing  cost.  170  C H A P T E R VIII I N T E R P R E T A T I O N O F FINDINGS F R O M T H EL . P. ANALYSIS O F T H E CASE  COMPANY  Introduction A m o d i f i e d v e r s i o n o f the p r o p o s e d m o d e l w a s on the c o m p u t e r i n s t e a d of the o r i g i n a l m o d e l .  solved  The modified model  49 does not t r e a t i n v e n t o r i e s  explicitly.  That is,  the m o d i f i e d m o d e l  d o e s not t a k e i n t o c o n s i d e r a t i o n the e x i s t e n c e o f y e a r - b e g i n n i n g and p l y w o o d p a n e l i n v e n t o r i e s .  Also,  veneer  a l t h o u g h the y e a r - e n d v e n e e r  and  p l y w o o d p a n e l i n v e n t o r i e s a r e p e r m i t t e d to b u i l d up w i t h o u t b e i n g s u b j e c t to a n y s t o r a g e s p a c e c o n s t r a i n t ,  t h e y a r e v a l u e d at  zero  dollars. How  might this s i m p l i f y i n g abstraction f r o m operating  r e a l i t y i n v a l i d a t e the f i n d i n g s f r o m the L . P .  analysis?  L e t us  f i r s t l i s t out the k i n d o f i n f o r m a t i o n we h o p e to o b t a i n f r o m the L . P . analysis:  C o m p a r e F i g u r e III to F i g u r e I o n p a g e s 56 a n d 60.  171  Firstly, i n the y e a r 1967,  (a) w i t h the g i v e n p r e d i c t i o n s of the  conditions  what m a y b e the b e s t c o m b i n a t i o n of l o g s to p e e l  a n d the b e s t c o m b i n a t i o n of v e n e e r to p u r c h a s e , (b) w h a t m a y b e the b e s t w a y to c h a n g e the  computed  o p t i m u m l o g i n p u t a n d v e n e e r p u r c h a s e to a c c o m m o d a t e  for any g i v e n  c h a n g e s i n the p l y w o o d p a n e l d e m a n d a n d / o r the l o g s u p p l y a n d / o r the v e n e e r  s u p p l y a n d / o r the p r o c e s s i n g  Secondly,  cost.  (a) w h a t m a y be the b e s t c o m b i n a t i o n o f p a n e l s  to p r o d u c e i n the g i v e n y e a r . (b) w h a t m a y b e the b e s t w a y to a d j u s t t h i s p a n e l output to a c c o m m o d a t e f o r a n y g i v e n c h a n g e s i n the p a n e l d e m a n d a n d / o r the l o g s u p p l y a n d / o r the v e n e e r  Lastly,  s u p p l y a n d / o r the p r o c e s s i n g  cost.  (a) what m a y b e the b e s t w a y to l a y u p the p l y w o o d  panels. (b) w h a t m a y be the b e s t w a y to a d j u s t the c h o i c e o f p a n e l c o n s t r u c t i o n s to a c c o m m o d a t e f o r c h a n g e s i n the l o g s u p p l y a n d / o r the v e n e e r  s u p p l y a n d / o r the p l y w o o d m a r k e t a n d / o r the  processing  cost.  In e f f e c t ,  the m o d i f i e d m o d e l a i m s to c o m p u t e the o p t i m u m  l o g i n p u t a n d v e n e e r p u r c h a s i n g f o r the y e a r w h i l e a s s u m i n g that the v e n e e r i n v e n t o r y s i t u a t i o n at the b e g i n n i n g of the y e a r i s a l s o m a i n t a i n e d  at the e n d of the y e a r .  T h i s a p p r o a c h d o e s not r e c o g n i z e  the  p o s s i b i l i t y of m a k i n g a s a v i n g i n w o o d c o s t b y c h a n g i n g the inventory situation.  Such possible  cost savings  m a y be  veneer  negligible  b e c a u s e the s i z e of the v e n e e r i n v e n t o r y u s u a l l y d o e s not a m o u n t to m o r e than h a l f a day's veneer  c o n s u m p t i o n at the m i l l .  Therefore,  the o p t i m u m l o g i n p u t a n d v e n e e r p u r c h a s i n g c o m p u t e d b y the m o d e l f o r the w h o l e y e a r m a y n o t b e f a r f r o m the t r u e o p t i m u m s .  It i s f o r the s a m e r e a s o n s t h a t no c o n s i d e r a t i o n was to c h a n g i n g the p l y w o o d p a n e l i n v e n t o r y s i t u a t i o n .  Besides,  d e s i r e d a d j u s t m e n t s i n the p a n e l i n v e n t o r y m a y b e  conveniently  given  any  p r o v i d e d f o r o u t s i d e the L . P . m o d e l b y a d d i n g o r d e d u c t i n g the d e s i r e d p a n e l i n v e n t o r y a d j u s t m e n t f r o m the p a n e l d e m a n d b e f o r e u s i n g the f o r e c a s t i n the L . P .  Therefore,  forecast  analysis.  the i n f o r m a t i o n d e r i v e d f r o m the m o d i f i e d  m o d e l m a y not b e m u c h l e s s u s e f u l t h a n that w h i c h c o u l d b e f r o m the o r i g i n a l m o d e l .  obtained  F u r t h e r m o r e , the m o d i f i c a t i o n s i n the  way  i n w h i c h the i n v e n t o r i e s a r e t r e a t e d m a k e s i t p o s s i b l e to r e d u c e the s i z e o f the L . P .  m o d e l f r o m 557 r o w s to 375 r o w s a n d f r o m  v e c t o r c o l u m n s to 605 v e c t o r c o l u m n s . saving in computer time.  This means  1096  a substantial  173  However, n u m b e r of r e a s o n s .  the o r i g i n a l m o d e l was f i r s t p r e s e n t e d f o r a Firstly,  i t s h o w s how i n v e n t o r i e s m a y be  t r e a t e d i n an L . P . m o d e l for a p l y w o o d b u s i n e s s .  Secondly,  it also  h e l p s to f o c u s a t t e n t i o n o n the a l m o s t i m p o s s i b l e t a s k of p l a c i n g a c o r r e c t v a l u e o n the i n d i v i d u a l g r a d e s of v e n e e r t h a t m a k e up the veneer inventory.  N e i t h e r i s i t e a s y to c o m p u t e the d r y i n g c o s t f o r  the v e n e e r as i t i s d r i e d i n b a t c h e s ,  i n combinations of m a n y  50 different  grades.  P r o f i t a b i l i t y of P l y w o o d P a n e l s Significant Findings:  T h e L . P . a n a l y s i s was  a b l e to  determine  that: (a) w i t h the g i v e n o p e r a t i n g c o n d i t i o n s i n 1967,  it m a y  b e m o r e p r o f i t a b l e f o r the m i l l to l e a v e p r o d u c t i o n f a c i l i t i e s i d l e t h a n to p r o d u c e the f o l l o w i n g p l y w o o d p a n e l s , 4' x 8 '  1/4", 3 / 8 " , 1/2"  51  namely, all grades  except  M a r i n e G r a d e and G o o d / S e l e c t 4' x 10'  1/4",  3/8" — a l l grades  Marine  except  Grade  (b) the p r i c i n g s y s t e m m a y b e f a v o u r i n g the t h i c k e r panels: Also,  i . e.  the t h i c k e r the p a n e l ,  the m o r e p r o f i t a b l e i t m a y  a s l i g h t l y h i g h e r p r e m i u m s e e m s to b e p l a c e d on 4 ' x l O ' p a n e l s  t h a n o n 4'xS' 50 R e f e r to p a g e 38 51  become.  S e e A p p e n d i x VIII f o r the o p t i m u m p r o d u c t m i x .  than on 4'x8' panels. Comparison of Computed Optimum Panel Output with Actual: In 1967, about 7 0 % of the mill's production (in terms of the number of panels) was made up of these possibly unprofitable thin panels. In another word, about 30% of the dollar sale might have been made at a loss. It i s not possible to compute the size of the possible loss f r o m the sale of these panels by multiplying the number of such panels 53 sold by the marginal profit contribution of the panels .  Yet,  assuming an average loss of $12. 50 per 250 panels, the total loss i n 54 the year could amount to $100, 000 for the m i l l .  This is deduced f r o m the marginal profit contribution (or 'shadow price' as some people call it) of the panels. This measure of profitability i s almost equivalent to a point measure. The marginal profit contribution of the sale of the nth unit of a panel may change as the value of n changes. Also, any substantial change in the log supply or in the total panel demand could cause a change i n the value of the marginal profit contribution of a panel. However, the marginal profit contribution of the various kinds of panels computed under the conditions given i n 1967 do persistently show a higher premium placed on panel thickness and 4'xlO' panels. For a sensitivity analysis of the marginal profit contribution of the panels, see the later section on sensitivity analysis. 53 Ibid. , Footnote #52 54 An L. P. model may be used to compute the total net profit f r o m a panel output equal to that of the m i l l i n 1967. The difference between this profit figure and that computed for the optimum panel output may give us a good measure of the profit lost due to selling the unprofitable thin panels.  175  Implication for F u t u r e Sales P o l i c y :  A complete stoppage of the  supplying of these unprofitable thin panels to the m a r k e t is l i k e l y to affect the sales of the thicker panels adversely. panels are sold jointly with the thicker panels.  Many of the thin F o r example,  a house  b u i l d e r is l i k e l y to o r d e r panels ranging f r o m the thickest panel to the thinnest panels.  It might therefore be profitable to maintain the  production of a certain amount of these thin panels,  although b y t h e m -  selves they m a y be unprofitable.  However,  it appears that future p o l i c y for guiding sales  might p o s s i b l y be to "avoid selling the unprofitable thin panels unless it is found n e c e s s a r y for pulling the sales of the thicker panels along. " T h i s might mean r e q u i r i n g the switch of the sales effort f r o m one section of the m a r k e t to another.  Implication for P a n e l P r i c i n g : r e v i s e the p r i c i n g s y s t e m .  It might also be n e c e s s a r y to  A p o s s i b l e approach may be to m a r k up  the p r i c e of the thin panels while granting a p r i c e reduction for the thick panels when they are jointly p u r c h a s e d with the thin panels. In this way, there may be no net loss to those customers who purchase thin and thick panels jointly.  On^the other hand, the sales of thin  panels alone might then at least break even.  A n y w a y when the facts  c o n c e r n i n g the u n p r o f i t a b l e p a n e l s  w e r e k n o w n t h e s a l e s d e p a r t m e n t w o u l d h a v e to w o r k out the b e s t s a l e p o l i c y to a c c o m m o d a t e f o r t h e m .  A C h e c k on Data A c c u r a c y :  T h e m a j o r determinants of panel  p r o f i t a b i l i t y a r e the l o g s u p p l y , the p r o c e s s i n g c o s t , time,  the p r o c e s s i n g  the t o t a l p a n e l d e m a n d , the l o g p r i c e s a n d the p a n e l p r i c e s .  A m o n g t h e s e , the p r e d i c t i o n of the l o g s u p p l y and the p a n e l d e m a n d , a n d the m e a s u r i n g o f the p r o c e s s i n g c o s t a n d the p r o c e s s i n g  time  c o u l d v e r y w e l l h a v e b e e n s u b j e c t i n t h i s s t u d y to a d e g r e e o f inaccuracy.  Ln p a r t i c u l a r , the p r o c e s s i n g c o s t m i g h t h a v e b e e n estimated.  In m o s t c a s e s ,  over-  the v a r i a b i l i t y o f a c o s t i t e m was  55 d e t e r m i n e d b y guess and judgment. b e e n t r e a t e d as a v a r i a b l e i t e m .  A fixed cost i t e m might have  In t h i s w a y ,  the p r o f i t a b i l i t y o f the  t h i n p a n e l s m i g h t h a v e b e e n u n d e r - e s t i m a t e d i n the L . P . O n the o t h e r h a n d , the L . P .  analysis.  a n a l y s i s d i d not t a k e i n t o a c c o u n t the  56 loss a r i s i n g f r o m panel downgrading.  Also,  a completely  free  c h o i c e o f the l o g s f o r i n p u t was a s s u m e d w h i l e i n p r a c t i c e the m i l l i s 5 5  S e e Table XIV  56 It i s e s t i m a t e d that o n t h e a v e r a g e ,  a b o u t 10% o f the p a n e l s l a i d up  a r e d o w n g r a d e d i n one w a y o r a n o t h e r .  177  also forced to accept some of the less economical logs which come i n the same booms with the more desirable logs. The unaccounted for loss i n these two areas of the operation of the m i l l might have been adequate to cancel out the effect of any possible over-estimation of the variable processing cost. However, it i s possible to test the sensitivity of panel profitability to various measures of processing cost, log supply and so on. Sensitivity Analysis: The Li. P. model can be used to compute a series of optimum panel outputs for various log supply conditions, various measures of processing cost and processing time and various panel demands. F r o m these series of optimum panel outputs, we may be able to see which of the panels become profitable and which become unprofitable under the different operating conditions. However it i s not conceivably practical to compute an optimum panel output for every conceivable set of operating conditions. A more helpful measure of the sensitivity of panel profitability to changes in operating conditions may be given by the marginal profit contribution ('shadow price') of the panels.  The way i n which the  shadow prices of the panels change i n response to changes i n the  o p e r a t i n g c o n d i t i o n s c a n p o s s i b l y p o i n t out w h i c h o n e s of the o p e r a t i n g f a c t o r s a r e the m o r e c r u c i a l i n d e t e r m i n i n g p a n e l p r o f i t a b i l i t y .  T h e s h a d o w p r i c e s of the p a n e l s a r e c o m p u t e d t o g e t h e r w i t h the o p t i m u m p a n e l output f o r the d i f f e r e n t s e t s o f o p e r a t i n g conditions.  T h e shadow p r i c e s c o m p u t e d m a y be c l a s s i f i e d into  two c a t e g o r i e s ,  namely:  (a) the s h a d o w p r i c e s o f the n t h u n i t of a p a r t i c u l a r panel,  under various operating conditions. (b) the s h a d o w p r i c e s o f the (n+x)th u n i t o f a p a r t i c u l a r  p a n e l u n d e r a g i v e n s e t of o p e r a t i n g c o n d i t i o n s , s e r i e s of v a l u e ,  namely,  1, 2, 3, . . .  where x takes a  etc.  F r o m the f i r s t set o f s h a d o w p r i c e s o f the p a n e l s , we m a y get a g o o d i n s i g h t i n t o the r e l a t i v e i m p o r t a n c e o f the v a r i o u s o p e r a t i n g f a c t o r s i n d e t e r m i n i n g the p r o f i t a b i l i t y of the p a n e l .  The  s e c o n d s e t o f s h a d o w p r i c e s m a y i n d i c a t e to us o v e r w h a t r a n g e o f v a l u e f o r the p a n e l d e m a n d m e a s u r e o f the s h a d o w p r i c e of the p a n e l m a y b e t r e a t e d as p r a c t i c a l l y c o n s t a n t .  In o t h e r w o r d s ,  i t t e l l s us  to what e x t e n t the m e a s u r e o f s h a d o w p r i c e s of the p a n e l m a y b e t r e a t e d as l i n e a r .  See s e c t i o n on A p p r o p r i a t e P o s t O p t i m a l A n a l y s i s .  Some manufacturers have developed a comprehensive set shadow prices for the operation of their business, covering many 58  conceivable sets of operating conditions.  They call this the  'Value Index" which they may use to gauge the impact of any given change i n the business opportunities on the optimality of the existing program of activities in their business. Only when the change of business opportunities i s found to be crucial, then may the manufacturer take steps to find and to implement a new program of activities. Guidance for Future Operations: The optimum panel production computed for 1967 may not be applicable to future years. to change over time.  Operating conditions are likely  In particular, the supply of logs may change,  because f i r s t growth F i r logs tend to become scarce.  Production  labour cost w i l l l i k e l y increase. Panel prices and production efficiency are also not likely to remain stagnant. The 'Value Index' may be used to determine at what point a new optimum program of activities should be found and implemented. 58  An example i s the Columbia Cellulose Co. , Vancouver, B. C. This information was obtained through a communication with Dr. J . Swirles, who was at one time personally associated with the company.  180  O p t i m u m L o g Input Significant Findings: p r e d i c t e d f o r 1967,  59  G i v e n the o p e r a t i n g  conditions  the L . P . a n a l y s i s f o u n d that:  (a) F i r P e e l e r #1,  P e e l e r #4 a n d S u i t a b l e - f o r - P e e l i n g m a y be  the l e a s t e c o n o m i c a l l o g s to u s e c o m p a r e d to the o t h e r l o g s .  (b) T h e o p t i m u m l o g i n p u t m a y r e l y o n F i r ; : P e e l e r s #2 a n d #3 to p r o v i d e t h i n (. 104") h i g h q u a l i t y v e n e e r , l o w q u a l i t y v e n e e r a n d F i r S a w l o g #3,  I n t e r i o r F i r f o r . 130"  H e m l o c k - B a l s a m M i x and  S p r u c e M i x f o r t h i c k (. 171") l o w q u a l i t y v e n e e r .  ,  (c) It m a y b e u n e c o n o m i c a l to p u r c h a s e a n y A / B M i x v e n e e r f r o m the m a r k e t .  (d) I n c r e a s i n g the s u p p l y o f H e m l o c k - B a l s a m M i x a n d I n t e r i o r F i r m a y b r i n g a b o u t a s u b s t a n t i a l s a v i n g i n w o o d c o s t b y p e r m i t t i n g the use of a m o r e e c o n o m i c a l l o g - g r a d e s  and l o g - s p e c i e s  combination.  T h o u g h to a m u c h l e s s e r extent, i t m a y a l s o p a y to i n c r e a s e the  supply  60 of F i r P e e l e r  #2 a n d S a w l o g  #3.  59 60  R e f e r to A p p e n d i c e s I X a n d X T h e m a r g i n a l p r o f i t c o n t r i b u t i o n (shadow cost) of H e m l o c k - B a l s a m M i x  a n d I n t e r i o r F i r e x c e e d $200 p e r 10, 000 F B M , w h i l e that of P e e l e r a n d S a w l o g s #3 i s about $50 o n l y . A s e x p l a i n e d i n F o o t n o t e #51, m a r g i n a l p r o f i t c o n t r i b u t i o n of the l o g s i s not c o n s t a n t .  #2  the  Y e t , i t shows  m u c h s c o p e i n i m p r o v i n g the l o g i n p u t b y i n c r e a s i n g the s u p p l y o f t h e s e logs.  181  C o m p a r i s o n o f C o m p u t e d O p t i m u m L o g Input W i t h A c t u a l : T h e a c t u a l p a n e l output o f the m i l l i n 1967 d i f f e r e d s i g n i f i c a n t l y f r o m the c o m p u t e d o p t i m u m p a n e l output.  It i s t h e r e f o r e not p o s s i b l e  to 61  c o m p a r e the c o m p u t e d l o g i n p u t d i r e c t l y w i t h the a c t u a l l o g i n p u t . T h e a c t u a l l o g i n p u t m i g h t h a v e b e e n v e r y c l o s e to the b e s t p o s s i b l e i n p u t f o r the output o f the m i l l i n 1967.  log  T h e g r e a t e r e m p h a s i s on thin  panels w h i c h m e a n s u s i n g a h i g h e r p r o p o r t i o n of face v e n e e r m i g h t have h e l p e d to a c c o u n t f o r the u s e o f a h i g h e r p r o p o r t i o n o f g o o d q u a l i t y l o g s i n the m i l l . I m p l i c a t i o n for L o g P u r c h a s i n g P o l i c y :  In p r a c t i c e ,  it is  almost  i m p o s s i b l e to p u r c h a s e f r o m the l o g m a r k e t a n y b o o m o f l o g s w h i c h totally excludes  a n y one p a r t i c u l a r g r a d e o f l o g s .  Y e t , the l o g  p u r c h a s i n g p o l i c y m i g h t p o s s i b l y b e to s e l e c t t h o s e l o g b o o m s w h i c h c o n t a i n t h e m i n i m u m a m o u n t o f the u n e c o n o m i c a l g r a d e s , P e e l e r #1,  s u c h as  P e e l e r #4 a n d S u i t a b l e - f o r - P e e l i n g .  T h e c o m p a n y a l s o c o n t r a c t s to p u r c h a s e f r o m s o m e s u p p l i e r s whatever they h a r v e s t f r o m their t i m b e r l a n d .  In s u c h c a s e s ,  the  c o m p a n y m a y c o n s i d e r r e s e l l i n g s o m e o f the u n e c o n o m i c a l l o g s o r m a y  61  T h e l o g supplies shown i n A p p e n d i x I X i s a good r e p r e s e n t a t i o n of the r e l a t i v e i m p o r t a n c e o f the v a r i o u s t y p e s o f l o g s c o n s u m e d b y the m i l l .  presently  182  e v e n n e g o t i a t e f o r a c h a n g e i n the p r i c e s set o n the l o g s .  Likewise,  the c o m p a n y m a y e v e n c o n s i d e r s e l l i n g o f f s o m e g r a d e s o f the l o g s f r o m i t s o w n t i m b e r l a n d i n o r d e r to p u r c h a s e t h e m o r e  suitable  grades.  T h e c o m p a n y m a y a l s o c o n s i d e r e x p e n d i n g m o r e e f f o r t to a c q u i r e a g r e a t e r s u p p l y o f the s u i t a b l e l o g s l i k e I n t e r i o r F i r a n d Hemlock-Balsam Mix.  Sensitivity A n a l y s i s :  T h e m a j o r d e t e r m i n a n t s o f the o p t i m a l i t y  of a l o g i n p u t a r e the y i e l d o f v e n e e r f r o m the v a r i o u s t y p e s o f l o g s , the l o g s u p p l y a n d the p a n e l d e m a n d . F r o m e a c h one t y p e o f l o g s , a c o m b i n a t i o n of m a n y g r a d e s of v e n e e r i s p r o d u c e d . T h e d i f f e r e n t types of l o g s t h e r e f o r e i n m a n y w a y s c o m p l e m e n t a n d s u p p l e m e n t one a n o t h e r as w e l l as s u b s t i t u t i n g f o r one a n o t h e r i n p r o v i d i n g f o r the t o t a l r e q u i r e m e n t f o r v e n e e r . s u p p l y a n d i n the p r i c e s  T h e r e f o r e , a n y c h a n g e i n the  o f the l o g s m a y c a u s e a c h a n g e i n the  c o m b i n a t i o n o f l o g s to p e e l .  Likewise,  a n y c h a n g e i n the p a n e l  d e m a n d m a y c a u s e a c h a n g e i n the t o t a l r e q u i r e m e n t f o r v e n e e r w h i c h i n t u r n m a y c a u s e a c h a n g e i n what c o n s t i t u t e s the b e s t l o g c o m b i n a t i o n to p e e l .  T h e p r e d i c t e d l o g s u p p l y a n d p a n e l d e m a n d f o r 1967 m a y t u r n out to b e q u i t e d i f f e r e n t i n p r a c t i c e .  In the f o l l o w i n g y e a r s ,  the l o g  183  s u p p l y a n d the p a n e l d e m a n d a r e l i k e l y to h a v e c h a n g e d t o o .  How then  m u s t the c o m p u t e d o p t i m u m l o g c o m b i n a t i o n f o r i n p u t be c h a n g e d i n o r d e r to h a v e i t r e m a i n as the b e s t l o g i n p u t u n d e r the  changed  conditions ?  A s e r i e s of o p t i m u m l o g inputs m a y be c o m p u t e d for v a r i o u s , 62 log supply a n d / o r panel demand conditions.  In a d d i t i o n , the  series  of m a r g i n a l p r o f i t c o n t r i b u t i o n s c o m p u t e d f o r the d i f f e r e n t t y p e s of l o g s u n d e r the v a r i o u s o p e r a t i n g c o n d i t i o n s i n d i c a t e to u s the  relative  i m p o r t a n c e o f the d i f f e r e n t o p e r a t i n g c o n d i t i o n s i n d e t e r m i n i n g the o p t i m a l i t y o f the l o g c o m b i n a t i o n to p e e l .  F r o m t h i s the  company  c o u l d b e a b l e to d e c i d e at what p o i n t i t s h o u l d c o n s i d e r c h a n g i n g the percentage  c o m b i n a t i o n of the d i f f e r e n t t y p e s of l o g s to p e e l i f  operating conditions  changed.  Optimum Plywood Panel Constructions: The panel constructions  s e l e c t e d f o r l a y i n g up the  s u g g e s t e d two g u i d i n g p r i n c i p l e s f o r l a y i n g up the p a n e l s ,  panels 63  namely:-  (1) as a g e n e r a l r u l e , u s e t h i n (. 104") v e n e e r f o r the f a c e a n d the b a c k o f the p a n e l a n d u s e t h i c k v e n e e r (. 130" a n d . 171") f o r the  62 63  See the s e c t i o n o n A p p r o p r i a t e P o s t O p t i m a l A n a l y s i s See o p t i m u m p a n e l c o n s t r u c t i o n i n A p p e n d i x X I  184  i n n e r p l i e s o f the p a n e l .  F o r low quality panels like  sheathings,  . 130" m a y a l s o b e u s e d f o r the f a c e a n d the b a c k o f the p a n e l .  (2) e x c e p t i o n s to the r u l e i n c l u d e the u s e o f t h i n v e n e e r (. 104") f o r i n n e r p l i e s of the p a n e l a n d a l s o . 130" h i g h q u a l i t y v e n e e r f o r the f a c e of the p a n e l . panel constructions  However,  subsidiary  i n o r d e r to u t i l i z e t h e s e v e n e e r w h i c h a r e j o i n t l y  p r o d u c e d w i t h the o t h e r v e n e e r . graded,  t h e s e a r e u s e d as  Also,  s o m e v e n e e r m a y be  e. g. , f r o m B a c k s #1 to C e n t r e s  down-  #1.  Some panel construction alternatives  i n c l u d e the u s e of two  a d d i t i o n a l p l i e s i n a p a n e l i n o r d e r to a l l o w the u s e of . 104" v e n e e r f o r the f a c e a n d the b a c k of the p a n e l i n s t e a d of . 130" v e n e e r .  The  u s e of a d d i t i o n a l p l i e s i n a p a n e l i s f o u n d w o r t h w h i l e o n l y w h e n i t a l s o m e a n s the u s e o f l e s s w o o d i n t o t a l i n the c o n s t r u c t i o n o f t h e p a n e l .  T h e s h a d o w c o s t of the d i f f e r e n t p a n e l s t r u c t u r e i n d i c a t e s that i t i s v e r y c o s t l y to u s e . 1 3 0 " panel.  G o o d v e n e e r to l a y up a  B u t i t i s a l m o s t e q u a l l y e c o n o m i c a l to u s e  o r . 104" v e n e e r f o r the f a c e a n d the b a c k of  e i t h e r . 130" v e n e e r  Sheathings.  I m p l i c a t i o n for C h o o s i n g P a n e l S t r u c t u r e :  T h e r e f o r e the  o f p a n e l s t r u c t u r e i s not to b e b a s e d o n the e c o n o m i c s construction alternatives  alone.  alternatives  choice  of the i n d i v i d u a l  It i s a l s o n e c e s s a r y to c o n s i d e r  the  t o t a l s u p p l y o f v e n e e r j o i n t l y p r o d u c e d f r o m the l o g s a n d a l s o the t o t a l  p a n e l s to b e l a i d u p .  T h i s c o u l d m e a n t h a t s o m e t i m e s the  second  b e s t c o n s t r u c t i o n h a s to b e u s e d f o r a p a n e l a n d s o m e t i m e s d o w n g r a d i n g s o m e o f the v e n e e r i s  P r e s e n t l y at the m i l l ,  necessary.  at the s h i f t l e v e l ,  the d e c i s i o n o n what  p a n e l s to p r o d u c e a n d w h e n a n d h o w to l a y t h e m up a r e m a d e at the press.  T h e p r o d u c t i o n of v e n e e r i s t h e n c o o r d i n a t e d to t h e n e e d s  at the p r e s s .  V e n e e r downgrading and different choices of p a n e l  c o n s t r u c t i o n s a r e u s e d to h e l p s y n c h r o n i z e t h e s u p p l y o f v e n e e r  to  m e e t t h e n e e d s o f t h e p a n e l output t h a t h a s b e e n set f o r the p a n e l press.  T h e r e a r e s t r o n g a r g u m e n t s f o r u s i n g the p r o d u c t i o n o f v e n e e r to d e t e r m i n e w h a t p a n e l to p r o d u c e a n d h o w to l a y t h e m u p . b e l i e v e d that i n this way,  It i s  o p t i m u m c h o i c e of p a n e l c o n s t r u c t i o n s  might  be m o r e r e a d i l y a c h i e v e d .  Sensitivity Analysis:  F r o m the s e r i e s o f o p t i m u m p a n e l outputs  computed for v a r i o u s supply conditions a n d / o r panel demand conditions we a l s o d e r i v e a s e r i e s o f o p t i m u m p a n e l c o n s t r u c t i o n s to b e u s e d unde various operating conditions.  F r o m this,  one m a y o b t a i n a n i d e a as  to h o w the c h o i c e of p a n e l c o n s t r u c t i o n s s h o u l d be a l t e r e d w i t h in log supply a n d / o r panel demand.  changes  186  A p p r o p r i a t e P o s t O p t i m a l A n a l y s i s to T e s t the S e n s i t i v i t y o f P a n e l P r o f i t a b i l i t y to C h a n g e s i n the S u p p l y o f the C r u c i a l L o g s : (1) W h i l e a s s u m i n g t h a t t h e p a n e l d e m a n d i s t h e s a m e  as  before, (a) a n d a l s o a s s u m i n g the s u p p l y o f l o g s i s the s a m e as b e f o r e e x c e p t t h a t the s u p p l y o f F i r P e e l e r #2 i s g r a d u a l l y i n c r e a s e d to a m a x i m u m of,  say,  t w i c e the o r i g i n a l a m o u n t ,  c o m p u t e the new  64 optimum solutions.  ( A n i n c r e a s e i n the s u p p l y o f F i r P e e l e r  #2 i s e x p e c t e d to i n c r e a s e the p r o f i t a b i l i t y o f the p a n e l s b y l o w e r i n g the w o o d c o s t .  We may, therefore,  o b s e r v e to s e e i f a n y of the  u n p r o f i t a b l e p a n e l s m a y b e c o m e p r o f i t a b l e a n d at what c o m b i n a t i o n of l o g input.  Also,  we m a y o b s e r v e to s e e h o w the s h a d o w p r i c e s o f  the p a n e l s m a y r e s p o n d to the i n c r e a s e i n the p r o p o r t i o n of P e e l e r  #2  used.) (b) m a k e the s a m e c o m p u t a t i o n s as i n (a) a b o v e ,  e x c e p t that  t h i s t i m e i n c r e a s e o n l y the s u p p l y o f F i r S a w l o g s #3, s a y to a m a x i m u m e q u a l to t w i c e the o r i g i n a l s i z e o f the s u p p l y . A n d t h e n do i t f o r a n i n c r e a s e i n the s u p p l y o f I n t e r i o r F i r a n d thenfor a n i n c r e a s e i n the supply of H e m l o c k - B a l s a m M i x .  (c) m a k e the s a m e c o m p u t a t i o n s as i n (a) a b o v e b u t now i n s t e a d o f i n c r e a s i n g the s u p p l y o f the f o u r c r u c i a l t y p e s o f l o g s i n d i v i d u a l l y ,  64  By a DO. P L P analysis.  See C h a p t e r V I I f o r d e f i n i t i o n .  we i n c r e a s e the s u p p l y o f t h e s e l o g s  simultaneously.  (d) m a k e the s a m e c o m p u t a t i o n s as i n (a) but now i n s t e a d o f i n c r e a s i n g the s u p p l y o f the l o g s as i n (a) to (c) a b o v e ,  we  decrease  the s u p p l y o f the f o u r t y p e s o f l o g s .  T h e a b o v e a n a l y s e s s h o w how i m p r o v e m e n t ( o r  deterioration)  i n the l o g s u p p l y m a y a f f e c t the p r o f i t a b i l i t y o f the p a n e l s .  They will  a l s o s h o w what the t o t a l c o s t s a v i n g m a y be l i k e f r o m i m p r o v i n g the log input.  (2) the a b o v e c o m p u t a t i o n s a l s o g i v e the s h a d o w p r i c e s of the n t h u n i t o f a p a n e l p r o d u c e d u n d e r v a r i o u s l o g s u p p l y c o n d i t i o n s , w h e r e n i s the s i z e o f the d e m a n d p r e d i c t e d f o r that p a r t i c u l a r p a n e l i n 1967.  T o get a n i d e a as to w h a t e x t e n t the s h a d o w p r i c e  t r e a t e d as a l i n e a r m e a s u r e o f the p r o f i t a b i l i t y of a p a n e l , the s h a d o w p r i c e of the n t h , (n + l ) ( t h ,  maybe we  comput  (n + 2) t h , (n + 3) t h . . .  etc.  u n i t o f a p a n e l u n d e r a g i v e n set of l o g s u p p l y c o n d i t i o n a n d o t h e r operating conditions.  These computations are obtained by first  s e t t i n g the d e m a n d o f a p a n e l to n u n i t s ,  then n + 1  units,  then n + 2  65 units,  etc.,  (3) c o m p u t e the o p t i m u m s o l u t i o n w i t h the s u p p l y o f the f o u r c r u c i a l t y p e s o f l o g s ( F i r P e e l e r #2, __  _ By a DO. P L P analysis.  S a w l o g #3,  Interior F i r and  188  H e m l o c k - B a l s a m ) d o u b l e d a n d the d e m a n d f o r the t h i c k (5/8" and higher) also doubled.  panels  ( T h i s t e l l s u s w h a t w i l l be the  i m p r o v e m e n t i n the p r o f i t p i c t u r e w i t h a t w o - p r o n g e d i m p r o v e m e n t i n the o p e r a t i o n of the b u s i n e s s ,  namely,  i n the l o g i n p u t a n d i n the s a l e  strategy.)  T o T e s t the S e n s i t i v i t y of P a n e l P r o f i t a b i l i t y to C h a n g e s i n the Processing  Cost:  66 C o m p u t e the o p t i m u m s o l u t i o n , processing  (a) w h i l e a l l o w i n g the  c o s t t o d e c r e a s e by a m a x i m u m of 1%, t h e n 2%, t h e n 3%,  t h e n 4% a n d t h e n 5%.  ( T h i s i s to p o i n t out the s e n s i t i v i t y  p r o f i t a b i l i t y to a n o v e r e s t i m a t i o n of p r o c e s s  of p a n e l  cost.)  (b) w h i l e t r e a t i n g the d i r e c t p r o d u c t i o n l a b o u r c o s t as only variable p r o c e s s cost i t e m .  (This practically removes  all  p o s s i b i l i t y of h a v i n g t r e a t e d f i x e d c o s t i t e m s as v a r i a b l e c o s t T h o s e p a n e l s that r e m a i n as u n p r o f i t a b l e m i g h t t h e r e f o r e  the  be  items. considered  as c e r t a i n l y u n p r o f i t a b l e . )  (c) w h i l e a l l o w i n g the p r o c e s s c o s t to i n c r e a s e b y a m a x i m u m of 1%,  t h e n 2%, t h e n 3%, t h e n 4% a n d t h e n 5%.  possible  ( T h i s i s to  s h o w h o w p a n e l p r o f i t a b i l i t y w i l l r e s p o n d to f u t u r e i n c r e a s e s i n tne processing  cost. )  "66 By a D O . P C R analysis.  See C h a p t e r VII for definition.  189  To Test the Sensitivity of the Optimality of the L o g Input to Changes i n the L o g Supply and/or Panel Demand: (The computations in (1) above also produce a series of optimum log input under various sets of log supply conditions and a given set of panel demand conditions. These solutions show how best to adapt the log input to shortages i n the supply of any of the suitable kinds of logs.  The computations made for (1) (c) above gives the 'perfect'  optimum log grade and log species proportion to use (for the given panel demand) when every kind of log i s i n adequate supply.) 67  Now, also compute a series of optimum solutions, increasing the supply of F i r Peeler #2, F i r Sawlog #3, Interior F i r and Hemlock-Balsam M i x by a possible maximum of 100% and for various relative rates of changes i n the demand for the panels. ( F r o m these optimum log input, the company may derive an insight into how the 'perfect' percentage combination of log-type has to be changed with changes i n the combination of panel-type constituting the panel output.  By doing a series of DO. P L P analysis setting a different relative rate for changing the demand for the different kinds of panels each time.  C H A P T E R IX  AREAS FOR FURTHER IN T H E C A S E  E c o n o m i c s o f the L . P . One  INVESTIGATION COMPANY  Analysis:  q u e s t i o n that m a y be a s k e d i s w h e t h e r o r not the Lu P .  a n a l y s i s p a y s off f i n a n c i a l l y .  A c c o r d i n g to the e x p e r i e n c e of s o m e  68 of the l e a d e r s i n the p l y w o o d i n d u s t r y , off h a n d s o m e l y ,  L . P . a n a l y s i s has p a i d  v a l u e d at h u n d r e d s o f t h o u s a n d s of d o l l a r s p e r  in cost savings.  F o r the C a s e C o m p a n y , the L . P .  year  a n a l y s i s h a s so f a r  p o i n t e d out p o s s i b l e a r e a s f o r a s u b s t a n t i a l c o s t s a v i n g s u c h as r r u n i m i z i n g the s a l e of u n p r o f i t a b l e t h i n p a n e l s .  A n o t h e r a r e a i n the  o p e r a t i o n of the b u s i n e s s that m a y b e i m p r o v e d i s i n the c h o i c e of l o g s to b e p e e l e d .  T h e t o t a l c o s t s a v i n g m a y l i e i n the r e g i o n o f  f i f t y t h o u s a n d to one h u n d r e d t h o u s a n d d o l l a r s p e r y e a r .  S e e C h a p t e r III.  191  T h e t i m e t a k e n to f i n d the f i r s t o p t i m u m s o l u t i o n a n d to do a s u f f i c i e n t l y a d e q u a t e s e n s i t i v i t y a n a l y s i s a m o u n t s to about 6 h o u r s of 69 c o m p u t e r t i m e o n a n I B M 7044 m a c h i n e .  This machine time  c o s t s $1, 800 i n t h e m a r k e t . T h e n t h e r e i s a l s o the c o s t i n c u r r e d i n c o l l e c t i n g a c c u r a t e d a t a o n v e n e e r r e c o v e r y f r o m the l o g s ,  in  determining cost behaviour and p r o c e s s i n g t i m e .  the i n i t i a l  L.P.  In t o t a l ,  a n a l y s i s m i g h t c o s t as m u c h as f i v e to s i x t h o u s a n d d o l l a r s .  B u t f u t u r e y e a r l y u p - d a t i n g of the s o l u t i o n m i g h t c o s t about one thousand dollars only.  T h e r e a r e also other less obvious costs like  t h a t o f the e x e c u t i v e ' s t i m e ,  personnel relation problems,  O f c o u r s e the e c o n o m i c s o f the L . P . a c c u r a t e study than is p r e s e n t e d above.  etc.  analysis need a m o r e  H o w e v e r , it is a l r e a d y  q u i t e c l e a r t h a t the Ca.se C o m p a n y s h o u l d m a k e a v e r y c o m p r e h e n s i v e s t u d y o f the e c o n o m i c s o f the p r o j e c t as i t i n v o l v e s s o m e  substantial  e x p e n d i t u r e a n d a l s o p o s s i b l y s o m e f a r r e a c h i n g c h a n g e s i n the o p e r a t i o n o f the  business.  T h e t i m e e s t i m a t e h e r e a s s u m e s t h a t no C O S T R A N G I N G i s c a r r i e d out.  analysis  It i s f o u n d that t h i s k i n d o f a n a l y s i s i s not v e r y  i n f o r m a t i v e as c h a n g e s i n the v a l u e o f the c o e f f i c i e n t s  o f the  objective  function takes m e a n i n g only when a whole group of these  coefficients  are  eg.  c h a n g e d at the s a m e t i m e a n d not j u s t one at a t i m e ;  a  c h a n g e i n a n y one o f the c o s t i t e m s o r the p r i c e o f a n y o f the t y p e s o f l o g s w i l l s i m u l t a n e o u s l y a f f e c t m o r e t h a n one c o e f f i c i e n t o f the o b j e c t i v e f u n c t i o n i n the m o d e l .  I n d e e d the v a l u e o f the C O S T  a n a l y s i s s e e m s not w o r t h the c o m p u t e r t i m e i n t h i s c a s e . computer time includes only N O R M A L , : D O . P L P . and D O . P C R a n a l y s e s . puter r u n used.  RANGING  The estimated  RHS. RANGING,. DO.DJ  A l s o see A p p e n d i x K I I for an account of the c o m -  192  O p t i m u m C e n t r a l A l l o c a t i o n of P r o d u c t i o n O r d e r s and L o g S u p p l i e s to the I n d i v i d u a l M i l l s : T h e C a s e C o m p a n y o p e r a t e s four p l y w o o d p r o d u c t i o n m i l l s . T h e s a l e o r d e r s a r e c e n t r a l l y r e c e i v e d at the h e a d q u a r t e r s a n d t h e n a l l o c a t e d to e a c h of the m i l l s f o r p r o d u c t i o n . T h e l o g s u p p l i e s a l s o be l i k e w i s e  allocated.  C i r c u m s t a n c e s h a v e l i m i t e d the p r e s e n t L . P . one o f the m i l l s ,  may  the l a r g e s t o n e .  However,  a n a l y s i s to o n l y  the o p t i m u m s o l u t i o n  a r r i v e d at f o r t h i s one m i l l m i g h t n o t b e the t r u e o p t i m u m f r o m the p o i n t o f v i e w o f the f o u r m i l l s t a k e n t o g e t h e r .  Possible  o f s p e c i a l i z a t i o n a m o n g the m i l l s a n d a l s o p o s s i b l e  economics  cooperation in  the p r o d u c t i o n o p e r a t i o n s a m o n g the m i l l s h a v e b e e n o v e r l o o k e d .  Also,  w h a t c o n s t i t u t e s the o p t i m u m o p e r a t i o n f o r one m i l l m a y not b e o p t i m u m f o r the  others.  It i s b e l i e v e d w o r t h w h i l e f o r the c o m p a n y to i n v e s t i g a t e e x t e n d i n g the L . P .  a n a l y s i s to the f o u r m i l l s ,  F i g u r e I V s h o w s how a n L . P .  taken  together.  a p p r o a c h m a y b e u s e d to f i n d  the o p t i m u m a l l o c a t i o n o f the p r o d u c t i o n o r d e r s a n d the l o g to the m i l l s . A t the s a m e t i m e ,  supplies  the m o d e l m a y a l s o f i n d the c o m p a n y -  w i d e o p t i m u m l o g i n p u t a n d p a n e l output.  It m a y a l s o p r o v i d e f o r the  p o s s i b l e t r a n s f e r of v e n e e r f r o m one m i l l to a n o t h e r .  F I G U R E IV AN OF  L . P.  MODEL  - OPTIMISING  LOG -  MILL X  X  /./  U  P L F L / NC-x  X  Li  X  X  X  X  Li- LS LL Lt  X  X  X  X  CL  FJ>1)  X  To M'LL  M  X X X X  X  MILL M  X  X  X  Lrtt L»2 LUi L * LVrLiL L»r Mil /oo  sneers  ( / OO  )  To MILL  X  L-iV  C  M-tot'' A  3  6tt££T£  X  X  L. X  X  MILL X  LS Lf Lio LH  )  X Ll  X  HAUi> Si2>£  M X  X  X  Lf L? Lio L,I PMELSj  C-Zi'O  fo  l-o  Z-S fo  fl  ZS  i'-o  ft  fo  f-o  i 0 S'O  fo  /is  zs-  fo hO 10  fo  F-o 31  f-0  i. 0  S-o  zs  i- 0 4 0  so  £ 0  S-o X-S  i-1  *'  fo  Fe '*  Zs  To  4 0  j.s  ± 0  s-o S-o s-o  f-o  fo fo  ZS 1-0  fo s  s-o £ 0 1-0  fo  Ft  * 0  S-O  (-0  fh  •i 0  S-o  Z-5  1-0  fa  vi <t  So So  1-0  fo  fl  4 0  /••!>-  10  fl  zs-a.  ± 0  S-o  fo  B>  *. ft•/)<>" fl  X  Lf Hit rlLZ MLb ML7  f-0  5!  X  MILL  LE:  4 /oo  l-o  l-o  X  L  s4  1.0 f.O  &  7-X  fUjMob PANEL fRDM ICTIOM  i  L'Z  is  X  MUMti  M  (  FROM  i/£A/t-.5R  < 300.  f.o1-0  I  L  of  l-o f-0  » w  flf  X  TRMsF£R  T H E MILLS  l-o t-o  /.» f-o  I.(of'fl  MILL  Lz Li LH LS  l.o /.» ?  M  ( /o,ooo  (10, OOO F&M ) ?#/  //V  MILL  L  ALLOCATION  PRODUCTION ORDERS AND L O G SUPPLIES TO  -  Partl-  ID  5- 0  SO  40 CO  FIGURE  MODEL  MILL  X  L,  L}  (lO,000 'fl  1,  L  X X X  LZ  pEELIiV<J  -  L0Cx  Lf-  Li'  f&M  XX X  L(, M>  L . P.  OF  PRODUCTION ORDERS AND  I/V  —  M/LL  M  X X  ri&  rii  X  rft  (/0,00a  )  Part  AN  -OPTIMISING  TO  -  IV  -  TRANSFER  M//-L L  x x  iii-  X  in LMi  OF  Tt> M/LL.  X X  X  ALLOCATION LOG  SUPPLIES  MILLS  VEN EER  X  FR.OM  M/LL M  M  X X  LHZ LMi LMI LdsLlt (/Off  fan)  THE  L*1  $//££ TS )  X ML/  X  To M/LL  X X  Uft)00b?MeL  — L.  -  x * x  x  MILL  L  -  -  A x x,  x  MLX MU>MUf NLs MLI.ML1 LI Lf L9 Lio LU SHEETS ) ( ZS'O PANELS)  /• A  X  LI  SALE  MILL  L  X. X  L?  X  LI  C ~iOO.  cmcir)  MILL M  jinyep. Miu  L  -ez -a  -oi  A  -II  -II  -II  fun  C»?*urj  MILL M  SBHMUL  »n  "if  ID  ./f  i300-  -IS •ti  -ro -ti  io  iS-00-  L  • Of .oi  -Of .01 -Dt • oi  L  -et  .07  -ol  Zf  2-7, Zl  3D f-J  /ti' ZZ  2-2 10  /.?  /.7  /ii' • Of  -of  .oif .of  -pf  -of  -of  • Of  -pf . lr .of 0  oLf. .glf.  tf (,•? (,•? y-7  a  Ci  D(. 1/76i/iO.  •02, -Oi- 02 •/>& •Oil -oif -oif  FuNCTIOfJ ro ( niNlMtSS. )  ts'oo. i2oo-  .oii, -on, .027 on •13. -II  ± boo/•  .02 .oiy  CAPKlTy M'LU M ?Rts$  i.1,00.  A •oi  SiDi  Lil  pfiinas)  I-  MILL L  X  Lio  A  Wto  IHTHE  fitGHT  -  I-  /•  ss  cf  ( Zi-o /.  via. J;  III  pROJi ICT'ON  (/DO  Ml  '//  2  i-8  6-t  s-1  -oil  i/?o-  M  K4.  195  Panel  Down-grading: The present L . P .  analysis  o f the C a s e C o m p a n y has  not  c o n s i d e r e d the d o w n g r a d i n g o f p a n e l s b e c a u s e o f a l a c k o f a d e q u a t e data on p a n e l d o w n - g r a d i n g .  It i s e s t i m a t e d b y the C a s e C o m p a n y  t h a t a b o u t 10% of the p a n e l l a i d up m a y b e down g r a d e d i n o n e or another.  way  T h e l o s s f r o m d o w n - g r a d i n g could be d e c i s i v e i n  d e t e r m i n i n g p a n e l u n p r o f i t a b i l i t y o r the r e l a t i v e p r o f i t a b i l i t y o f the different kinds of panel.  It i s t h e r e f o r e  r e c o m m e n d e d that the  company  c o l l e c t d a t a o n the l o s s f r o m d o w n - g r a d i n g f o r the d i f f e r e n t t y p e s o f panel.  196  CHAPTER X  CONCLUSIONS  The research study was c a r r i e d out with two main objectives in mind, namely: (a) to provide an approach by which to analyse the profit margin of the various specifications of plywood panel produced by the Case Company and also to provide a method by which to find the best log combinations and the best panel constructions to use and (b), in so doing, also to provide an examination of the way to use the L.P. technique and to evaluate its usefulness as a management tool for the plywood manufacturing business. The L.P. analysis suggested that about 30% of the dollar sales of the Case M i l l in 1967 were made i n unprofitable (thin) panels. Even after allowing for an over estimation of the variable processing cost, this may s t i l l call for a thorough re-examination of the sales strategy and the panel pricing system. F o r the panel output selected for 1967, the best log combination  to use apparently includes the use of a much higher proportion of F i r Peeler #2 and Sawlog #3, Interior F i r and Hemlock-Balsam M i x than what the Company had made available to its m i l l . Also, the model suggested that proportions of F i r Peeler #1, #4 and S. F.P. might be much lower than what the Company tended to use. The L i . P. model suggested that the best choice of panel construction alternatives may be to peel Peeler logs for thin (. 104") face veneer, to peel Interior F i r for . 130" low quality face veneer and veneer to be used as the inner plies ::of the panel and also to peel the other low quality logs for . 171" veneer to be used as inner plies. It also suggested downgrading some veneer and using some subsidiary panel construction alternatives to make full use of the total supply of veneer f r o m the logs peeled. The usefulness of the L. P. analysis is not l i m i t e d to finding the optimum log input and panel output for just one set of log supply/ panel demand/processing cost situations. The model also provides an analysis of the sensitivity of the optimality of the solution to any changes in the operating conditions of the business. This analysis may enable the company to determine which ones of the operating factors are crucial i n determining the profitability of the panels and what may constitute the best log combination to use.  F r o m this, the  198  c o m p a n y m a y k n o w w h e n a n d h o w to a d j u s t i t s p r o g r a m o f o p e r a t i o n i n r e s p o n s e to a n y f u t u r e c h a n g e s i n ( o r a n y r e v i s i o n i n the  forecast  of) the l o g s u p p l y a n d / o r the p a n e l d e m a n d a n d / o r the p r o c e s s i n g  In the L . P .  analysis,  simplifying assumptions  i t w a s f o u n d n e c e s s a r y to m a k e  cost.  some  i n i d e n t i f y i n g the v a r i a b l e c o s t i t e m s .  It  w a s a l s o a s s u m e d t h a t the r e l a t i o n s h i p w h i c h the v a r i o u s c o s t i t e m s b o r e to one a n o t h e r ( p e r u n i t of m a c h i n e t i m e ) i n 1966 was a p p l i c a b l e i n 1967.  also  T h e s e n s i t i v i t y a n a l y s i s m a y a l s o b e u s e d to  e x a m i n e the r e s u l t s o b t a i n e d b y v a r y i n g t h e s e a s s u m p t i o n s , i n d i c a t i n g to u s the i m p o r t a n c e o f t h e s e a s s u m p t i o n s  thereby  in determining  w h a t m a y c o n s t i t u t e the o p t i m u m l o g i n p u t a n d the o p t i m u m p a n e l output.  In the L . P ' . a n a l y s i s ,  the p o s s i b l e  existence of  characteristics  o f a j o i n t n a t u r e i n the s u p p l y o f l o g s a n d i n the d e m a n d f o r p a n e l s not g i v e n c o n s i d e r a t i o n .  It m a y be m o r e s u i t a b l e to m a k e a l l o w a n c e  s u c h a d d i t i o n a l c o n s t r a i n t s o u t s i d e the L . P . the f i n d i n g s o f the a n a l y s i s .  was for  analysis when i m p l e m e n t i n g  The same recommendations  m a y also  a p p l y to m a k i n g a n a l l o w a n c e f o r l o s s f r o m p a n e l d o w n - g r a d i n g .  BIBLIOGRAPHY  199  A. 1.  BOOKS Dantzig,  G. B. ,  L i n e a r P r o g r a m m i n g and Extension, University Press, 2.  Dorfman,  Princeton,  R. & Samuelson,  P ; A . & Solow,  L i n e a r P r o g r a m m i n g and E c o n o m i c . M c G r a w - H i l l Book Co. Inc., 3.  Garvin,  Princeton  1963. R. M . , Analysis,  N. Y. ,  W.W.,  I n t r o d u c t i o n to L i n e a r P r o g r a m m i n g , Co. 4.  Inc.,  Greenwald,  Spivey,  McGraw-Hill  D. U . , Ronald P r e s s C o . , N . Y . ,  1957.  W.A.,  • L i n e a r P r o g r a m m i n g - A n Introduction, Co. , N . Y o r k ,  B.  PERIODICALS  6.  Bethel,  J . S.  The M a c M i l l a n  1963.  fk H a r r e l l ,  C. ,  T h e A p p l i c a t i o n o f L i n e a r P r o g r a m m i n g to P'roduction and Distribution, Vol. 7.  Book  I960.  Linear Programming, 5.  1958.  Business  Vn,  No.  7,  July  Plywood  Forest Products  Journal,  1957.  Week,  C o m p u t e r P o i n t s W a y to P r o f i t s i n L u m b e r ,  January  1st,  1966. 8.  Forest  Industries,  Operations Research Vol. 9.  Jackson,  16,  No.  2,  Feb.  N . D. & Smith,  - T o o l f o r G r o w t h at B o i s e  G. W . ,  Linear P r o g r a m m i n g in L u m b e r Production, Product Journal,  Cascade,  1966.  V o l . XI, June  1961.  Forest  200  10.  Konigsberg, E . , A p p l y i n g L i n e a r " P r o g r a m m i n g to the P l y w o o d I n d u s t r y , F o r e s t P r o d u c t J o u r n a l , V o l . X , Sept.  11.  Mayhew,  I960.  W. E . ,  A N e w a n d R e v o l u t i o n a r y M e t h o d of A l l o c a t i n g C o s t s to V e n e e r b y G r a d e s ,  Forest Products Journal, April,  1958. 12.  Pearse,  P . H . & S y d n e y s m i t h , . S. ,  M e t h o d for A l l o c a t i n g L o g s A m o n g S e v e r a l U t i l i z a t i o n Process, Sept.  C. 13.  F o r e s t P r o d u c t J o u r n a l , V o l . 16,  UNPUBLISHED PAPERS,  9,  PROCEEDINGS  Carpenter, C . E . , Raw  M a t e r i a l M a n a g e m e n t i n the F o r e s t I n d u s t r y ,  Wayerhaeuser 14.  No.  1966.  Donnelly,  C o . , (date a n d p l a c e not  available).  R. H . ,  Linear P r o g r a m m i n g in Plywood - Manufacturing, The P r o c e e d i n g s o f the I B M C o n f e r e n c e o n O p e r a t i o n s R e s e a r c h i n the . P r o d u c t I n d u s t r y , 15.  Giles,  November,  1965.  E . N ., The  C o m p u t e r i n P l y w o o d M a n u f a c t u r i n g at S i m p s o n  T i m b e r C o m p a n y , S e m i n a r P a p e r (date a n d p l a c e not available.) 16.  U . S . Plywood Corporation, Oregon Procedures  F o l l o w e d i n P i l o t L i n e a r P r o g r a m m i n g Study,  (Unpublished Paper).  D. 17.  DISSERTATION Dorfman,. R. , A p p l i c a t i o n o f L i n e a r P r o g r a m m i n g to the T h e o r y of the Firm  - I n c l u d i n g a n A n a l y s i s of M o n o p o l i s t i c F i r m s b y  Non-linear Programming, of C a l i f o r n i a ,  1951.  P h . D.  Dissertation,  University  201  18.  Hansen,  H . G. ,  Some Implications  of the C o s t D a t a R e q u i r e m e n t s  of  L i n e a r P r o g r a m m i n g A n a l y s i s for C o s t A c c o u n t i n g , Ph.D. 19.  Dissertation,  U n i v e r s i t y of M i n n e s o t a ,  1963.  Randell, W. C . , L i n e a r P r o g r a m m i n g in a S m a l l F o r e s t Product P h . D. Dissertation, 1963.  Sycracuse,  University,  Firm,  U.S.A.  APPENDICES  202  APPENDIX I A S A M P L E O F T H EL O GGRADING BRITISH  SYSTEM  COLUMBIA  ( G a r r e t t L o g S e r v i c e Ltd..)  Douglas F i r P e e l e r G r a d e s : P e e l e r #1  L o g s 18' a n d o v e r i n l e n g t h , diameter, clear,  30" a n d o v e r i n  o f #1 S a w l o g q u a l i t y  fine g r a i n ,  i . e.  surface  slight s p i r a l grain, and free  f r o m defects that w o u l d i m p a i r r o t a r y cutting.  P e e l e r #2  L o g s 18' a n d o v e r i n l e n g t h , diameter,  30" a n d o v e r i n  o f #2 S a w l o g q u a l i t y — i . e.  50% s u r f a c e c l e a r i . e. i n top h a l f of l o g  m u s t be  s m a l l sound knots  allowed  f r e e f r o m s u c h defects that  would i m p a i r r o t a r y cutting.  P e e l e r #3  L o g s 18' a n d o v e r i n l e n g t h , diameter,  24" a n d o v e r i n  o f #2 S a w l o g q u a l i t y a n d h a v i n g one  c l e a r p e e l e r b l o c k (8* 6") at b u t t e n d . 30" i n d i a m e t e r a n d o v e r ,  O n logs  a knot i n d i c a t i o n could  b e a l l o w e d i n the butt e n d of l o g s i f the r e s t o f log is of p a r t i c u l a r l y high grade.  203  APPENDIX I  A S A M P L E O F T H E L O GGRADING BRITISH  SYSTEM  COLUMBIA  (Garrett L o g Service Ltd.)  P e e l e r #4  L o g s 18" a n d o v e r i n l e n g t h ,  Part 2  18" o r 20" to 23" i n  d i a m e t e r a c c o r d i n g to p u r c h a s e r ' s s p e c i f i c a t i o n s otherwise  S. F . P . ( S u i t a b l e f o r  s a m e as #3  -~  peelers.  Peeling)  T h e s e l o g s a r e o f #2 S a w l o g q u a l i t y , i n length,  18" a n d o v e r  20" o r o v e r i n d i a m e t e r ( a c c o r d i n g to  purchasor's specifications)  b u t do n o t r e q u i r e a c l e a r  p e e l e r b l o c k i n the butt e n d o f l o g .  Peeler Blocks  L o g s s h o r t e r t h a n 18' separately,  s h a l l b e c l a s s i f i e d c ...  to s u i t b u y e r a n d s e l l e r  specifications.  Note: In a l l c a s e s p e e l e r l o g s w i l l b e f r e e f r o m s u c h d e f e c t s t h a t would, bad rot,  i n the s c a l e r ' s  splits,  opinion, i m p a i r r o t a r y cutting,  ringhshake, break,  shatter,  i.e.  deep sap r o t and butt  that w o u l d r e q u i r e o v e r a 6' d e d u c t i o n .  T h e s e logs w i l l also be free f r o m l a r g e knots or b u n c h knots fine g r a i n e d a n d r e a s o n a b l y  straight.  A P P E N D I X II A SAMPLE OFPANEL  PRESSING INSTRUCTIONS  GlueTotal Panel Thickness Rough Sanded  Nol  Green  of  Thick-  Plies  Spread Face &  ness  Back  Core  5/16"  1/4"  3  •312"  •104"F .104' ' F  5/16"  1/4"  3  •338"  .104 " F •130 ' F  3  .338"  .104"F  1  .130' ' F  Centres  Press  l b s /000  Panels per  s q . ft.  Press  2-side  Opening  P a r t 11  Time  minutes per  load o  o 285  F  300  F  Pressure  52  2  4  -  53  2  5  200  54  2  5  162 1 /2  -  58  2  7  1/2  7  200  60  2  7  1/2  7  162 200  1/2  200  7/16"  3/8"  3  .431"  . 1 3 0 " F .171' ' F  7/16"  3/8"  3  .431"  .130 " F .171' 'B  9/16"  1/2"  5  • 587"  •104"F  .104' ' F  .171"F  53  1  5  1/2  5  9/16"  1/2"  5  . 1 0 4 " F .104' ' F  .171"B  55  1  5  1/2  5  162  5  1/2  5  200  5  1/2  5  200  9/16"  1 /2"  5  .587" .598"  . 1 0 4 " F .130' ' F  .130 " F  53  1  9/16"  1 /2"  5  •598"  -130"F  •104' • F  .130 " F  53  1  5  .721"  •104"F .171' ' F  .171"F  56  1  6  200  .130"F  56  1  6  200  •130 " F  59  1  6  162  11/16" 5/8" 11/16" 5/8"  5  .732"  •130"F  11/16" 5/8"  5  .732"  .130"F  •171' ' F .171' ' F  1/2  1/2  1/2  APPENDIX  II  A SAMPLE OF PANEL-PRESSING  INSTRUCTIONS  GlueTotal Panel Thickness Rough Sanded  No of Plies  Press  Spread  Panels  Green  Face  lbs/000  Thick-  & Back  s q. ft.  per Press  2-side  Opening  ness  Core  Centres  Part 2 time  minute s per  load  285°F  300°F  Pressure  •104"F  54  I  6 3/4  .104"F  •104"F .104"F  •130 " F  54  1  7  200 100  •780"  -104"F  •104"F  •130"B  55  1  7  162  7  •858"  •130"F  -130"F  •104"F  56  1  7  1/2  £00  3/4"  7  •862"  •104"F  •104"F  •171"F  56  1  7  1/2  200  1 3/16"  1 1/8"  •130"F -104"F  •171"F  •104"F  62  1 1/8"  9 9  1-256"  1 3/16"  .104"F  .130"F  65  11/16"  5/8"  7  3/4"  11/16"  7  3/4"  11/16"  13/16"  3/4"  13/16"  .728" •780"  •104"F  1-248"  1 1  i  14  200  14  200  1/2  APPENDIX  III  A SAMPLE OF VENEER  GRADING  S Y S T E M A T PRESS Part 1  ( D E F E C T S P E R M I T T E D IN G R A D E )  Select  Solid  Good  (A)  (B)  Sel-Sheathing (U/L)  < i» B  Backs & StdSheathings (Backs  T y p e of Defect P i n Knots (3/16" M . D . )  0  0  0  Any No.  Sound Knots  0  0  0  Any No.  #1)  Any No. 1/2"  Any No.  1/2" M . D .  3/8"  Any No. 3/4" M . D .  M . D. Starred Knots  0  0  0  Any No. M . D.  Open  Defects  P i t c h P'ockets  0  0  0  0  0  0  0  Any No.  3/4" M . D.  Any No. ,  3/4"  M a x "Width P i t c h Streaks .  l / 4 " x l 2 " A n y No. & Size  A n y No. & Size  Max. Size  l/4"xl2"  M a x . Size  Sheets &  Sheets and compon-  Sheets-3  Sheets-3  Components  nents  Components -1  Compon -  nets-1  A P P E N D I X LU A SAMPLE OF VENEER  GRADING  S Y S T E M A T PRESS Part 2  ( D E F E C T S P E R M I T T E D IN G R A D E ) Select -(A)  Good  Solid  ( )  Sel-Sheathings (U/L)  < i> B  B  B a c k s & Stdsheathings (Backs  #1)  T y p e of D e f e c t 0  Splits  1/8 " t a p e r e d  l/8"tapered  1 /8" tapered,  3/16"  sheets -4,  sheets-4,  sheets-4,  sheets -5,  Components 1  Components  Decay  0  0  0  P i n w o r m holes  0  0  0  S t a i n (not  0  pitchstreak)  Rough P e e l  1/64" M a x . Depth  Any Amount 1/64" M a x . Depth  0  0  Patchable  Defects - per sheet 0  12  P atchable  Defects  Feather  J  Grain  1 Components 1  Components p Sound  Sound  Any No.  0  Any Amount  Any Amount  Any  1/32"  1 /32"  1/32"  Max.  Max.  Max. 6"  Depth  square 18  tapered,  Depth  Amount  Depth  Any  Amount  Any  Amount  Any  No.  Any  No.  Any  No.  Any  No.  components 0  2 p e r foot  3 p e r foot  of w i d t h  of w i d t h  Note: M . D .  & Size  - M a x i m u m Diameter  A P P E N D I X IV A SAMPLE O F PLYWOOD P A N E L CONSTRUCTION No.  Panel  of  Thicke  Plies  ness  9  1"  (per 250 A  II  Part 1  Centres # 1 XB XC . 130" . 104" . 130" . 171" . 104" . 130" . 171" . 104" . 130" . 171"  B  . 104" . 130 " . 104 £5)  ALTERNATIVES  panels)  1"  (5)  II  5  11  5  7. 5  10  7. 5B  10  9  1 1/8"  5  7. 5  10  11  11  5  7. 5B  10  II  II  5  10  II  II  5  10B  II  11  11  1  5 1/4%  10  5  10  12. 5  5  10B  12. 5  5 N o t e : (1) V e n e e r i n u n i t s of  12. 5  250 s h e e t s or  10 sheet-equivalent  12. 5 each  (2) V e n e e r a m o u n t i n b r a c k e t s r e f e r s to a v e n e e r d o w n - g r a d i n g (3) " B " r e f e r s to v e n e e r of w o o d s p e c i e s o t h e r t h a n D o u g l a s F i r .  o oo  A P P E N D I X IV A SAMPLE O F PLYWOOD P A N E L CONSTRUCTION (per No. of G2S  Plies  Part  ALTERNATIVES  250 p a n e l s )  Panel Thickness  A  B  C e n t r e s #1  XB  XC  . 104" . 130" . 104" . 130" . T04" . 130" . 171" . 104" . 130" . 171" . 104" . 130" . 171"  3  1/4"  5  2.5  "  "  5  2. 5 B  5  1/2"  5  "  "  5  "  "  5  5/8"  5  2. 5  5  "  "  5  2. 5B  5B  "  "  7  5/8"  7  3/4"  "  "  "  "  5  "  "  5  7  7/8"  5  'i  it  t i l l  2.5 2. 5 5  5  5  2. 5  5  5 5  7^5  5  (5)  7.5 5  7.5  5  7.5 5  5 5  c  5  2_J5  5  5  5  5  7.5 7.5?.. 7.5B  5  7.5B  2  APPENDIX  V  THE COMPONENTS O F SOME O F T H E COEFFICIENTS O F T H EOBJECTIVE (FOR  UNITS,  1  Part 1  FUNCTION  S E E F I G U R E II)  P E E L I N G LOGS F O R V E N E E R 0F1EX  Boom Process  Costs  Green-end Process  Costs  D r y - e n d P'rocess Costs Veneer Patching  0F8EZ  1F8EZ  0H9EZ  OSOEZ  0F1TX  33. 00  33. 00  33. 00  35. 00  35. 00  35. 00  33. 00  33. 00  110.66  110.66  98. 33  76. 14  76. 14  56. 50  55. 25  9 7 . 39  8 8 . 47  88. 47  79,81  62. 21  62. 21  67. 74  67. 23  8 5 . 29  142.21  100.73  35.99  35.99  2.57  30.57  126.16  44. 21  37. 15  136.04 Edge-glueing  Process Log  0F1EY  Process  Costs Veneer  1F1EX  Costs  Costs  44.21 1400. 0  ( N e t B y - p r o d u c t R e v e n u e ) 114 . 4 3 T o t a l ($)  1697.94  1400.0  1400.0  38. 90 685. 0  685. 0  664.0  730.0  1400.0  114. 43  114.43  114.43  114.43  152.51  152. 51  114. 43  1714.00  1552.99  779.91  792.31  694.49  763.55  1664.30  Cost  i—• o  APPENDIX V THE COMPONENTS O F SOME O F T H ECOEFFICIENTS OF T H E OBJECTIVE (.FOR U N I T S ,  FUNCTION-  S E E F I G U R E II)  PEELING LOGS F O R V E N E E R 1F1TX  Part 2  0F8TZ  32. 00  32.00  34. 00  32.00  32. 00  -  97.38  86.53  83.49  53.86  52. 52  -  85.29  76.62  59.72  65. 03  64.54  139.77  125.07  139.77  125.07  130.73  92.67  33.12  2 3 . 69  28.13  256.67  209.14  2 3 6 . 13  192.40  38.90  32. 69  -  -  -  1400.00  1400.00  685.00  664.00 730.51  4 1 5 0 . 00  4150.00  4150.00  4150.00  (Net B y - P r o d u c t Revenue) 114.43 T o t a l ($) 1678.67  114.43 1606.08  114.43 780.89  152.51 152.51 686.08 752.15  25. 4521.  00 2 5 . 00 25.00 44 4 4 5 9 . 2 1 4 5 0 0 . 9 0  25.00 4 4 4 2 . 48  Costs  Green-end Process Dry-end Process  Costs  Costs  OSOTZ  WFMEX  WFMEY  VENEER  OF1TY  Boom Process  0F9TZ  PURCHASING  WFMTX  WFMTY  V e n e e r Patching P r o c e s s Costs Veneer Process Log  Edge-glueing Costs  Costs (or V e n e e r  Costs)  APPENDIX V THE COMPONENTS O F SOME O F T H ECOEFFICIENTS O F T H EO B J E C T I V E ('FOR U N I T S ,  FUNCTION  S E E F I G U R E II)  PLYWOOD PANEL 2YQZEC  4XZZEC  - Part 3  PRODUCTION  4XVZEC  4XXXEC  4XXZEJ  46X8EJ  4XVZTC  4XZZTC  4XXXTC  P a n e l Lay-up & P r e s s Process  Costs  Panel Glue Costs Panel  40. 02  70. 44  70.44  77.65  65.64  65.64  70.44  70.44  70.44  20.88  40. 32  42.48  58.32  40.32  41.76  53.10  50.40  72.90  2. 01  2. 01  2. 01  2. 01  2.01  2.01  2.20  2.20  2.20  18. 52  18. 52  18. 52  20.35  20.35  20.35  7. 46  7. 46  7. 46  7. 46  11.17  11.17  11.17  1.78  1. 78  1.78  1. 78  1.52  1.52  2.55  2. 55  2.55  11.83  11.83  11.83  11.83  7.46  7.46  13.01  13.01  13.01  102.52  152.38  154.54  177.59  116.95  118.39  172.83  170.14  192.64  Trimming  Process  Costs  P a n e l Sanding P r o c e s s  C o s t s 18. 52  Plastic Patching Process Costs Davis R e c l a i m P r o c e s s Costs P a n e l Grading P'rocess Costs  T o t a l C o s t ($)  t—'  213  A P P E N D I X VI CODE NAMES FOR COMPUTER-RUN  COLUMN  NAMES  1.  L o g Peeling O  Part 1  . . . 0 f o r '01' l e v e l o f v e n e e r u p g r a d i n g , 1 for  F  '02' l e v e l  . . . F for Douglas F i r , H for H e m l o c k - B a l s a m Mix,  2  . . .  S for S p r u c e M i x  1, 2, 3,  . . . . 9 and Blank for log grades  and l o g s p e c i e s ,  as i n the o r d e r s h o w n i n T a b l e I V  E  . . . E for 8-ft and T for  X  . . . X f o r . 104",  10-ft  Y f o r . 130",  Z f o r . 171"  P l y w o o d P a n e l Construction and P a n e l Sale 4  . . .  1, 2, 3, . . . . 9 a n d B l a n k f o r v a r i o u s p a n e l t h i c k n e s s as. i n the o r d e r s h o w n i n T a b l e I  X  . . .  This specifies  t h e t h i c k n e s s a n d the w o o d  s p e c i e s o f the v e n e e r u s e d f o r F a c e & B a c k , X f o r . 104",  Y f o r . 130",  Z f o r . 171" a n d  V f o r . 171" o f s p e c i e s o t h e r t h a n D . F i r Q  V  . . . Q specifies  no C e n t r e p l y i n the p a n e l ,  other letters  specify thickness and wood  species for C e n t r e p l y Z  . . .  This specifies  the t h i c k n e s s a n d w o o d s p e c i e s  of the v e n e e r u s e d f o r . t h e C o r e p l y E  T  . . . E for 8-ft and T for  10-ft  C  D  . . . A , B , C . . . . K s p e c i f y p a n e l g r a d e s i n the o r d e r as s h o w n i n T a b l e I  E x c e p t i o n : 4 6 X 8 E C . . . T h i s i s a m o d i f i c a t i o n o f the one p a n e l c o n s t r u c t i o n p r e c e e d i n g i t . . . T h i s p r o v i d e s f o r a d o w n - g r a d i n g o f a 6th g r a d e v e n e e r (. 104") to b e u s e d as a n 8 t h g r a d e .  A P P E N D I X VI CODE NAMES FOR COMPUTER-RUN  ROW  Part 2  Definition  NAMES  Objective function  PRO FT F 1 R P 1 -.  .•'-"D. F i r P e e l e r s FIRP4- •' ' FIRSP  D.  F i r - Suitable for P e e l i n g  HEMBM  Hemlock-Balsam Mix  SPRUM  Spruce M i x  V1EX-. V2EX Veneer rows, .•  V9TY  VOTV  veneer  specified by grade,  by species, b y length and by thickness  ''  SL3EB . SL4EB  M a r k e t l i m i t f o r s a l e of p l y w o o d p a n e l s ,  panels  '.•specified b y t h i c k n e s s , SLOEB  by length and b y grade  SL1TK SR2ED  panel sale contractual committment, specified by grade,  LTLTH  Lathe capacity  L T DRY  Dryer  capacity  LTPRS  Press  capacity  Li T S A N  Sander capacity  panel  length and thickness  APPENDIX - VI I -S P A U S E $JOB  MG UN-T—TAPE 19077  15  -SP-AGE-  -2-5-  I 9  I  ; L  <' 8. " G  —  L E E MING  S T I ME  HYE  • Ol-  THESIS  TT ~Zl  SDISK  S.SUlOt1000  SDISK  S.SU13»2500  _$.SWI-T-GHr  INSTRUCTION  -S-.-S U0-2-»-S-.-S U4-3-  $LP40 ASSIGN  GRT=S.SU05»MED=S.SU10,ATAPE=S.SU04. -B^-A-P-E^.^U-0-3-»4^T-AP-E^  INPUT FILE  S0.URCE = F I L E 1 / S . S I N 1 » I 0 E N T = D A T A 1 .  FILE1 •—OA-T-A  T-N-P-U-T-  END*** SET  OBJ=PROFT,RHS=RHS01  -NORMAL— OUTPUT ENDLP -  IJ  APPENDIX -SP-AUSE$JOB  V I I  INSTRUCTION  -MOUNT-TAPE 19077  L E E MING  $T I ME  250  -SP-AGE-  -2-5-0-  HYE  SDISK  S.SU10.1000  SDISK  S.SU13»2500  -SSWI-T-eH-  -S-.-S U O-l-t-S-.-S U-l-2-  SSWITCH  S.SU02tS.SU13  THESIS  SLP40 -ASSIGN-  -£>L-G>G R-T-=-S .-S U O 5-»M r?D«-S-,-&U10^-AT-A-RE=^5-»-SU04-»-B T A P E =S . S U 0 3 »FTAPE=S.SU13»UTAPE=S.SU12.UNITS  RESTART -SE-T SETSW.  S0URCE=DATA1/GRT - 0 B J = PROF-T-»-R H S - R - H S O - 1 NFS=HELP  NORMAL -SAVE OUTPUT ENDLP  -K>EN-T-=-5-A-VE-l-  II  APPENDIX -$ P A U S E $JOB  VII  INSTRUCTION  MOUNT—TAPE 19077  LEE  STIME  150  -SP-AGE-  -1-00-  MING  HYE  SDISK  S.SU10»1000  SDISK  S.SU13»2500  _$.SWI-T-GHSSWITCH  THESIS  -S-.-S U 04--»-S-.~S U -1-2S.SU02  »S.SU13  SLP40 -A-S-SI-GN-  -O L-DG R-T-= S-.-S U 0 5-»-M ED«-S-r5y-l-G-,-A-T-A-P-E=^-.-SU0-^-rB T A P E =S . S U 0 3 » F T A P E = S . S U 1 3 » U T A P E = S . S U 1 2 . U N T T S  RESTART -RE-ST-0 R E DO. DJ . RHS.RANGING -GO-S-T-.RANG-I-NGOUTPUT ENDLP  S0URCE=DATA1/GRT - S O U R-GE-^S A-V-E-1-/G R-T-  I I I  APPENDIX  VI11 - A  OPTIMUM PLYWOOD PANEL  SALE  ( F i g u r e s e x p r e s s the % of the s a l e o p p o r t u n i t i e s u t i l i z e d i n the o p t i m u m s o l u t i o n )  Panel ness  Thick-  M a r i n e Goody/l. G o o d - 2 G o o d / - ! G o o d - 1 S o l i d G r a d e Select Side Solid Side 2-Side  PART  Solid 1-Side  CementCementSelect Standard F o r m - F o r m - Sheath-Sheath1-Side  (4' x 8") 1/4"  100*  3/8" 1/2" 5/8"  80 100 100  0*  0 0  0  100 100  0* 100  0* 0 0  Q  0* 0* 0 100  0* 0 0  1  2-Side  ing  ing  0  5  0*  0*  0*  0*  0 0* 0*  0  65 100  100  100  100  85  100  -  -  -  -  -  -  -  3/4"  100  100  100  100  100  100  100  7/8"  -  -  100  100  100  100  100  100  100  -  -  100  100  100  100  100  100  100  -  -  100  100  100  100  100  100  100  100  100  100  100  100  100  100  11/16"  1" 1  1/8"  1  1/4"  * T h i s d i f f e r s f r o m that i n A p p e n d i x V l l l - B  i n that it a s s u m e s  that t h e r e i s n o p r i o r c o m m i t m e n t to s e l l t h i s p a r t i c u l a r p a n e l .  co  A P P E N D I X VI11 - A OPTIMUM PLYWOOD PANEL  SALE  ( F i g u r e s e x p r e s s the % of the s a l e o p p o r t u n i t i e s  utilized  i n the o p t i m u m s o l u t i o n )  Part 2  M a r i n e Good/-I G o o d - 2 G o o d / - l G o o d - 1 S o l i d  Solid  Grade  1-Side Forra-i F o r m  Select  Side  Solid  Side  2-Side  C e m e n t C e m e ntS e l e c t 1-Side  1 00  -  Standard  Sheath-Sheath-  2-Side  ing  ing  -  100  1  -  100  0  -  100  0  0  0  0  0  0  100  0  0  0  0  0  100  0  0  100  0  100  100  100  100  30  100  -  -  100  100  100  100  100  100  100  -  -  100  100  100  100  100  100  100  -  -  100  100  100  100  100  100  100  -  -  100  100  100  100  100  100  100  -  -  100  100  100  100  100  100  100  -  -  100  100  -  220 A P P E N D I X VI11 - B OPTIMUM PLYWOOD PANEL SALE (in units of 250 panels each) 4' x 8' Plywood Kinds  Market Demand  Part 1  4' x 10' Amount Supplied  Market Demand  Amount Supplied  Marine Grade 1/4" 1.77 3/8" 1.72 1 /2" 0. 90 5/8" 0. 08 3/4" 0. 84  1. 77 1. 36 0.90 0. 08 0. 84  2.0 0. 97 0.4  2. 0 0. 97 0.4  Good/Select 20. 72 1/4" 3/8" 5. 75 1/2" 9. 25 5/8" 0. 4 33. 2 3/4"  0 0 9. 25 0.4 33. 2  -  -  Good- 2--Side 32. 66 1/4" 7. 70 3/8" 21. 33 1/2" 5/8" 6. 59 3/4" 61.98 7/8" 2. 64 1" 2. 2 1 1/8" 1. 1 1 1/4" 1. 1  4. 0* 0 4. 0* 6. 59 61.98 2. 64 2. 2 1. 1 1. 1  0. 62 0. 79 0.7 0. 58 2. 29 0. 22 1. 14 0. 22 0. 22  0 0 0 0. 58 2. 29 0. 22 1. 14 0. 22 0. 22  Good/Solid 1/4" 67. 26 37. 11 3/8" 86.42 1/2" 49. 01 5/8" 204.74 3/4"  4. 0* 0 0 0 204.74  1. 5 1. 2 3.7 0.98 14. 75  0 0 0 0.98 14. 75  -  -  -  -  -  A P P E N D I X VI11 - B OPTIMUM PLYWOOD P A N E L SALE  Plywood Kinds  (in units of 250 panels each) Part 2 4' x 8' 4' x 10' Market Amount Market Amount Demand Supplied Demand Supplied  Good/Solid 7/8 " 1" 1 1/8" 1 1/4"  0. 22 8. 8 0. 22 0. 22  0. 22 8. 8 0. 22 0. 22  Good- 1-Side 1/4" 2013, 8 3/8" 717. 8 80. 33 1/2" 5/8" 365. 8 3/4" 1055. 2 7/8" 8. 8 1" 13. 2 1 118" 2. 2 1 1/4" 2. 2  20. 0* 20. 0* 0365. 8 1055.2 8. 8 13. 2 2. 2 2. 2  Solid-2- Side 1/4" 58. 5 3/8" 47. 7 124.3X 1/2" 5/8" 61. 4 3/4" 293. 4 4. 4 7/8" 1" 13. 2 1 1/8" 2. 2 1 1/4" 2. 2  4. 0* 0 0 0 293.4 4.4 13. 2 2. 2 2. 2  Solid-1- Side 1/4" 966. 8 3/8" 269. 4 1/2" 258. 7 5/8" 121. 8 3/4" 522.9  0 20* 478. 5 522.9  0. 22 1. 90 0. 22 0. 22  0. 22 1.90 0. 22 0. 22  96.27 . 44. 0 47.29 14. 12 75. 11 0. 22 2.96 0. 22 0. 22  0 0 47. 29 14. 12 75. 11 0. 22 96 0. 22 0. 22  3.7 8.2 18. 7 7. 1 28. 8 1. 32 2.0 1.3 1.3  0 0 0 2. 0 28. 8 1. 32 2. 0 1. 3 1. 3  16. 57 7. 97 10. 29 5. 92 26.48  0 0 10. 29 5. 92 26. 48  1  222 APPENDIX V l l - B OPTIMUM PLYWOOD P A N E L SALE  Plywood Kinds  (in units of 250 panels each) 4' x-8' 4' x 10' Market Amount Market Demand Supplied Demand  Solid- 1-Side 7/8" 2.2 1" 2.2 1 1/8" 2.2 1 1/4" 2.2 Cement F o r u m One-Side 5/8" 53.57 11/16" 372.12 3/4" 50.87 Cement F o r m Two-Side 5/8" 33.32 11/16" 52.86 3/4" 24.24 Select Sheating 1/4" 3/8" 1/2" 5/8" 3/4" 7/8" 1" 1 1/8" 1 1/4"  1243.6 553.5 516.7 493.3 502.2 0.22 0.22 0.22 0.22  Standard Sheathing 1/4" 2538.8 3/8" 1472.0 1/2" 724.5 5/8" 451.2  2. 2 2. 2 2. 2 2. 2  53. 57 372. 12 50. 87  33. 32 52. 86 24.24 .  Part 3 Amount Supplied  0.66 0. 88 0.66 0. 66  0.66 0. 88 0. 66 0. 66  -  -  -  -  -  -  -  -  -  0 4. 0* 4. 0* 420.9502. 2 0. 22 0. 22 0. 22 0. 22  28. 1 34. 37 27.95 28. 14 34. 23 0. 22 0.22 0. 22 0. 22  28. 1 34. 37 27.95 28. 14 34. 23 0. 22 0. 22 0. 22 0. 22  75. 6 20* 20* -0  72. 6 183. 75 50 27.04  0. 7 0 4* 27,04  223  APPENDIX •OPTIMUM  PLYWOOD  (in u n i t s 4'  x  VI11  of  250  -  B  PANEL  panels  SALE  each)  8'  4'  Part x  4  10'  Plywood  Market  Amount  Market  Amount  Kinds  Demand  Supplied  Demand  Supplied  Standard Sheathing 3/4"  325.55  7/8"  0. 22  0. 22  0. 22  0. 22  1"  325.55  1  1/8"  0. 22  0. 22  1  1/4"  0. 22  0. 22  *  These In fact, No  are  the  these  33. 0. 0. 0. 0.  9 22 22 22 22  contractual are  s u c h panel is  sold  33. 9 0. 22 0. 22 0. 22 0. 22  sales  at a  commitment  -  loss.  p r o g r a m m e d for  i n the  L . P .  model.  APPENDIX  VIII-C  MARGINAL PROFITABILITY  OF PLYWOOD  PANELS  ( M a r g i n a l profit contribution e x p r e s s e d as % of p a n e l s a l e p r i c e ) (a) MG G/Sel  (b) 1/4"  43  21  -  *  s  G2S  (a) 3/8  (b) II  (a) (b) 5/8"  33  56  58  69  *  -  *  17  *  27  *  -  -  13--  G/Sol  -  -  -  G-l-S  -  -  -  S-2-S  -  S-l-S  -  CF-l-S  *  8  (a) (b) 11/16" •A*  *P  'P  o> -P  'P*  "P  -  *  *  'p  CF-Z-S*  *  'P  Sel/Sh 0  14  -  8  'p  9  -  (b)  3/4"  1  39  'P*  *  *  >!<  39  27  46  49  48  47  62  'P  >!<  (b) 1/8"  •A*  .A*  "P  «A#  'P  •JA  'P  *p  *A#  *"P  •A*  *p  (a)  (b)  1  1/4"  'p  *v*  'p  -fc  62  67  65  o> *p  >P*  15  28  37  44  43  45  57  63  64  64  10  10  'p  o> -p  29  31  47  41  49  49  63  64  67  66  'p  10  23  34  44  40  45  56  60  63  64  *"p  20  31  42  48  45  49  60  64  65  66  *P  28  >\<  *  *  *p  o> *p  -.1«*p  -  10 *  24  'P  16  *  32  9  -  23  *  30  31  -  6  *  26  28  •J*  •"P  10'  P a n e l s whose m a r g i n a l profit contribution -  * P a n e l s n o t p r o g r a m m e d i n the  *  (b) (a)  85  11  -  (a) 1"  (a) (b) 7/8 !"  3  (a) 4' x 8' (b) 4' x  (a)  -  'p  -  Std/Sh  (a) (b) 1 /2"  model  $0  34  'P  *  *A>  *p  *  'p \  *  *  *  *v  31  42  50  49  49  55  55  57  35  36  41  42  51  5 1  56  53  >'<  A P P E N D I X VHI-C MARGINAL PROFITABILITY OF UNPROFITABLE  Part 2 PANELS  (loss expressed as % of the sale price of the panel) 1/4"  4' x 8' Good/Select Good-2-Side Good/Solid Good-l-Side Solid-2-Side Solid-l-Side Sel-Sheathing  33. 5 120. 6 183.5 77,1 225.2 167.1 52. 0  Good/Select Good-2-Side Good/Solid Good-l-Side Solid-2-Side Solid-l-Side Sel-Sheathing Std-Sheathing  74. 2 31. 3 62. 3 25.3 8 3.3 53.4 28.4 32. 1  Good-2-Side Good/Solid Good-1-Side Solid-2-Side Solid-l-Side Sel-Sheathing Std-Sheathing  8.2 28. 1 8.3 41.2 21.7 20. 5 45. 0  Good/Solid Solid-2-Side Std-Sheathing  4.8 14.2 0.7  4' x 10' 58.8 67.3 34.0 67.2 33.6  3/8' 20.9 27".-7 14.1 27.8 14.0 10. 2  1/2'  5/8'  0.7 6.0 6.2 12. 5  A P P E N D I X DC PLYWOOD PANEL SALE PRICE (per 250 panels) G/Sel  MG 4'x8' 1 /4" 3/8" 1 /2" 5/8" 3/4" 7/8" 1"  907.67 1400.61 2024.65 2707.10 3645.06 • -  CF1 4'x8' 5/16" 3/8" 1/2" 5/8" 11/16" 3/4" 7/8" 1" 1 1/8" 1 174"  357.75 585. 41 891.37 1182.10 1640.06  -  -  CF2  -  -  -  -  -  715. 00 920. 00 1080. 00  780.00 1000.00 1200.00  G/Sol  G2S 257. 75 485. 41 771. 37 1052. 10 1490. 06 2019. 00 2679.07  227.65 440. 25 . 711. 16 978. 85 1399. 75 1915. 78 2558. 68  Sel-Sh  Std-Sh  188. 268. 468. 677.  75 09 29 75  150. 12 219.84 403. 92 550. 00  1008. 06 1366. 50 1837.33 2402. 10 3281. 50  911. 50  -  G1S 197. 54 395. 09 650. 96 907.60 1309.44 1812.57 2438. 25  Part 1  S2S 222.00 431. 78 699.87 966. 30 1382. 81 1896.42 2536. 08  SIS 191. 89 386. 62 639.67 893. 90 1292. 50 1793. 21 2415. 50  1256. 21 1708. 67 2247.70 3088. 50  ro  A P P E N D I X IX PLYWOOD P A N E L SALE PRICE (per 250 panels) MG  G2S  G/Sol  G1S  1124.39 1617.33 2277.53  474. 47 702. 13 1024. 25 1304. 98 1779.02 2307.96 2999. 83 3978. 15 5389.25  444.37 656. 97 964. 04 1232. 72 1688.71 2204.74 2879. 43 3833. 65 5208.62  414. 26 611. 81 903. 84 1160. 48 1598. 40 1841.47 27 59.00 3689.25 5028. 00  Sel-Sh  Std-Sh  360. 35 439.69 674. 21 883. 67 1297. 01 1655. 46 2212. 97 2777. 74 3657. 14  321. 72 39 i . 44 609.84 755. 92 1200. 46 1545. 17 2084. 31 2623. 34 3464. 14  Part 2 S2S  SIS  4'xlO' 1 /4" 3/8" 1/2" 5/8" 3/4" 7/8" 1" 1 1/8" 1 1/4"  -  438. 72 648.50 952. 75 1219.18  1671. 77 2185. 38 2856. 83 3806. 65 5174. 75  408. 62 603. 34 892. 55 1146. 78 1581. 46 2082. 17 2736. 25 3662. 02 4994. 12  4'xlO' 5/16" 3/8" 1/2" 5/8" 3/4" 7/8" 1" 1 1/8" 1 1/4"  ro ro  228  APPENDIX X - A OPTIMUM L O G INPUT  Log  Kinds  Total Supplied (10, 000 F B M )  Total Called (10, 000 F B M )  Increase in total net p r o f i t (per unit i n c r e a s e i n supply)  $ F I R . . P e e l e r #1  55. 1  4. 6  F I R P e e l e r #2  364. 2  364. 2  F I R P e e l e r #3  1318. 6  564. 6  F I R P e e l e r #4  364. 2  9. 1  53. 80  F I R - suitable 7. 2 for p e e l i n g  1120.0 294. 0  F I R - S a w l o g #2  794. 0  F I R - S a w l o g #3  371.5  F I R - Interior  977. 6  Hemfock-Balsam Mix 2 Spruce-mix 1  263.0 . 700. 6  Footnote: 1 & 2 - F o r definition,  371. 5  32. 90  977. 6  2 0 3 . 91  263. 0  219- 13  421. 5  see T a b l e I V .  229  APPENDIX X-B OPTIMUM LOG-PEELING AND VENEER  UPGRADING  ( A m o u n t i n u n i t s o f 10, 000 F B M each)  Veneer Up-Grading Level*  A m o u n t P e e l e d at  Log  .104"  Kind  02  F i r - P e e l e r #1  01  F i r - P e e l e r #2  02  -  .130"  Thickness .171"  4. 6  Total  Used % of  Amount  Supply  4.6  0.9  75. 8 287.2  364. 2  100  42.8  1.2  01  F i r - P e e l e r #3  564. 6  564. 6  02  F i r - P e e l e r #4  9. 1  9. 1  2. 5  01  Fir-SFS  7.2  7. 2  0. 6  01  F i r - S a w l o g #2  01  Fir-Sawlog  294  294 355.7  #3  02 01  01  371.5  100  977.6  100  100  15. 8 Fir-Interior  945. 1  02 01  37. 0  32. 5 Hemlock-Balsam Mix  263  263  Spruce M i x  421. 5  421. 5  * F o r definition  see page  104  chapter  VII  60. 2  230  APPENDIX X - C CONDITION F O R PURCHASING A / B MIX V E N E E R  4' x 8'  4' x 10'  . 104"  . 130"  . 104"  . 130';'  4150  4150  4150  4150  1730  1354  1249  1846  $2420  $2796  $2901  $2304  M a r k e t p r i c e per c a r l o a d (50, 000 sq. ft-3/8") Necessary price * reduction  *  T h i s is the reduction in the total net profit of the business if 1 c a r - l o a d (50, 000 sq. ft. 3/8") of such veneer were p u r c h a s e d i n 1967.  Note: The p r o c e s s i n g costs for the four different kinds of veneer were estimated at $421, $359, $401 and $342 per c a r - l o a d , respectively.  A P P E N D I X XI OPTIMUM P A N E L CONSTRUCTION  Part 1  ( v e n e e r t h i c k n e s s i n t h o u s a n t h s o f an i n c h ) OPTIMUM STRUCTURE  4'x8'  No  Plywood Kind 1/4"  Face  of  Marine G r .  No  &  Plies  Back  3  Good/Select  -  104  Good-2-Side  3  104  Good/Solid  3  104  Good-1-Side  3  104  Solid-2-Side Solid-l-Side  -  2nd B E S T S T R U C T U R E of  Centre -  Core  Plies  Face & Back  3rd B E S T No of  Centre  Core  Plies  STRUCTURE  Face & Back  Centre  3 $  Core  .2 $  130  130  3  104  -  -  Sel-Sheathing  3  104  -  104  Std-Sheathing  3  104  Marine Grade 3  130  3  104  130  3  104  130  3  104  104  4.8  3  104  130  3  104  104  3.8  3  130  3  130  171  0  130 130  86. 2  130  104  3/8"  Good/Solid  -  Good-1-Side  3  Good/Select Good-2-Side  -  -  -  130  0  Soli d-2-Side  -  Solid-l-Side  3  130  Sel-Sheathing  3  104  Std-Sheathing  3  -  130  -.  171  -  0  3  130  171B 171B  3  130  171  0  3  130  171  3  130  171B  0  -  3  130  171  3  130  171B  0  171  3  130  171B  171B 130  3  104  171  17 I B  3  104  171B  -  3 3  130  130  130  171  •  -  67. 7 0  0. 1 0. 7 76.  1  OJ  A P P E N D I X XI OPTIMUM P A N E L CONSTRUCTION ( v e n e e r t h i c k n e s s i n t h o u s a n t h s o f an i n c h )  Part 2  OPTIMUM STRUCTURE  2nd B E S T S T R U C T U R E  3rd B E S T  No  No of  Face  No  Plies  Back  Plywood Kind  Face &  of Plies  Back  Centre Core  &  of  .&  Centre Core  STRUCTURE  Face  Plies  Back Centre Core  104 104*  130 104*  130 171*  5  130  130;  104  5* Good/Select  5  104  171  104  5  104  130  130  5  104  171B  Good-2-Side  5  104  130  130  104  171  104  5  104  -  -  -  5 5  104  130  130  5  130  171B 104  5  130  130  130  130 130  5  5  104 104  5  130  130  5  130  130  104  5  5  Marine Gr  5  -  3 $  $  393. 4 104 104  2.9 0.4  Solid-2-Side  -  Solid-1-Side  5  104  Sel-Sheathing  5  104  104  104  Std-Sheathing  5  104  104  104  Marine Gr Good/Select  5 5  104 104  171 171  171 171  7 5  104 104  104 171B  104 171B  5  130 104  Good-2-Side  5  130  130  171  5  104  171  171  5  104  0. 3  5  104  171B 171B  171B  171  171B  0.7  Good/Solid Good-1-Side  -  -  2  7.4 2. 5  104  0.7  104  130 171  104 104  0.4 2.6  104  171  104  130  171 1 8 5 . 7 6 9 8 . 5 0. 4 171B 0.4  0. 4  5/8"  Good/Solid  -  Good-1-Side  5 5*  -  -  -  5  104  171  5  104  171B  171B  5  104  171  171B  0.4  -  5  104  171  171  5  104  171B  171B  0.3  5  104  171B  171B  5  104  171  171B  0.7  104  171  171  130*  130*  171*  Solid-2-Side  -  Solid-1-Side  5  104  171  171  5  130  130  171  -  -  171:-  32.9 0.4  0. 4  A P P E N D I X XI O P T I M U M P A N E L CONSTRUCTION (veneer thickness in thousanths of an inch) O P T I M U M S T R U C T U R E 2nd BEST S T R U C T U R E 3rd BEST S T R U C T U R E No Face No Face No Face of of of & & & Back Centre Core Back Plies Plies Centre Core P l i e s Back Centre Core 1  4'x8' Plywood Kind _ • . ..5/8" Cement F o r m 1-side Cement F o r m 2-side Sel-Sheathing Std-Sheathing 11/16" Cement F o r m 1-side Cement F o r m 2-side 3/4" Marine Grade Good/Select Good-2-Side Good/Solid Good-l-Side Solid-2-Side Solid-1-Side  1  $  ^ 3  7  $  2  5  104  104  171B  5  130  130  130  5  104  104  171  15.3 26.4  5 5 5 5  104 104 130 104  130 104 130 104  104 171B 130 171  5  130  171B  171B  5  130  171  171  1.9 113. 2  5  130  130  130  5  104  104  171  144. 1 126  -  -  •*  -  5  104  171B 171B  5  104  171  171  5  130  171  130  5  104  130  104  5  130  171B  171B  5  130  171B  171  7 7 7 7 7 7 7 '7 7  104 104 104 104 104 104 104 104 104  171 171B 130 130 130 171 171B 171 171B  104 104 130 130 130 104 104 104 104  7 7 7 7 7  104 104 104 104 130  130 130 171 171 104  130 130 104 104 130  7 7 7 7  104 104 104 104  171 171B 171B 171B  104 104 104 104  701 0 0. 01 0.4181.9 0.4 0.4 47.6 12.8  7  104  130  130  7  104  104  130  19.7  3.0  7  104  171  104  7  104  130  130  0  12.8  1.5  2.5 2.5  A P P E N D I X XI OPTIMUM PANEL  CONSTRUCTION  ( v e n e e r t h i c k n e s s i n t h o u s a n t h s of a n i n c h )  4'x8' Plywood Kind  OPTIMUM STRUCTURE  2nd B E S T S T R U C T U R E  No  No of  Face  of & Plies Back  Centre Core  1  Face  & Plies Back  Centre  Core  Part 4  3rd BEST S T R U C T U R E No Face of & Plies Back  Centre Core  1  $  3  $  2  3/4" Cement-Form 1-side Form  7  130  171B  171B  7  130  171  171B  7  130  171B  171  0. 3  1. 1  2-side Sel-Sheathing  7  104  130  104  7  130  171B  171B  7  130  171  171  1. 1  5  130  171B  171B  5  130  171  171B  90.9 1. 0c  Std-Sheathing 7/8"  5  130  171B  17 I B  5  130  171  171B  5  130  171  171  1. 4  Good-2-Side Good/Solid  7 7  130  171B  130 130  171 171  130 130  7 7  130  104  130  171B 171  190 2. 2 180.22.2  Good-l-Side  7  171B 171B  7 7  104  130 130  130 130 130  7  130  171  130  7  104  130  171B  190  171  180. 2 2. 2  Cement  -  1. Oi  2. 2  Solid-2-Side  7  130  171B  130  7  130  171  130  7  104  130  Solid-l-Side  7  130  171B  130  7  130  171  130  7  104  130  171B  190  104  171B  0  104  171B  0 221. 5  2. 2 67.7  Sheathing  7  130  130  130  7  104  104  171  7 :  104  Std-Sheathing  7  130  130  130  7  104  104  171  7  104  9  104  171  104  9  104  171B  104  1. 1  171B  104  4. 3  Sel  i I  11  Good-2-Side Good/Solid  9  104  171  104  9  104  Good-1-Side  9  104  171  104  9  104  171B  104  1. 1  104  9  104  171B  104  1. 1  Solid-2-Side  9  104  171  Solid-1-Side Sel-Sheathing  9 7  104  171  104 171B  130  171B 130  104  171B  9 7  104  104  171  7  130  130  171B  4. 2 2 0 8 . 5  St d - S h e a t h i n g  7  130  130  171  7  130  171B  171B  7  130  130  171B  2. 0  1. 0 2. 1  A P P E N D I X XI OPTIMUM P A N E L CONSTRUCTION ( v e n e e r t h i c k n e s s i n thousanths of an i n c h ) 4"x8' Plywood Kind 1  No  Face  & Plies Back Centre Core of  Part 5  No  Face  No  Face  of  & Back  of Centre Core  & Back Centre Core  $  104  171B  130  9  130  104  171B  260  Plies  Plies  3  $  2  1/8"  Good-2-Side  9  104  171  130  9  1. 1  Good/Solid  9  104  171  130  9  104  171B  130  9  130  104  171  278  1. 1  Good-1-Side  9  104  171  130  9  104  171B  130  9  130  104  171  1. 1  Solid-2-Side Solid-1-Side  9  104  130 130  9 9  171B  130  9  130  104  171 171  104  9  104  171B  130  9  130  104 104  171 171  269 77 268  104  171  9  104  104  171B  1. 5  132  9  104  104  171B  1.4  276. 3  1. 1 1. 1  Sel-Sheathing  9  130  130  130  9  104  Std-Sheathing  9  130  130  130  9  104  104  171  Good-2-Side  11  104  11  104  171B  104  11  130  130  130  9. 5  1. 1  11  104 104  171  Good/Solid  171  104  11  104  171B  104  11  130  130  130  1. 1  Good-1-Side  11  104  171  104  11  130  130  130  11  104  171B  104  9. 5 0. 4  0. 6  Solid-2-Side Solid-1-Side  11  104  171  11  17 I B  104  11  130  130  130  11  104 130  130  130  11  104  171B  104  9. 5 0. 4  1. 1 0. 6  9 9  130 130  130  171B  9  104  104  171B  132  1. 4  60  0. 7  1  1/4"  Sel-Sheathing :Std-Sheathing  11  104  171  104 104  9 9  130 130  130  171  130  171  130  171B  9  130  104  130  CO OJ Ul  236  Footnotes  1.  to A p p e n d i x X I  panel construction alternatives  ( o r the p a n e l i t s e l f ) w h i c h  w e r e not s e l e c t e d as o p t i m u m  2.  T h i s i s the m a r g i n a l d e c r e a s e i n the t o t a l n e t p r o f i t f o r p r o d u c i n g 250 p a n e l s u s i n g the 2 n d b e s t c o n s t r u c t i o n o f the o p t i m u m o n e .  T h i s indicates (in a m a r g i n a l sense)  the s u p e r i o r i t y of the o p t i m u m c o n s t r u c t i o n to the best  3.  instead  second  construction.  This represents  the d i f f e r e n c e  i n the m a r g i n a l l o s s of  t o t a l n e t p r o f i t f o r p r o d u c i n g 250 p a n e l s b e t w e e n u s i n g the s e c o n d b e s t a n d the t h i r d b e s t p a n e l  *  constructions.  w h e r e m o r e t h a n one p a n e l c o n s t r u c t i o n s l a y i n g up a p a n e l , of i m p o r t a n c e .  a r e u s e d for  they are a r r a n g e d in descending  order  237  APPENDIX  XH  HISTORY O F T H EL P R U N O NT H E I B M 7044  The  COMPUTER  L . P . m o d e l f o r the C a s e C o m p a n y was s o l v e d o n the  I B M 7044 c o m p u t e r s y s t e m at the U n i v e r s i t y of B r i t i s h C o l u m b i a . In o r d e r to b e s t m e e t the n e e d s o f the l o c a l c o n d i t i o n s , s y s t e m is being run O F F - L I N E . a n d the O N - L I N E  PRINTER  T h i s m e a n s that the C A R D  a r e no l o n g e r a v a i l a b l e to the  S y s t e m ( w h i c h w a s i n f a c t e x p e c t e d to b e r u n O N - L I N E ) units.  the U B C  T A P E units a r e u s e d i n their p l a c e .  READER  LP-III  as w o r k i n g  This therefore  leaves  o n l y t h r e e o f the f i v e t a p e u n i t s a v a i l a b l e f o r the L P - I I I s y s t e m u s e r to c h o o s e as w o r k i n g u n i t s .  It b e c o m e s n e c e s s a r y  f o r the p r o g r a m  u s e r to u s e s o m e D I S K u n i t s as w o r k i n g u n i t s .  The  d i f f e r e n c e i n the t o t a l c a p a c i t y of the D I S K u n i t s a n d  the T A P E u n i t s m a k e s i t n e c e s s a r y to u s e two s e p a r a t e r u n s to a r r i v e at the o p t i m a l s o l u t i o n f o r a n L . P . p r o b l e m of the p r e s e n t  magni-  tude.  The  1  f i r s t r u n ^ i s m a i n l y f o r the p u r p o s e of r e a d i n g i n the  R e f e r to A p p e n d i x "VII, I n s t r u c t i o n I.  238  c a r d d a t a onto the G R T T a p e i n b i n a r y f o r m .  A T A P E unit is b e i n g  u s e d f o r the c a r d i n p u t b e c a u s e o f the s i z e o f the d a t a i n p u t . However, (see  i n a d e q u a t e D i s k c a p a c i t y h a s b e e n p r o v i d e d f o r the  ASSIGN card).  The U T A P E overflows  after  123  c a u s i n g a t e r m i n a t i o n o f the J O B w i t h a s u c c e s s f u l  iterations,  s a v i n g o f the  i n p u t d a t a o n the G R T T A P E b u t not the c o m p u t e d r e s u l t s  (unless  t h e J O B w a s f i r s t m a n u a l l y i n t e r r u p t e d b y the o p e r a t o r w i t h S e n s e S w i t c h #2,  R e a d y R e a d e r and P u s h Start').  UTAPE  'Restore  A n d t h o u g h the  p u r p o s e o f t h i s r u n i s m a i n l y to i n p u t the d a t a onto the G R T T A P E , the N O R M A L A g g e n d u m w a s a l s o c a l l e d b e c a u s e the L P - I I I S y s t e m i s n o t a b l e to I N P U T the d a t a u n l e s s N O R M A L w a s a l s o c a l l e d .  2 The  second run  u s e s a D I S K U N I T f o r t h e c a r d i n p u t a n d so  the f r e e d T A P E U N I T i s b e i n g u s e d f o r the U T A P E . now c a l l e d i n f r o m the O L D G R T The  TAPE.  L . P . m o d e l s o l v e d h a d 37 5 r o w s ,  structural vectors (columns)  Input d a t a i s  229 s l a c k s ,  a n d a % d e n s i t y of 1. 4332,  7 50  including  slacks.  The  total effective t i m e u s e d is s u m m a r i z e d as  R e f e r to A p p e n d i x V I I , I n s t r u c t i o n II.  follows:-  239  Minutes O p t i m u m Solution T o R e c a l l Input D a t a f o r R E S T A R T To Restore Saved Computations RHS.  R A N G I N G (all rows)  C O S T : R A N G I N G (whole b a s i s ) D O . D J (all non-optimal columns)  Total time  The  214. 05 0. 63 1.42 16.90 102. 40 4. 60  340. 00  o p t i m u m v a l u e o f the t o t a l n e t p r o f i t c o m p u t e d f o r the  y e a r w a s $1, 622,  i.  315.  

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