UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Physical distribution analysis for the traffic manager Schmirler, David Joseph 1964

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1964_A4_5 S3.pdf [ 9.17MB ]
Metadata
JSON: 831-1.0102392.json
JSON-LD: 831-1.0102392-ld.json
RDF/XML (Pretty): 831-1.0102392-rdf.xml
RDF/JSON: 831-1.0102392-rdf.json
Turtle: 831-1.0102392-turtle.txt
N-Triples: 831-1.0102392-rdf-ntriples.txt
Original Record: 831-1.0102392-source.json
Full Text
831-1.0102392-fulltext.txt
Citation
831-1.0102392.ris

Full Text

PHYSICAL DISTRIBUTION ANALYSIS FOR  THE TRAFFIC MANAGER  A Thesis Presented t o the F a c u l t y of Commerce and B u s i n e s s  Administration  U n i v e r s i t y of B r i t i s h Columbia  In P a r t i a l F u l f i l l m e n t of the Requirements f o r the Degree Master of B u s i n e s s  Administration  by David Joseph May  Schmirler  1964  ACCEPTANCE  T h i s T h e s i s has been accepted i n p a r t i a l fulfillment  o f the requirements f o r the Degree o f  Master of B u s i n e s s A d m i n i s t r a t i o n i n the F a c u l t y o f Commerce and B u s i n e s s A d m i n i s t r a t i o n o f the U n i v e r s i t y of B r i t i s h  Columbia.  Date  Dean, F a c u l t y of Commerce and B u s i n e s s A d m i n i s t r a t i o n  Chairman  In  presenting this thesis i n p a r t i a l fulfilment of  the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t available for reference and study,  freely  I further agree that per-  mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It i s understood that, copying or publi-  cation of this thesis for financial gain shall not be allowed without my written permission*  Department of  ^o-iv^MiMJLy  &s~^JL  The University of B r i t i s h Columbia, Vancouver 8, Canada Date  /  W  l  /f*4.  .  ABSTRACT The  p h y s i c a l d i s t r i b u t i o n concept r e c o g n i z e s the  i n t e r r e l a t i o n s h i p s between t r a n s p o r t a t i o n , handling,  materials  warehousing and the other p r o c e s s e s that are  i n v o l v e d i n the p h y s i c a l flow of t r a f f i c of raw m a t e r i a l s , through p r o d u c t i o n facilities,  t o the f i r m ' s customers.  concept i s that i t i s the t o t a l cost processes,  from the source  and d i s t r i b u t i o n The essence of the of the s e v e r a l  r a t h e r than the cost of i n d i v i d u a l processes,  that must be taken i n t o account i n d e c i s i o n s i n which there  are a l t e r n a t i v e s f o r the p h y s i c a l movement of  materials  and p r o d u c t s .  i n v o l v e s the f o r m u l a t i o n for  traffic  Physical d i s t r i b u t i o n analysis and comparison o f the a l t e r n a t i v e s  flow.  T h i s t h e s i s i s concerned p r i m a r i l y w i t h the development of a procedure f o r p h y s i c a l d i s t r i b u t i o n a n a l y s i s that may be u s e f u l i n the f o r m u l a t i o n  of d e c i s i o n s that are  w i t h i n the T r a f f i c Manager's sphere of r e s p o n s i b i l i t y . I n order  t o i d e n t i f y the nature of these d e c i s i o n s and i n  order t o develop a s u i t a b l e framework f o r the T r a f f i c Manager's analyses,  the second chapter d e s c r i b e s  the major  d e c i s i o n s i n which p h y s i c a l d i s t r i b u t i o n p r i n c i p l e s should be  a p p l i e d ; r e l a t e s these a p p l i c a t i o n s t o successive  2 planning  i n t e r v a l s ; and  considers  the  scope of these  d e c i s i o n s i n terms of the a u t h o r i t y that i s necessary for their The  implementation. author suggests that the major a p p l i c a t i o n s of  the p h y s i c a l d i s t r i b u t i o n concept i n c l u d e d e c i s i o n s r e l a t e d to the  s p a t i a l a l l o c a t i o n of  c a p a c i t i e s , intermediate-term i n the f i x e d f a c i l i t i e s short-term  for physical distribution,  and  the u t i l i z a t i o n  and  of  physical distribution f a c i l i t i e s .  Of these a p p l i c a t i o n s , i t i s only the  short-term  d e c i s i o n s that are l i k e l y to be made by the Manager.  production  d e c i s i o n s i n v o l v i n g changes  d e c i s i o n s concerning  e x i s t i n g production  long-term  Chapters three  to f i v e ,  Traffic  t h e r e f o r e , are  w i t h the procedures f o r f o r m u l a t i n g  and  concerned  comparing  short-  term a l t e r n a t i v e s . To  f a c i l i t a t e presentation,  the  author  deals  s p e c i f i c a l l y w i t h the development of a procedure f o r a n a l y s i s f o r two problems -- the orders  out  of the  short-term  day-to-day problem of meeting customer  of i n v e n t o r i e s that are on hand at  b u t i o n warehouses; and  distri-  the problem of a l l o c a t i n g s h o r t -  term output among the f i r m ' s The  physical distribution  plants.  author recommends the  l i n e a r programming  technique as the method f o r s e l e c t i n g the  optimum  3 alternative  f o r each of these problems.  The  application  of t h i s technique i s d e s c r i b e d i n d e t a i l i n Chapter V. The major determinants o f p h y s i c a l alternatives,  the i d e n t i f i c a t i o n of f e a s i b l e  and the development the  distribution  of u n i t v a r i a b l e  alternatives,  costs required  by  l i n e a r programming models are d e a l t w i t h i n Chapters  I I I and  IV.  TABLE OF CONTENTS CHAPTER I.  PAGE  THE PROBLEM AND DEFINITIONS OF TERMS USED The Problem  1  Statement of the problem  3  Importance  3  of the study  L i m i t a t i o n s of the study  4  D e f i n i t i o n s of Terms Used System of p h y s i c a l d i s t r i b u t i o n  6  Method of p h y s i c a l d i s t r i b u t i o n  7  Organization II.  6  of the Remainder of t h i s T h e s i s  .  7  .  9  THE FRAMEWORK AND OBJECTIVES FOR PHYSICAL DISTRIBUTION ANALYSIS E s t a b l i s h i n g the Framework and O b j e c t i v e s f o r Physical D i s t r i b u t i o n Analysis  10  The Role o f the T r a f f i c Manager i n P h y s i c a l D i s t r i b u t i o n Analysis The C r i t e r i a of E f f i c i e n c y III.  24 . . . .  30  THE MAJOR DETERMINANTS OF PHYSICAL DISTRIBUTION ALTERNATIVES  . . . . .  34  . .  38  •  38  Marketing S p e c i f i c a t i o n s Delivery  s e r v i c e requirements of customers  Market dimensions .  40  iv CHAPTER  PAGE Sales forecasts Flexibility  57  i n P r o d u c t i o n and P h y s i c a l  Distribution Facilities  58  Production f a c i l i t i e s  58  . . .  D i s t r i b u t i o n warehouses  IV.  . . . . .  62  T r a n s p o r t a t i o n and h a n d l i n g  62  O r d e r - p r o c e s s i n g and communications . . . .  64  COLLECTION AND PREPARATION OF DATA Flow Diagrams  66 . . . . . .  66  Cost Schedules and Other Data  71  Raw m a t e r i a l s data  72  T r a n s p o r t a t i o n data  73  P r o d u c t i o n data . . . . . . . .  74  Warehousing data  78  Inventory  80  data  O r d e r - p r o c e s s i n g and communications data  .  T o t a l Route Cost  81 82  E s t i m a t i n g the cost o f p h y s i c a l d i s t r i b u t i o n from p l a n t t o warehouse  . •  84  E s t i m a t i n g the cost f o r the f i r s t h a l f of a traffic  route  106  V CHAPTER V.  PAGE  DETERMINING THE OPTIMUM ALTERNATIVE  • 112  L i n e a r Programming Model f o r Output A l l o c a t i o n Decisions  . . . .  114  Demands, c o n s t r a i n t s and c o s t s  116  The Simplex f o r m u l a t i o n  118  . . . . .  C o n v e r s i o n of the Simplex m a t r i x  . . . . .  125  S o l u t i o n through the t r a n s p o r t a t i o n procedure . . . . .  . . . .  132  I n t e r p r e t a t i o n of the optimum . . . . . . .  146  Solution implications  150  . . . .  L i n e a r Programming Model f o r Day-to-day P h y s i c a l D i s t r i b u t i o n Decisions VI.  153  SUMMARY AND CONCLUSIONS  162  Summary  162  Major a p p l i c a t i o n s o f the p h y s i c a l d i s t r i b u t i o n concept The t r a f f i c  . . . .  manager's r o l e  The day-to-day problem  167 . . . . .  The output a l l o c a t i o n problem . . . . . . . Conclusions BIBLIOGRAPHY  163  169 171 178 189  LIST OF TABLES TABLE I. II. III. IV. V. VI. VII.  PAGE Raw M a t e r i a l s Data  73  T r a n s p o r t a t i o n Data  74  P r o c e s s i n g Cost Data  75  P l a n t C a p a c i t y Data  78  Warehousing Data  79  O r d e r - P r o c e s s i n g and Communications Data . • •  82  Inventory Value P e r U n i t  87  VIII.  Volume and Value  of T r a n s i t Inventory  IX.  Volume and Value  of Cycle Inventory  X. XI. XII. XIII.  . . . .  94  Lead Time Volume and Value  98 of S a f e t y Stock  Cost of C a r r y i n g Inventory  102 . . . . .  103  T o t a l V a r i a b l e Cost of P h y s i c a l D i s t r i b u t i o n P l a n t t o Warehouse  XIV.  89  104  Simplex M a t r i x  122  XV.  Simplex M a t r i x a f t e r Step 1  12 7  XVI.  Simplex M a t r i x a f t e r Step 2  129  XVII.  Simplex M a t r i x a f t e r Step 3  130  Transportation Matrix  133  XVIII. XIX. XX.  T r a n s p o r t a t i o n M a t r i x - I n i t i a l Assignment T r a n s p o r t a t i o n M a t r i x - F i r s t Adjustment  . .  135  . . .  143  vii TABLE XXI. XXII.  PAGE T r a n s p o r t a t i o n M a t r i x - Optimum S o l u t i o n . . . P l a n t C a p a c i t y Absorbed i n t h e Transportation Solution  XXIII.  Inventory A v a i l a b i l i t y  . . .  148  and D i s t r i b u t i o n  Record XXIV.  Inventory A v a i l a b i l i t y  156 and D i s t r i b u t i o n  Record XXV. XXVI. XXVII.  145  157  Customer Orders S h i p p i n g and T r a n s p o r t a t i o n Cost Transportation Matrix  158 . . . . .  . .  159 160  LIST OF FIGURES FIGURE  PAGE  1.  D e l i v e r y Range of Warehouses A, B and  2.  D e l i v e r y Range of Warehouses A and B  3.  The  Reduction  C  42 46  i n D e l i v e r y Range of  D i s t r i b u t i o n P o i n t s A and B t o t h e i r Handling 4.  Capacity  . . . . . . . .  T r a n s p o r t a t i o n Rate Areas W i t h i n Overlapping  47  the  D e l i v e r y Range of Warehouses  A and B  52  5.  S h i p p i n g and T r a n s p o r t a t i o n Cost Per U n i t  6.  Optimum A l l o c a t i o n of D i s t r i b u t i o n P o i n t  . . . .  53  A's  A v a i l a b l e Capacity  55  7.  Flow Diagram  69  8.  Flow Diagram  70  9.  Average C y c l e , T r a n s i t and  Safety Inventories  . •  88  Intervals.  97  10.  D i s t r i b u t i o n of Demand over Twelve Day  11.  D i s t r i b u t i o n of Demand over I n d i c a t e d Lead Time  12.  Determining the Cost  99 of an Unused T r a f f i c  Route 13.  Determining the Cost Route  139 of an Unused T r a f f i c 140  CHAPTER I THE PROBLEM AND DEFINITIONS OF TERMS USED In the not too d i s t a n t p a s t , the b u s i n e s s f i r m was r e q u i r e d t o adapt i t s d i s t r i b u t i o n f a c i l i t i e s and operat i o n s t o the r a i l w a y monopoly on i n l a n d t r a n s p o r t a t i o n . The  railways  opened new markets by p r o v i d i n g  r a p i d and inexpensive  relatively  t r a n s p o r t a t i o n f o r m a t e r i a l s and  products.  B u s i n e s s f i r m s expanded t h e i r  operations  t o accommodate these markets and e s t a b l i s h e d  warehouses and other  production  d i s t r i b u t i o n f a c i l i t i e s t h a t were  complimentary t o the r a i l w a y method o f t r a n s p o r t a t i o n . The  b a s i c f u n c t i o n of the t r a f f i c manager i n t h i s  environment was t o n e g o t i a t e  w i t h the r a i l w a y s f o r  s u i t a b l e f r e i g h t r a t e s and s e r v i c e s . traffic —  The r i g h t t o route  t h a t i s t o s e l e c t the c a r r i e r —  e f f e c t i v e bargaining  t o o l i n t e r r i t o r i e s that were  by two o r more r a i l w a y s . agencies i s s t i l l  was an served  Negotiation with transportation  a b a s i c f u n c t i o n o f the t r a f f i c  department and the e f f e c t i v e n e s s of t h i s a c t i v i t y has been c o n s i d e r a b l y  enhanced i n recent  years as a l t e r n a t i v e  t r a n s p o r t a t i o n agencies s t r i v e t o improve i n d i v i d u a l competitive  position.  their  2 The available  a l t e r n a t i v e methods of t r a n s p o r t a t i o n t h a t i n today's environment, however,  o p p o r t u n i t i e s that are f a r g r e a t e r reduction of raw  i n freight rates.  i n scope t h a n a mere  markets and  new  sources  facilities  are now  spatial  c a p a c i t i e s and d i s t r i b u t i o n  f r e e o f the  a v a i l a b i l i t y , r a t e s and  p l a n t s and  not  reached through r a i l w a y f a c i l i t i e s ;  a l l o c a t i o n s for production  at  provide  m a t e r i a l s have become a v a i l a b l e that c o u l d  p r e v i o u s l y be  railway  New  are  constraining influenoe s e r v i c e ; inventory  of  levels  at d i s t r i b u t i o n p o i n t s have become more  f l e x i b l e w i t h the range of d e l i v e r y s e r v i c e that i s o f f e r e d through a l t e r n a t i v e c a r r i e r s ; and  packaging  demands as w e l l as the equipment f o r l o a d i n g and  unloading  materials  the  and p r o d u c t s are no l o n g e r d i o t a t e d by  requirements o f a s i n g l e c a r r i e r .  These and  other  o p p o r t u n i t i e s that have emerged w i t h c o m p e t i t i o n  i n the  t r a n s p o r t a t i o n i n d u s t r y demand a new  the  approach t o  problems that are a s s o c i a t e d d i r e c t l y and the p h y s i c a l movement of m a t e r i a l s and approach must recognize t r a n s p o r t a t i o n and the  the  i n d i r e c t l y with  products.  The  new  i n t e r r e l a t i o n s h i p between  other p r o c e s s e s t h a t are  involved  i n the flow of t r a f f i c t o p l a n t s and through d i s t r i b u t i o n p o i n t s to customers.  Dr. Plowman, v i c e - p r e s i d e n t ,  traffic,  3 of the U n i t e d  States  S t e e l Corporation  of Delaware  has  said: T r a f f i c management ... has become a complex problem, a t r a n s p o r t c o n t r o l problem, of s e l e c t i o n o f the best combination, In t h i s s e l e c t i o n p r o c e s s , which i n v o l v e s not only the best form of t r a n s p o r t a t i o n but a l s o the most d e s i r a b l e among the numerous competing c a r r i e r s , there i s need f o r c a r e f u l and a c c u r a t e c a l c u l a t i o n o f t r a n s p o r t a t i o n cost and of i t s r e l a t i o n or balance w i t h o t h e r f a c t o r s such as inventory and warehousing oosts and oustomer s e r v i c e r e q u i r e m e n t s . ! P h y s i c a l d i s t r i b u t i o n i s the nomenclature that i s most f r e q u e n t l y used i n r e f e r r i n g t o t h i s complex of interrelated variables. I.  THE  PROBLEM  Statement of the Problem.  The  purpose of t h i s  study i s to i n d i c a t e the e s s e n t i a l c o n s i d e r a t i o n s  i n an  a n a l y s i s of the p h y s i c a l d i s t r i b u t i o n f u n c t i o n ; and develop a model that may  to  be used by a b u s i n e s s f i r m t o  e s t a b l i s h i t s optimum method of p h y s i c a l d i s t r i b u t i o n . More s p e c i f i c a l l y , the o b j e c t i v e s are 1) 1  Determine the  to:  considerations  necessary i n the  Edward W, Smykay (ed. ) Essays on P h y s i c a l D i s t r i b u t i o n Management (New York: The T r a f f i c S e r v i c e s C o r p o r a t i o n , 1961), p. 59.  development of a p l a n f o r p h y s i c a l distribution Z)  analysis,  Determine, examine and r e l a t e the cost components of the p h y s i c a l d i s t r i b u t i o n f u n c t i o n , and  3)  I n c o r p o r a t e these components i n t o a mathematical model capable of i n d i c a t i n g the optimum method o f p h y s i c a l d i s t r i b u t i o n .  I t i s the hope o f the w r i t e r that t h i s study strengthen the t r e n d  toward p h y s i c a l d i s t r i b u t i o n ,  a n a l y s i s and a s s i s t management i n the e v a l u a t i o n physical distribution  and  The l a c k o f a t t e n t i o n i n  area of p h y s i c a l d i s t r i b u t i o n i s apparent when one  considers cost  of i t s  operations.  Importance of the Study. the  will  that  few b u s i n e s s f i r m s are able  of moving t h e i r m a t e r i a l s  t o i s o l a t e the  and products t o the f a c t o r y  from the f a c t o r y to consumer.  Dr. Smykay s t a t e s :  I n those companies that are not p r e s e n t l y a p p l y i n g the p r i n c i p l e s of p h y s i c a l - d i s t r i b u t i o n a n a l y s i s and p l a n n i n g , a cost r e d u c t i o n of a t l e a s t 10 p e r cent can g e n e r a l l y be a t t a i n e d q u i t e e a s i l y . 2  ^Edward W. Smykay, " P h y s i c a l - D i s t r i b u t i o n Management: Concepts, Methods, and O r g a n i z a t i o n a l Approaches", New Concepts i n Manufacturing Management, AMA Management Report Number 60, Manufacturing D i v i s i o n , American Management A s s o c i a t i o n Inc., New York: 1960, p. 43.  5  This reduction  must be r e a l i z e d i f the b u s i n e s s f i r m  i s t o m a i n t a i n i t s c o m p e t i t i v e p o s i t i o n , and i f the economic r e s o u r c e s that  are a v a i l a b l e t o the e n t e r p r i s e  are to be a l l o c a t e d e f f i c i e n t l y .  Management must become  aware of the p o t e n t i a l i n t h i s area and must be g i v e n the  t o o l s w i t h which d i s t r i b u t i o n a l t e r n a t i v e s can be  measured. Recent managerial l i t e r a t u r e has i n d i c a t e d an interest  i n the p h y s i c a l d i s t r i b u t i o n f u n c t i o n .  majority  of w r i t i n g s  cost the  The  have s u c c e s s f u l l y i d e n t i f i e d the  components and have s t r e s s e d  the need t o  consider  i n t e r r e l a t i o n s h i p s between these f a c t o r s . I t appears, however, that the types o f problems t o  whioh the p h y s i c a l d i s t r i b u t i o n concept should be have not been c l e a r l y d e f i n e d ;  and that  applied  the procedures or  techniques that w i l l be u s e f u l i n an a n a l y s i s of p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s have not r e c e i v e d adequate attention.  An attempt i s made i n t h i s t h e s i s to i s o l a t e  the major a p p l i c a t i o n s of the p h y s i c a l d i s t r i b u t i o n concept; and one of the o b j e c t i v e s  of t h i s study i s t o  6  o u t l i n e a technique that may he of use t o a b u s i n e s s f i r m i n s e l e c t i n g i t s optimum method of p h y s i c a l d i s t r i b u t i o n . Limitations l i t e r a t u r e that the v a r i o u s  o f the Study.  describes  A s u b s t a n t i a l volume o f  the p h y s i c a l c h a r a c t e r i s t i c s o f  transportation,  materials  handling, ware-  housing, and communications f a c i l i t i e s are a v a i l a b l e i n writings  s p e c i f i c a l l y r e l a t e d to these areas.  reason, a review of these c o n s i d e r a t i o n s included  For this  w i l l not be  i n t h i s study.  Procedures f o r f o r e c a s t i n g s a l e s have been excluded f o r the same reason, although a w e l l developed forecast  i s e s s e n t i a l to p h y s i c a l d i s t r i b u t i o n a n a l y s i s .  The physioal  sales  procedures that  are suggested f o r comparing  d i s t r i b u t i o n a l t e r n a t i v e s i n c l u d e the technique  commonly r e f e r r e d to as l i n e a r programming. does not i n c l u d e  This  thesis  the mathematical t h e o r y upon which t h i s  technique i s based. II.  DEFINITIONS OF TERMS USED  System o f Physi c a l D i s t r i b u t i o n . p h y s i c a l d i s t r i b u t i o n may be d e f i n e d  A system o f  f o r purposes o f t h i s  t h e s i s as the f i x e d f a c i l i t i e s t h a t are a s s o c i a t e d s p e c i f i c alternative f o r materials  with a  and product movement,  7  eg.,  warehouses, m a t e r i a l s  processing  and  h a n d l i n g equipment, order-  communications f a c i l i t i e s ,  Method of P h y s i c a l D i s t r i b u t i o n .  etc. A method of  p h y s i c a l d i s t r i b u t i o n may  be d e f i n e d  which the f a c i l i t i e s  comprise a system of  d i s t r i b u t i o n may  be  that  utilized.  Several  d i s t r i b u t i o n w i l l g e n e r a l l y be of  of the ways i n physical  methods of  physical  a v a i l a b l e with each system  facilities. III.  ORGANIZATION OF THE  REMAINDER OF  This thesis i s divided two  as one  to f o u r d e a l p r o g r e s s i v e l y  THIS THESIS  into six chapters. w i t h the problem of  e s t a b l i s h i n g a framework f o r a n a l y s i s , and  the problem of  identifying physical distribution alternatives quantifying  Chapters  these i n t o a form that  and  i s s u i t a b l e f o r use  the l i n e a r programming a p p l i c a t i o n d e s c r i b e d  in  i n chapter  five. Chapter two opportunities  that  examines the are  nature of the  major  a v a i l a b l e to the b u s i n e s s f i r m  through a p p l i c a t i o n of the p h y s i c a l d i s t r i b u t i o n concept and  considers  the  objectives  and  of each of these o p p o r t u n i t i e s . the  framework f o r an  analysis  T h i s chapter emphasizes  importance of r e l a t i n g d i s t r i b u t i o n o p p o r t u n i t i e s  to  8 successive  i n t e r v a l s of the f i r m ' s  order t o develop an a p p r o p r i a t e The  future  time p e r i o d  in  framework f o r each a n a l y s i s .  r o l e of the t r a f f i c manager i n p h y s i c a l d i s t r i b u t i o n  a n a l y s i s and  the c r i t e r i a to be  used i n a comparison of  a l t e r n a t i v e courses of a c t i o n are a l s o d i s c u s s e d  i n this  chapter. Chapters three to f i v e are w i t h the bution  specifically  s h o r t - t e r m a p p l i c a t i o n of the p h y s i c a l  ooncept s i n c e i t i s i n t h i s area that  f a l l w i t h i n the and  ooncerned  scope of the t r a f f i c  responsibility.  physioal  The  distri-  decisions  manager's  major determinants of  authority short-term  d i s t r i b u t i o n a l t e r n a t i v e s are i d e n t i f i e d i n  chapter t h r e e .  Chapter four d e a l s with the problems of  c o l l e c t i n g , preparing methods of m a t e r i a l s o u t l i n e s the  and and  r e l a t i n g cost data f o r a l t e r n a t i v e products movement and  chapter f i v e  l i n e a r programming technique i n s e l e c t i n g  optimum of these a l t e r n a t i v e s . of t h i s study i s i n c l u d e d  A summary of the  i n chapter s i x .  the  findings  CHAPTER  II  THE FRAMEWORK AND OBJECTIVES PHYSICAL DISTRIBUTION "The o b j e c t i v e the  right quantity  time."  ANALYSIS  of p h y s i c a l d i s t r i b u t i o n i s t o have  of goods i n the r i g h t p l a c e  To ensure that t h i s o b j e c t i v e  necessary t o d e f i n e  FOR  at the r i g h t  i s achieved, i t i s  the p h y s i c a l d i s t r i b u t i o n requirements  of the f i r m ; to formulate the a l t e r n a t i v e s f o r p h y s i c a l d i s t r i b u t i o n that w i l l meet these requirements; and t o compare the a l t e r n a t i v e s w i t h a view to s e l e c t i n g the optimum a c c o r d i n g to the c r i t e r i a of e f f i c i e n c y t h a t i s acceptable to the f i r m . The f i r s t  step i n p h y s i c a l d i s t r i b u t i o n a n a l y s i s  i s to e s t a b l i s h objectives that w i l l  serve as a b a s i s f o r the f o r m u l a t i o n  comparison of a l t e r n a t i v e s . the  and a framework f o r the study and  T h i s task, i s complicated by  need t o develop a framework that w i l l permit  evaluation  of p h y s i c a l d i s t r i b u t i o n o p p o r t u n i t i e s  s i g n i f i c a n t l y d i f f e r e n t i n scope and t h a t  that are  emerge at  Edward W. Smykay, Donald J . Bowersox, Frank H. Mossman, Phy s i c a l D i s t r i b u t i o n Management (New York: The M a c M i l l a n Company, 1961), p. 86 7.  successive the  i n t e r v a l s i n the  firm's future.  the types of  objectives  framework that are necessary t o an e v a l u a t i o n of each  of these o p p o r t u n i t i e s are d i s c u s s e d t h i s chapter.  The  the c r i t e r i a f o r the  included  i n the  s e c t i o n of  i n the  second s e c t i o n ,  comparison of a l t e r n a t i v e s i s  l a s t part  of the  E s t a b l i s h i n g the Framework and Distribution Analysis^ The  i n the f i r s t  r o l e of the T r a f f i c Manager i n p h y s i c a l  d i s t r i b u t i o n a n a l y s i s i s discussed and  nature of  s e v e r a l o p p o r t u n i t i e s that are a s s o c i a t e d w i t h the  p h y s i c a l d i s t r i b u t i o n concept, and and  The  chapter.  Objectives  for Physical  a l t e r n a t i v e s f o r p h y s i c a l d i s t r i b u t i o n are  adequate or inadequate depending upon the volumes of t r a f f i c , the and  the  l o c a t i o n s of m a t e r i a l s , p l a n t s and  standards of d e l i v e r y s e r v i c e .  These  markets,  specifi-  c a t i o n s are the b a s i c framework f o r p h y s i c a l d i s t r i b u t i o n analyses  and must be d e f i n e d  a l t e r n a t i v e s can be An  i n s p e c i f i c terms  i s o l a t e d and  before  compared.  i n i t i a l problem i n e s t a b l i s h i n g t h i s framework i s  t h a t the volume, p l a c e over time w i t h the  and  s e r v i c e p o s s i b i l i t i e s change  implementation of p r o d u c t i o n  and  marketing p l a n s and w i t h market growth or d e t e r i o r a t i o n , s h i f t s i n the the competitive  l o c a t i o n of m a t e r i a l s  or markets, changes i n  environment, t e c h n o l o g i c a l i n n o v a t i o n  and  11 o t h e r environmental changes. define  the time p e r i o d  I t i s necessary, t h e r e f o r e , t o  f o r a n a l y s i s i n order t o i s o l a t e the  p h y s i c a l d i s t r i b u t i o n p o s s i b i l i t i e s that  are a v a i l a b l e i n  that p a r t i c u l a r p e r i o d . It i s p o s s i b l e  t o s e l e c t any time p e r i o d  purposes; t o i s o l a t e the volume p l a c e  f o r analysis  and s e r v i c e  require-  ments, or the a l t e r n a t i v e s of these s p e c i f i c a t i o n s over t h i s period;  t o develop the a l t e r n a t i v e s f o r p h y s i c a l d i s t r i b u t i o n  f o r each of the r e l e v a n t  set of s p e c i f i c a t i o n s ; and t o  s e l e c t the optimum course of a c t i o n a c c o r d i n g to the criteria  of e f f i c i e n c y that  i s acceptable to the f i r m .  This  procedure, however, w i l l not ensure p h y s i c a l d i s t r i b u t i o n efficiency.  I f the p e r i o d  i s t o o long, the a l t e r n a t i v e s  w i l l be r e q u i r e d  to embrace t o o broad a range of  specifications.  As a r e s u l t , the f i r m may overlook  opportunities  t o improve p h y s i c a l d i s t r i b u t i o n e f f i c i e n c y  through changes i n methods or systems t h a t s h o r t e r p e r i o d s of time. that  are adequate f o r  I n o t h e r words, the a l t e r n a t i v e  i s s e l e c t e d on t h i s b a s i s w i l l be optimum when compared  with other a l t e r n a t i v e s covering  the same p e r i o d , but not  n e c e s s a r i l y optimum over the whole time p e r i o d . i f the s e l e c t e d p e r i o d  i s too s h o r t ,  look a l t e r n a t i v e s that  would prove more e f f i c i e n t  l o n g e r time p e r i o d  Conversely,  the a n a l y s i s may over-  than the s e r i e s of adjustments  over a indicated  12 on the  basis The  of s u c c e s s i v e s h o r t - t e r m a n a l y s e s . a p p r o p r i a t e time p e r i o d s f o r  d i s t r i b u t i o n analyses are i n the the  nature of the  firm.  opportunities  In g e n e r a l , there are  opportunities  for physical  r e l a t e d to separate and time p e r i o d . 1.  reflect  that  are  differences available  to  three d i s t i n c t  d i s t r i b u t i o n and  these  are  s u c c e s s i v e i n t e r v a l s i n the  These o p p o r t u n i t i e s  firm's  are:  A more e f f i c i e n t u t i l i z a t i o n of physical  2.  those that  physical  existing  distribution f a c i l i t i e s .  A more e f f i c i e n t  system of  physical  distribution. 3.  A more e f f i c i e n t production  are  related  e x i s t i n g system of p r o d u c t i o n and  distribution facilities  i s one  of the  i n the  sense  alternatives  i n a comparison of the  spatial allocations the that  i s relevant  system of p h y s i c a l  be  physical  I t i s only  e x i s t i n g system, however,  i n a study of a l t e r n a t i v e  d i s t r i b u t i o n systems.  to  alternative  for production capacities.  optimum u t i l i z a t i o n of the  that  physical  taken i n t o account i n a comparison of systems of d i s t r i b u t i o n , and  of  facilities.  These t h r e e o p p o r t u n i t i e s the  s p a t i a l arrangement  physical  S i m i l a r l y , i t i s only the  d i s t r i b u t i o n with existing  optimum  plant  13 l o c a t i o n s that  i s relevant  i n a study of a l t e r n a t i v e  s p a t i a l arrangements f o r p r o d u c t i o n c a p a c i t i e s . follows, therefore,  that  bution  be  f u n c t i o n may  a study of the p h y s i c a l  system of  d i s t r i b u t i o n t h a t i s optimum with g i v e n p l a n t and  a t h i r d to e s t a b l i s h the  for  production capacities.  d e f i n i n g the  be  in The  first  existing  a n t i c i p a t e d range of  d e l i v e r y s e r v i c e and  which changes i n these requirements are  not  locations;  followed  d u r i n g which the  f a c i l i t i e s can e f f i c i e n t l y handle the  j u s t i f y changes i n the  physical  f o r the three a n a l y s e s .  step i s to d e f i n e the p e r i o d  volume, markets and  first  optimum s p a t i a l a l l o c a t i o n  steps that may  time p e r i o d  A  optimum u t i l i z a t i o n of e x i s t i n g  a second t o determine the  There are two  distri-  d i v i d e d i n t o three p a r t s .  a n a l y s i s to e s t a b l i s h the facilities;  It  the p e r i o d sufficient  during to  system of p h y s i c a l d i s t r i b u t i o n , but  s i g n i f i c a n t enough t o warrant a s p a t i a l rearrangement  of p r o d u c t i o n f a c i l i t i e s . preliminary  survey of the  d i s t r i b u t i o n and v a l s i n the present  This  step r e q u i r e s  e x i s t i n g system of  a physical  a l t e r n a t i v e systems at s u c c e s s i v e  future  u n t i l the p o i n t  inter-  i s reached where the  system i s inadequate or i n e f f i c i e n t .  Similarly,  14 the p o i n t i n time i s reached where an a l t e r n a t i v e s p a t i a l arrangement of p r o d u c t i o n  facilities  the changes that can be made i n the distribution  becomes s u p e r i o r t o system of p h y s i c a l  alone.  T h i s step i d e n t i f i e s the p o i n t s i n time at' which i t becomes d e s i r a b l e to adopt a new  system of p h y s i c a l  d i s t r i b u t i o n or to change the s p a t i a l a l l o c a t i o n of production  facilities.  T h i s step alone  however, i n t h a t there may  be  is deficient,  significant  differences  between what i s d e s i r a b l e and what i s f e a s i b l e f o r the firm.  It i s conceivable,  f o r example, that the changes i n  p h y s i c a l d i s t r i b u t i o n requirements w i t h i n the next years w i l l suggest a s p a t i a l r e l o c a t i o n of facilities.  T h i s Information  few  production  i s of l i t t l e p r a c t i c a l  t o the f i r m , however, i f the c a p i t a l and  flexibility  value that  i s necessary f o r such a change Is not a v a i l a b l e . I n c o n s i d e r i n g the problem of d e f i n i n g time for  operations  flexibility  analyses, Baumol p o i n t s out that d e c i s i o n  w i t h i n the f i r m i s c i r c u m s c r i b e d  p o l i c y , c o n t r a c t s and flexibility  periods  other commitments, and  by  present  that  i n c r e a s e s with the time p e r i o d as these  15 commitments e x p i r e .  T h i s f a c t suggests t h a t the second  s t e p i n d e f i n i n g the time p e r i o d s f o r p h y s i c a l  distri-  bution  flexibility  a n a l y s i s i s t o r e l a t e these to d e c i s i o n  w i t h i n the f i r m . future  The goal i s t o determine the time i n the  at which i t becomes p r a c t i c a l f o r the f i r m to adopt  an a l t e r n a t i v e system of p h y s i c a l d i s t r i b u t i o n ; and the point  i n the d i s t a n t f u t u r e  consider  at which the f i r m i s f r e e t o  the a l t e r n a t i v e s p a t i a l a l l o c a t i o n of p r o d u c t i o n  facilities. The f i r s t i n t e r v a l o f time f o r a n a l y s i s can be defined  as the short-term p e r i o d  are l i m i t e d t o the f l e x i b i l i t y distribution facilities. run volume market  during which a l t e r n a t i v e s  of the e x i s t i n g p h y s i c a l  While i t i s p o s s i b l e  that  short-  and s e r v i c e requirements c a n be  accommodated more e f f i c i e n t l y through an a l t e r n a t i v e combination of h a n d l i n g , t r a n s p o r t a t i o n ,  inventory,  processing  a change i n  and communication  facilities,  system i n the short-term i s i m p r a c t i c a l . required  that  of an a l t e r n a t i v e system; the i n f l e x i b i l i t y of  short-term p o l i c y , contracts  Analysis p. 187.  The time t h a t i s  to e s t a b l i s h one or more o f the f a c i l i t i e s  are a p a r t  order-  and other commitments; and  W i l l i a m J . Baumol, Economic Theory and Operations (Englewood C l i f f s , N.J.: P r e n t i c e H a l l I n c . , 1961),  16 the r i g i d i t y of e s t a b l i s h e d r o u t i n e w i t h s u p p l i e r s consumers and not  i n the methods of p h y s i c a l d i s t r i b u t i o n do  permit a r a p i d change from one The  system t o another.  f l e x i b i l i t y that i s required  change i n the  and  to i n t r o d u c e  system of p h y s i c a l d i s t r i b u t i o n w i l l ,  course, vary with the nature of the a l t e r n a t i v e s .  a of  There  i s a s p e c i f i c i n t e r v a l of time, however, b e f o r e i t becomes p r a c t i c a l to introduce present  system.  any  of the a l t e r n a t i v e s t o  the  To d e f i n e t h i s i n t e r v a l of time i t i s  necessary t o review the p o t e n t i a l systems of p h y s i c a l d i s t r i b u t i o n i n the l i g h t that would be  of the  c a p i t a l and  flexibility A survey of  r e q u i r e d w i t h t h e i r adoption.  c a p i t a l a v a i l a b i l i t y w i t h i n the  f i r m , and  o t h e r short-term  c o n s t r a i n t s mentioned above, w i l l then i n d i c a t e the  point  i n time at which a change i n system becomes f e a s i b l e . Opportunities  up t o t h i s p o i n t  a l l o c a t i o n s of output among p r o d u c t i v e i n inventory  housing of goods and  u n i t s ; adjustments  handling  i n the u t i l i z a t i o n of  communications f a c i l i t i e s ;  do not  alternative  l e v e l s ; changes i n t r a n s p o r t a t i o n r a t e s  s e r v i c e ; g r e a t e r e f f i c i e n c y i n the  and  include  and  and t r a n s p o r t i n g  ware-  order-processing  other a l t e r n a t i v e s that  i n v o l v e changes i n system f a c i l i t i e s ,  houses, handling  and  and  equipment,  i e . , wareorder-  17 processing  and communications f a c i l i t i e s , e t c .  The p o i n t i n time at which c a p i t a l and is sufficient  flexibility  to permit the a d o p t i o n of a l t e r n a t i v e  physical distribution f a c i l i t i e s ,  should  such a c t i o n prove  d e s i r a b l e , marks the end of t h e short-term  p e r i o d and the  b e g i n n i n g of the second p e r i o d f o r p h y s i c a l d i s t r i b u t i o n analysis.  At t h i s p o i n t i n time, the o p p o r t u n i t y  from methods t o systems of p h y s i c a l d i s t r i b u t i o n . short-term  shifts The  a n a l y s i s seeks t o e s t a b l i s h the optimum method  of p h y s i c a l d i s t r i b u t i o n w i t h given  facilities  and  s p e c i f i c a t i o n s , while a n a l y s i s i n the second p e r i o d i s concerned w i t h t h e f o r m u l a t i o n  and comparison of the  optimum methods of system a l t e r n a t i v e s . is  only the most e f f i c i e n t  I n other words i t  u t i l i z a t i o n of the present  system and each o f the a l t e r n a t i v e systems of p h y s i c a l d i s t r i b u t i o n t h a t are r e l e v a n t  i n the i n t e r m e d i a t e  period  analysis. It  i s important t o recognize  that a l t e r n a t i v e  systems of p h y s i o a l d i s t r i b u t i o n emerge at s u c c e s s i v e p o i n t s i n t h e intermediate  p e r i o d as more and more of the  s h o r t e r term c o n s t r a i n t s e x p i r e and as changes i n p h y s i c a l d i s t r i b u t i o n requirements become more s i g n i f i c a n t .  18  I f a l l of the  costs associated  with a system o f  p h y s i c a l d i s t r i b u t i o n were v a r i a b l e , the a l t e r n a t i v e s would be to l i m i t  the  independent and  successive  i t would be  intermediate-term analysis  a l t e r n a t i v e s as they emerge over time.  possible  to a comparison of A system o f p h y s i c a l  d i s t r i b u t i o n , however, c o n s i s t s o f a s p e c i f i c set of f i x e d f a c i l i t i e s f o r the h a n d l i n g , t r a n s p o r t i n g materials  and  products and  communications s e r v i c e s . these f a c i l i t i e s that  f o r order-processing  and  I t i s a change i n one  or more of  c o n s t i t u t e a change i n the  physical distribution.  system of  Hence, a l t e r n a t i v e systems  c a p i t a l investment i n one and  o r s t o r i n g of  or more of the  fixed  facilities  these c o s t s , as w e l l as the v a r i a b l e o p e r a t i n g  must be taken i n t o account i n the  involve  costs,  intermediate-term  analysis. The  problem i n comparing i n d i v i d u a l systems of  p h y s i c a l d i s t r i b u t i o n i s that the economic l i f e i n c r e m e n t a l investment c o s t s may the  life  of the  part  include of the  not  An  are  i n i t i a l a l t e r n a t i v e , f o r example,  an investment i n warehouses t h a t facility  the  correspond w i t h  a l t e r n a t i v e system w i t h which they  i n i t i a l l y associated. may  o r may  of  are a l s o a  requirements of a l a t e r a l t e r n a t i v e .  I f the economic l i f e of these warehouses i s assumed to  be  19 e q u a l to the w i l l be  l i f e o f the  initial  alternative, this  l e s s a t t r a c t i v e from a cost  alternatives  whether or not  the  initial  adopted by the  firm.  the u s e f u l l i f e  d i s t r i b u t i o n f a c i l i t i e s w i l l or w i l l not system w i t h which they are  associated  are  available  incorrect  from the  to evaluate two  extend beyond  requireThe  alternative  on  the  nature of f i x e d f a c i l i t i e s  o r more s u c c e s s i v e  Hence, I t i s alternatives  r e l a t e d through common  approach to i n t e r m e d i a t e - t e r m a n a l y s i s  to formulate and  compare a l t e r n a t i v e p l a n s that  or more s u c c e s s i v e systems of p h y s i c a l  I n other words, each of the an a l t e r n a t i v e of the  the  distribution f a c i l i t i e s .  The  one  physical  p r e c e d i n g system.  independently when these are physical  of  systems have been a s c e r t a i n e d .  o t h e r hand, i s dependent upon the  the  It i s  u n t i l the  incremental investment oost of a f u t u r e  that  later  a l t e r n a t i v e , which i n c l u d e d  to assume that  ments of f u t u r e  The  more or l e s s a t t r a c t i v e depending upon  warehouse investment, was impractical  standpoint than other  with a lower investment content.  a l t e r n a t i v e w i l l be  system  system that  intermediate period  is available and  may  as p h y s i c a l  distribution.  at the  also i n c l u d e as  be  include  a l t e r n a t i v e plans w i l l  more' bh'anges i n system over the p e r i o d permits and  must  include  beginning one  or  flexibility  d i s t r i b u t i o n requirements demand.  80 In p r a c t i c e , many of the p l a n s w i l l c o n s i s t of s u c c e s s i v e modifications  of the i n i t i a l  houses or the c o n s o l i d a t i o n  system, eg., a d d i t i o n a l wareof d i s t r i b u t i o n o u t l e t s ; new  f a c i l i t i e s f o r h a n d l i n g o r t r a n s p o r t i n g m a t e r i a l s and p r o d u c t s ; new o r d e r - p r o c e s s i n g  or communications  f a c i l i t i e s , etc. The second p e r i o d f o r a n a l y s i s t e r m i n a t e s when there i s s u f f i c i e n t  c a p i t a l and f l e x i b i l i t y  to permit  changes i n the s p a t i a l a l l o c a t i o n o f p r o d u c t i o n should such a c t i o n prove d e s i r a b l e .  U n t i l t h i s time, the  systems o f p h y s i c a l d i s t r i b u t i o n that f i r m are l i m i t e d to those that market  facilities,  are a v a i l a b l e t o the  can accommodate the volume,  and s e r v i c e requirements of t h e f i r m from e x i s t i n g  production locations.  The framework f o r t h e second  period  a n a l y s i s i s the t o t a l range o f volume, markets and s e r v i c e p o s s i b i l i t i e s between the time at which a change i n system becomes f e a s i b l e t o the time at which t h e o p p o r t u n i t y inoludes  a change i n the s p a t i a l arrangement  facilities.  The o b j e c t i v e  of a n a l y s i s  o f production  i s t o determine the  optimum p h y s i c a l d i s t r i b u t i o n p l a n f o r the p e r i o d . A l t e r n a t i v e p l a n s may i n c l u d e  a s i n g l e system t h a t i s  capable of meeting t o t a l requirements over the p e r i o d ; a s e r i e s o f p h y s i c a l d i s t r i b u t i o n systems; or a s e r i e s o f  21 system m o d i f i c a t i o n s . The  t h i r d time p e r i o d f o r a n a l y s i s occurs when there  i s maximum d e c i s i o n f l e x i b i l i t y .  T h i s p o i n t i n time i s  u s u a l l y r e f e r r e d to as the f i r m ' s long-term o r v e r y  long-  run. The very-long run i s a p e r i o d over which the f i r m ' s present c o n t r a c t s w i l l have run out, i t s present p l a n t and equipment w i l l have been worn out or rendered obsolete and w i l l t h e r e f o r e need replacement, e t c . In other words, the long-run i s a p e r i o d of s u f f i c i e n t d u r a t i o n f o r the company t o become completely f r e e i n i t s d e c i s i o n s from I t s present p o l i c i e s , p o s s e s s i o n s and commitments. Thus the long-run i s a s u f f i c i e n t l y d i s t a n t p e r i o d i n which the f i r m i s f r e e to r e c o n s i d e r a l l of i t s p o l i c i e s . For example, i f the company f i n d s that the demand f o r i t s product has i n c r e a s e d subs t a n t i a l l y , i t may be ten years before i t can a f f o r d t o r e d e s i g n i t s p l a n t and equipment completely i n accord w i t h the requirements of t h i s development.3 The  major d i f f e r e n c e between i n t e r m e d i a t e  term f l e x i b i l i t y  operations  The  long-  i s that the f i r m i s f r e e i n the long-term  to c o n s i d e r a l t e r n a t i v e l o c a t i o n s f o r facilities.  and  geographical  production  l i m i t s of the  i n the intermediate-term  firm's  are those markets that  can be accommodated by the p h y s i c a l d i s t r i b u t i o n f u n c t i o n from f i x e d p l a n t l o c a t i o n s .  In the long-term, markets are  s i m i l a r l y l i m i t e d f o r each s p e c i f i c combination of p l a n t l o c a t i o n s and  systems of p h y s i c a l d i s t r i b u t i o n , but  William J .  Baumol, op_. c i t . . p.  187.  are  variable  i n that  locations  to s e l e c t  alternative  for production.  The and  the f i r m i s f r e e  o v e r a l l task i n the long-term i s to formulate  oompare the a l t e r n a t i v e  combinations of markets,  locations  and systems o f p h y s i c a l  objective  i s t o s e l e c t t h e optimum combination o f these  three i n t e r r e l a t e d The physical the  distribution.  plant  The  variables.  volume, market and s e r v i c e  possibilities for  d i s t r i b u t i o n i n the long-term are undefined  until  s p a t i a l a l l o c a t i o n of p r o d u c t i o n f a c i l i t i e s has been  decided.  This decision,  however, can be made only i f the  capacity  and e f f i c i e n c y of a l t e r n a t i v e  systems of  physioal  d i s t r i b u t i o n are taken i n t o account.  Henoe, t h e  s e l e c t i o n of the long-term system w i l l be simultaneous w i t h the s e l e c t i o n o f long-term markets and the s p a t i a l a l l o c a t i o n of p r o d u c t i o n f a c i l i t i e s . Physical  d i s t r i b u t i o n analysis  context i s only a part  i n the long-term  of the o v e r a l l a n a l y s i s .  The task  i s to p r o v i d e i n f o r m a t i o n r e l a t e d t o the c a p a c i t y and e f f i c i e n c y of systems of p h y s i c a l the  potential  objective physical  d i s t r i b u t i o n f o r each o f  combinations of p l a n t  i s t o ensure that  locations.  The  a l l of the a l t e r n a t i v e s f o r  d i s t r i b u t i o n i n the long-term a r e i d e n t i f i e d and  made a v a i l a b l e  f o r i n c l u s i o n i n the f o r m u l a t i o n and  23 comparison  of a l t e r n a t i v e combinations o f markets  and  plant  locations. In summary, the t o t a l b e n e f i t s t o the f i r m through the p h y s i c a l  are a v a i l a b l e  d i s t r i b u t i o n concept  be r e a l i z e d i f t h e r e i s an e f f i c i e n t physical  that  will  u t i l i z a t i o n of  d i s t r i b u t i o n f a c i l i t i e s over the s h o r t - r u n p e r i o d  of time d u r i n g which changes i n system are i m p r a c t i c a l ; i f changes i n the system of p h y s i c a l d i s t r i b u t i o n are o p t i m i z e d f o r the p e r i o d  p r i o r to a s p a t i a l r e l o c a t i o n o f  p r o d u c t i o n f a c i l i t i e s ; and i f the p r i n c i p l e s of p h y s i c a l d i s t r i b u t i o n are taken i n t o account i n p l a n s f o r the future  s p a t i a l a l l o c a t i o n of p r o d u c t i o n c a p a c i t i e s . Decision  flexibility  determines the p o i n t s  i n time  at which i t i s p r a c t i c a l f o r the f i r m t o adopt changes i n the  system o f p h y s i c a l d i s t r i b u t i o n , or to Introduce  changes i n the s p a t i a l a l l o c a t i o n of p l a n t s . points  i n time are i d e n t i f i e d i t Is p o s s i b l e  range of volume, market and s e r v i c e  I f these to define  requirements, or the  a l t e r n a t i v e s of these s p e c i f i c a t i o n s , f o r each o f the short-term, i n t e r m e d i a t e - t e r m and long-term p l a n n i n g periods.  the  .•  24  The Role o f the T r a f f i c Manager In P h y s i o a l D i s t r i b u t i o n Analysis P h y s i c a l d i s t r i b u t i o n a n a l y s i s i s a p a r t o f the p l a n n i n g process  and as such should be undertaken a t the  proper a d m i n i s t r a t i v e l e v e l o f the o r g a n i z a t i o n .  I n the  t y p i c a l o r g a n i z a t i o n s t r u c t u r e the v a r i o u s a c t i v i t i e s o f the business eg.,  are d i v i d e d among f u n c t i o n a l departments,  sales, production, t r a f f i c ,  c o - o r d i n a t i o n at headquarters  e t c , with p r o v i s i o n f o r  level.  P l a n n i n g by  i n d i v i d u a l department heads i s then l i m i t e d t o a c t i v i t i e s t h a t are w i t h i n t h e i r s p e c i a l i z e d sphere of o p e r a t i o n s , while p l a n s that are beyond the scope of a s i n g l e ment are developed  at a h i g h e r l e v e l .  depart-  Granger l i s t s three  l e v e l s i n the o r g a n i z a t i o n a l s t r u c t u r e at which p l a n n i n g takes p l a c e : (l) P l a n n i n g by the heads o f e x i s t i n g o p e r a t i n g u n i t s f o r f u t u r e earnings i n t h e i r own a r e a . (2) Headquarters l e v e l p l a n n i n g f o r g e n e r a t i n g f u t u r e sources of earnings from areas beyond the normal scope of the e x i s t i n g u n i t s ( i n c l u d i n g p r o f i t improvement by p o s s i b l e withdrawal from some o f the present o p e r a t i o n s ) ; and (3) P l a n n i n g by heads o f headq u a r t e r s s t a f f u n i t s , such as f i n a n c i a l p l a n n i n g , marketing p l a n n i n g , r e s e a r c h and development p l a n n i n g , etc. ( t o the extent that such a c t i v i t i e s e x i s t at the headquarters-staff l e v e l ) . 4  C h a r l e s H. Granger, "Best C o n t r o l l e r (August 1962), p. 44. 4  Laid Plans",  The  The unit  T r a f f i c Manager, as the head of an o p e r a t i n g  of the f i r m , p l a y s a major r o l e i n a l l t h r e e p h y s i c a l  d i s t r i b u t i o n a n a l y s e s because of h i s s p e c i a l i z e d knowledge of the a l t e r n a t i v e s f o r h a n d l i n g , moving and f i r m ' s m a t e r i a l s and products.  s t o r i n g the  His r o l e i s advisory,  however, whenever the d e c i s i o n s i n p h y s i c a l d i s t r i b u t i o n are l i k e l y to a f f e c t departments.  o p e r a t i o n s i n other f u n c t i o n a l  Of the three a n a l y s e s  suggested  i n the  f o r e g o i n g i t i s only the short-term a n a l y s i s that the T r a f f i c Manager i s i n a p o s i t i o n t o d i r e c t I n the  i n t e r m e d i a t e and long-term  and  co-ordinate.  periods, production,  marketing, f i n a n c i a l and other f a c t o r s t h a t are beyond the scope of the t r a f f i c  department's o p e r a t i o n s must be  taken  i n t o account i n the a n a l y s i s . I n the  intermediate-term,  a l t e r n a t i v e s w i l l enable  some of the  system  the f i r m t o serve a d d i t i o n a l  markets or to i n c r e a s e the volume of s a l e s i n e x i s t i n g markets —  up to the l i m i t s of p r o d u c t i v e c a p a c i t y .  Moreover, d i f f e r e n c e s i n the cost of system a l t e r n a t i v e s a f f e c t the margin of p r o f i t  on u n i t  o p p o r t u n i t i e s e x i s t f o r improving  s a l e s so that  the f i r m ' s o v e r a l l  f i n a n c i a l r e s u l t s through adjustments i n the t o t a l volume of o p e r a t i o n s . affect  Hence, the intermediate-term a l t e r n a t i v e s  o p e r a t i o n s i n the marketing and p r o d u c t i o n  depart-  86  ments as w e l l as i n the  traffic  department.  d i s t r i b u t i o n analysis for this period d i r e c t i o n and  co-ordination  Physical  requires  top-level  w i t h the p a r t i c i p a t i o n of  marketing, p r o d u c t i o n , t r a f f i c  and  the  other i n t e r e s t e d  departments.  A study of the  long-term s p a t i a l a l l o c a t i o n  of f a c i l i t i e s  should a l s o be  undertaken at an  i n the  organization  since  no one  of the  upper-level  operating  depart-  ments are i n a p o s i t i o n to i d e n t i f y the i n t e r r e l a t i o n s h i p between markets and  p r o d u c t i o n l o c a t i o n s with each of  the  alternatives for physical distribution. The  short-term a l t e r n a t i v e s f o r p h y s i c a l  d i s t r i b u t i o n are facilities. service  l i m i t e d t o the  flexibility  of  Moreover, the volume, markets and  given delivery  s p e c i f i c a t i o n s f o r p h y s i c a l d i s t r i b u t i o n are  i n f l e x i b l e during l i m i t e d to the  t h i s period  Markets  g e o g r a p h i c a l t e r r i t o r y that  with e x i s t i n g f a c i l i t i e s p o r t i o n of the  of time.  and  are  are  can be  served  f u r t h e r l i m i t e d to  t e r r i t o r y i n which the  the necessary marketing channels, eg.,  f i r m has  that  established  dealers,  d i s t r i b u t o r s , agents, w h o l e s a l e r s , or other channels through which output i s d i s t r i b u t e d . may  be  s e n s i t i v e t o the  is offered.  Short-term volume  standard of d e l i v e r y s e r v i c e  I t w i l l be e x p l a i n e d  i n the  following  that  chapter,  27 however, that the s h o r t - t e r m d e l i v e r y standard should be one t h a t the f i r m w i l l wish to m a i n t a i n on a l o n g e r - t e r m I n other words, while a change i n volume may  basis. possible  through a temporary adjustment  i n delivery  standard, the need t o m a i n t a i n a c o n s i s t e n t  and r e l i a b l e  standard of s e r v i c e to customers on a l o n g e r - t e r m will  be  g e n e r a l l y p r e c l u d e t h i s type of i n t e r i m  basis  action.  Given the markets and the d e l i v e r y standard t o be  offered  i n these markets, i t i s c l e a r that the c h o i c e of s h o r t - t e r m p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e w i l l not a f f e c t  marketing  plans or o p e r a t i o n s . The can be  e f f i c i e n c y w i t h which marketing  specifications  s a t i s f i e d i n the short-term depends upon the  l o c a t i o n of output  i n r e l a t i o n to markets and  the  a l t e r n a t i v e methods f o r p h y s i c a l d i s t r i b u t i o n . p r o d u c t i o n i s completed  Once  the l o c a t i o n s of output are f i x e d  and a l t e r n a t i v e s are l i m i t e d to methods of p h y s i c a l distribution.  The  choice of method i n t h i s case does not  affect production operations. The  objective  i n the short-term, however, i s not  only to optimize the p h y s i c a l d i s t r i b u t i o n of a v a i l a b l e output, but a l s o t o optimize the l o c a t i o n o f output a c c o r d i n g t o combined p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n  28  efficiency.  I n other words, there i s a second a p p l i c a t i o n  of the p h y s i c a l d i s t r i b u t i o n concept  i n the short-term  p e r i o d i n t h a t t o t a l o p e r a t i n g e f f i c i e n c y can be improved through an i n t e g r a t i o n of p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n planning.  I f cost i s the c r i t e r i a , f o r  example, the o b j e c t i v e i s t o a l l o c a t e output  among  p r o d u c t i v e u n i t s i n such a way as t o achieve minimum t o t a l d e l i v e r e d product  cost r a t h e r than minimum t o t a l  production  cost. I n the t y p i c a l b u s i n e s s o r g a n i z a t i o n , the P r o d u c t i o n Manager a l l o c a t e s output  among p r o d u c t i v e u n i t s  on the b a s i s of t o t a l p r o d u c t i o n cost —  subject t o v a r i o u s  short-term c o n s t r a i n t s i n c l u d i n g p o l i c y r e l a t e d t o employment s t a b i l i z a t i o n , equipment u t i l i z a t i o n , the use of overtime,  employee and p u b l i c r e l a t i o n s , e t c .  The  T r a f f i c Manager's d i r e c t r e s p o n s i b i l i t y i s g e n e r a l l y c o n s i d e r e d t o be the e f f i c i e n t movement o f m a t e r i a l s and products t o p l a n t s and t o markets. or r e s p o n s i b i l i t i e s of the t r a f f i c  "The major f u n c t i o n s department are those  concerned w i t h f r e i g h t movements".^  The T r a f f i c Manager,  "Charles A. T a f f , T r a f f i c Management P r i n c i p l e s and P r a c t i c e s (Homewood, I l l i n o i s : R i c h a r d D. I r w i n , I n c . , 1959), p. 11.  29  however, i s f a m i l i a r w i t h the p h y s i c a l a l t e r n a t i v e s that  distribution  should be taken i n t o account  in  determining the optimum a l l o c a t i o n of output among p l a n t s . The problem i s i n b r i n g i n g t o g e t h e r the knowledge of the two decision.  departments i n the output  I t i s suggested  desirable  allocation  T h i s can be done through c o - o r d i n a t i o n at an  upper l e v e l or through c o - o p e r a t i o n at the level.  specialized  departmental  that the l a t t e r i s the most  since the i n t e g r a t i o n that i s r e q u i r e d i s  continuous r a t h e r than p e r i o d i c .  Output p l a n s must be  geared t o marketing e x p e c t a t i o n s over the p r o d u c t i o n c y c l e . B e t t e r estimates become a v a i l a b l e over the c y c l e , however, and i t i s d e s i r a b l e to adjust output at s p e c i f i c p l a n t s i f f l e x i b i l i t y permits.  Hence, a continuous review of demand  i n r e l a t i o n to p r o d u c t i o n f l e x i b i l i t y  i s necessary to  achieve the optimum l o c a t i o n s f o r output. In  summary, the T r a f f i c Manager may  be c a l l e d upon  to  p r o v i d e i n f o r m a t i o n r e l a t e d to the cost and  of  a l t e r n a t i v e systems of p h y s i c a l d i s t r i b u t i o n i n the  i n t e r m e d i a t e - t e r m and long-term a n a l y s i s .  efficiency  His role i s  a d v i s o r y i n both analyses s i n c e marketing, p r o d u c t i o n , f i n a n c i a l and o t h e r f a c t o r s w i t h which the t r a f f i c ment i s u n f a m i l i a r must be taken i n t o account. the e f f e c t  depart-  Moreover,  of d e c i s i o n s that become necessary as a r e s u l t  30 of these a n a l y s e s extend beyond t h e T r a f f i c Managers sphere of r e s p o n s i b i l i t y and cannot, t h e r e f o r e , part  be c o n s i d e r e d a  of h i s a u t h o r i t y . Physical d i s t r i b u t i o n analysis  period  f o r the short-term  i n s o f a r as t h e movement o f a v a i l a b l e output i s  concerned, i s w i t h i n the T r a f f i c Manager's area of operations.  The a l l o c a t i o n of output among p r o d u c t i v e  u n i t s i s a c o - o p e r a t i v e f u n c t i o n t o be handled j o i n t l y by the  traffic  and p r o d u c t i o n departments.  Since t h e T r a f f i c Manager i s d i r e c t l y r e s p o n s i b l e only  f o r the short-term p h y s i c a l d i s t r i b u t i o n a n a l y s e s and  d e c i s i o n s , the balance of t h i s t h e s i s w i l l be r e l a t e d t o the methods f o r f o r m u l a t i n g  a l t e r n a t i v e s and s e l e c t i n g the  optimum a l t e r n a t i v e s f o r t h i s  period.  i  The  C r i t e r i a of E f f i c i e n c y The  desirability  of one a l t e r n a t i v e over another  depends upon t h e purpose t o be served by a n a l y s i s .  If  p r o f i t maximization i s the purpose of a n a l y s i s , f o r example, p r o f i t alternatives. the  i s the c r i t e r i a t o be used i n comparing A l t e r n a t i v e l y , maximum customer s e r v i c e i s  standard i f t h i s i s the purpose f o r a n a l y s i s .  Bowersox  suggests that maximum s e r v i c e , maximum p r o f i t and minimum  31 cost  are a l t e r n a t i v e standards f o r p h y s i c a l d i s t r i b u t i o n  analysis.  6  A maximum s e r v i c e c r i t e r i a i m p l i e s the use o f d e l i v e r y s e r v i c e as a marketing s t r a t e g y o b j e c t i v e would be intended t o i n c r e a s e  i n that  such an  s a l e s volume, t o  m a i n t a i n customer l o y a l t y , to improve customer r e l a t i o n s , etc.  While these o b j e c t i v e s may be v a l i d , i t i s  i n c o r r e c t t o assume that maximum d e l i v e r y s e r v i c e i s the most e f f i c i e n t Advertising,  strategy  increased  f o r t h e i r achievement. s a l e s e f f o r t , and other marketing  a l t e r n a t i v e s may. w e l l accomplish the d e s i r e d r e s u l t at l e s s economic c o s t . and  F o r t h i s reason the estimated cost  r e s u l t of a l t e r n a t i v e s e r v i c e standards should be  compared w i t h other s t r a t e g y marketing p l a n s . advise  i n the formulation of  The T r a f f i c Manager i s i n a p o s i t i o n t o  the marketing department w i t h respect  t o the range  of a v a i l a b l e s e r v i c e standards and the incremental of adopting s u c c e s s i v e l y higher standards.  cost  Once the  marketing department has determined the standard of  zz d e l i v e r y s e r v i c e that strategy, to be  i s optimum i n r e l a t i o n to o t h e r  t h i s standard becomes one  of the  specifications  s a t i s f i e d by p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s .  other words, d e l i v e r y s e r v i c e guide i n the  formulation  i s more a p p r o p r i a t e  as a  of p h y s i c a l d i s t r i b u t i o n  a l t e r n a t i v e s than as a c r i t e r i a f o r s e l e c t i n g the A minimum cost c r i t e r i a would be the  s p e c i a l case where demand f o r the  is associated market and  criteria  alternative —  wish t o a c h i e v e . speculation,  which i s the  "In contrast  with very few  in  The  however, when i t  w i t h f i x e d product p r i c e s and  g i v e n volume,  In t h i s case minimum  cost p h y s i c a l d i s t r i b u t i o n i s e q u i v a l e n t profit  only  firm's products i s  i s also applicable,  service s p e c i f i c a t i o n s .  optimum.  applicable  i n s e n s i t i v e to v a r i a t i o n s i n d e l i v e r y s e r v i c e . minimum cost  In  t o the maximum  goal that most  firms  t o much academic  exceptions, firms  seek to  maximize p r o f i t s i n d i s t r i b u t i o n d e c i s i o n making".  7  The  minimum cost standard w i t h i n the framework of g i v e n p r i c e s and  g i v e n volume, market and  l e a s t two 1.  s e r v i c e requirements has  a d d i t i o n a l advantages: Minimum cost  i s a generally  understood  commonly used c r i t e r i a of e f f i c i e n c y .  Ibid*  and  at  33 2.  The need to d e f i n e of the f i r m —  the marketing s p e c i f i c a t i o n s  including delivery service  —  p l a c e s the proper emphasis on s e r v i c e as a marketing s t r a t e g y .  I f the marketing  department i s r e q u i r e d t o j u s t i f y the standards of s e r v i c e , the cost  defined  and r e s u l t of  t h i s a l t e r n a t i v e w i l l be taken i n t o account i n the marketing p l a n s of the  firm.  CHAPTER I I I THE MAJOR DETERMINANTS OF PHYSICAL DISTRIBUTION ALTERNATIVES In r e l a t i n g the problems o f p r o d u c t i o n and i n v e n t o r y c o n t r o l , Magee s t a t e s :  "A r e a l i s t i c  must recognize l i m i t a t i o n s i n f l e x i b i l i t y advantage of elements of f l e x i b i l i t y T h i s statement  system  but take  that do e x i s t .  n l  i s p a r t i c u l a r l y r e l e v a n t i n the  f o r m u l a t i o n o f short-term p h y s i c a l d i s t r i b u t i o n alternatives.  O p p o r t u n i t i e s i n t h i s area emerge w i t h  elements o f f l e x i b i l i t y  i n the p r o d u c t i o n , h a n d l i n g ,  t r a n s p o r t a t i o n and warehousing of m a t e r i a l s and p r o d u c t s , but a c t i o n i s l i m i t e d t o the a l t e r n a t i v e s that s a t i s f y g i v e n marketing the f l e x i b i l i t y  requirements  will  and that are w i t h i n  of g i v e n p o l i c y , commitments and p h y s i c a l  facilities. Flexibility  i s a meaningless term unless i t i s  r e l a t e d to a s p e c i f i c p o i n t i n time.  I n the day-to-day  problem o f moving m a t e r i a l s and products t o p l a n t s , s t o c k  John F. Magee, P r o d u c t i o n P l a n n i n g and Inventory C o n t r o l (New York, N.Y.: McGraw H i l l Book Company, 1958) p. 22.  35  p o i n t s and  customers, f l e x i b i l i t y  a l t e r n a t i v e s f o r s h i p p i n g and  i s l i m i t e d to  transportation.  speaking of next month's o p e r a t i o n s ,  I f we  are  however, there may  be  s u f f i c i e n t time to adapt f a c i l i t i e s to a broader range of t r a n s p o r t a t i o n a l t e r n a t i v e s ; t o adjust the r a t e of output at some of the p l a n t s ; t o adjust the r a t e of h a n d l i n g l e v e l of i n v e n t o r i e s at o e r t a i n warehouses; e t c .  and  the  It i s  important to i d e n t i f y the p o i n t s i n time at which the v a r i o u s elements of f l e x i b i l i t y become a v a i l a b l e so that d e c i s i o n s that are r e l a t e d t o these o p p o r t u n i t i e s can made i n time f o r t h e i r implementation.  Finally,  p e r i o d of time can be taken f a r enough i n t o the  be  the short-term  f u t u r e to permit a review of the a l l o c a t i o n of a n t i c i p a t e d demand among the  firm's productive  v a r i o u s p o l i c y and  commitments, but  units —  subject  f r e e from the  c o n s t r a i n i n g i n f l u e n c e of e x i s t i n g p r o d u c t i o n and  the  current lo  schedules  l e v e l of a o t i v i t y at d i s t r i b u t i o n p o i n t s .  r e c a p i t u l a t e , the extremes of  short-term  p h y s i o a l d i s t r i b u t i o n d e c i s i o n s d e a l w i t h the t r a n s p o r t a t i o n problem and among p l a n t s .  to  During the  elements of f l e x i b i l i t y involved i n t r a f f i c  day-to-day  the f u t u r e a l l o c a t i o n of output i n t e r v a l between these extremes,  i n the v a r i o u s p r o c e s s e s that  flow permit d e c i s i o n s t h a t are  are  greater  36 i n scope than the d a i l y d e o i s i o n s , but l e s s e r i n scope t h a n the  output a l l o c a t i o n d e c i s i o n .  T h i s t h e s i s w i l l be l i m i t e d  t o c o n s i d e r a t i o n of the two extremes since the methods of a n a l y s i s f o r other  short-term  i n t e r v a l s w i l l be a  m o d i f i c a t i o n of those f o r day-to-day and f o r output allocation decisions. In the day-to-day problem, g i v e n customer are t o be f i l l e d  from the g i v e n q u a n t i t i e s of products  that are a v a i l a b l e f o r d i s t r i b u t i o n at f i n a l The  orders  stock  points.  determinants o f p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s i n  t h i s s i t u a t i o n are simply  the d e l i v e r y s e r v i c e r e q u i r e -  ments o f customer orders,  and the a v a i l a b i l i t y o f  a l t e r n a t i v e methods o f s h i p p i n g and t r a n s p o r t a t i o n . The  short-term  planning  problem i s e s s e n t i a l l y t o  determine the optimum a l l o c a t i o n o f a n t i c i p a t e d demand among the f i r m ' s p l a n t s a c c o r d i n g of production  t o the combined  and p h y s i o a l d i s t r i b u t i o n .  t r a f f i c flow that i s i m p l i c i t  costs  The p a t t e r n of  i n the s o l u t i o n t o t h i s  problem w i l l i n d i c a t e the mix and volume of t r a f f i c each of the p r o d u c t i o n  and p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s  w i l l be r e q u i r e d to accommodate. provide  that  The o b j e c t i v e i s not t o  a d e t a i l e d p l a n of o p e r a t i o n s ,  i n d i c a t e the optimum flow of t r a f f i c  but r a t h e r t o  sufficiently in  3.7 advance t o permit  p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n  f a c i l i t i e s t o be geared  to t h i s requirement.  p l a n t and warehouse l a y o u t , p r o d u c t i o n agreements with t r a n s p o r t a t i o n agencies,  Changes i n  schedules, employment  adjustments and other d e t a i l e d p l a n n i n g t h a t may be r e q u i r e d t o adapt f a c i l i t i e s left  t o the optimum flow can be  t o the i n d i v i d u a l p l a n t managers, p u r c h a s i n g  agents,  warehouse managers and other personnel who are r e s p o n s i b l e f o r the v a r i o u s segments of o p e r a t i o n s that are i n v o l v e d i n the p r o c e s s i n g and movement o f m a t e r i a l s and p r o d u c t s . that  I t i s necessary  are c o n s i d e r e d  only t h a t the a l t e r n a t i v e s  i n a n a l y s i s be f e a s i b l e i n terms o f  the r e q u i r e d changes i n o p e r a t i o n s .  The optimum o f these  a l t e r n a t i v e s , broken down i n t o i t s component p a r t s  will  then provide the necessary d i r e c t i o n and c o - o r d i n a t i o n f o r d e t a i l e d operating plans. A l t e r n a t i v e s f o r short-term t r a f f i c  flow are  determined by: 1.  Market, s e r v i c e and volume s p e c i f i c a t i o n s .  2.  Flexibility  i n the u t i l i z a t i o n o f g i v e n  p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n Marketing  facilities.  s p e c i f i c a t i o n s and the r e l a t i v e  Importance o f i n d i v i d u a l customers i n a n a l y s i s i s  38  d i s c u s s e d i n the f i r s t  h a l f of t h i s chapter.  The l a s t  h a l f d e a l s w i t h the nature and f l e x i b i l i t y of p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n I.  facilities.  MARKETING SPECIFICATIONS  D e l i v e r y S e r v i c e Requirements of Customers The  a l t e r n a t i v e methods of p h y s i c a l d i s t r i b u t i o n  are r e l e v a n t only i f they w i l l s a t i s f y the d e l i v e r y s e r v i c e requirements  o f customers.  The f i r s t  step i n  d e f i n i n g the d e l i v e r y standard i s to i d e n t i f y the e x p l i c i t o r apparent  p o l i c y of the f i r m toward customer s e r v i c e .  Some of the more common p o l i c i e s i n c l u d e : 1.  S e r v i c e e q u i v a l e n t t o that o f competitors.  2.  A s i m i l a r standard f o r a l l of the f i r m ' s customers.  3.  A s i m i l a r standard f o r a l l customers ? d t h i n defined geographical  4.  areas.  Consumer o r i e n t e d d e l i v e r y s e r v i c e , i e . , s e r v i c e as s p e c i f i e d by some or a l l of the f i r m ' s customers.  I n the absence of s p e c i f i c a l l y d e f i n e d d e l i v e r y requirements,  the t r a f f i c manager may use the present  l e v e l of d e l i v e r y s e r v i c e as a standard i n f o r m u l a t i n g  39 alternatives —  provided  p o l i c y c o n s t r a i n t s are  I t i s p o s s i b l e , however, that present reflect  satisfied.  d e l i v e r y standards  the method of t r a n s p o r t a t i o n that has been used i n  the past  r a t h e r than the minimum d e l i v e r y s e r v i c e that i s  acceptable  to the  f i r m ' s customers.  I t i s suggested,  t h e r e f o r e , that the e x i s t i n g d e l i v e r y s e r v i c e be used as a guide i n the f o r m u l a t i o n judgement be  employed i n a c c e p t i n g  a l t e r n a t i v e s that f a i l Some o f the  of a l t e r n a t i v e s , but or r e j e c t i n g  to meet t h i s assumed standard.  f a c t o r s that w i l l be important i n d e c i d i n g  whether the d e v i a t i o n from the present significant  that  standard  is  i n c l u d e the s a l e s volume of the a f f e c t e d  customers, the nature of the p r o d u c t , the environment, and  competitive  customer r e a c t i o n i n the past  to delivery  delays. I f the optimum a l t e r n a t i v e i s one  i n which s e r v i c e  t o c e r t a i n customers or areas i s substandard, i t s a d o p t i o n should be  subject  to approval  by the marketing department.  T h i s procedure i s a necessary safeguard against e v a l u a t i o n of customer r e a c t i o n by the I n a d d i t i o n t o the l i m i t  standard  t r a f f i c department.  on substandard d e l i v e r y  s e r v i c e , i t i s a l s o d e s i r a b l e to l i m i t improvements i n the  improper  short-term  of s e r v i c e .  Onoe the  firm's  40  customers have a d j u s t e d t o a l e v e l of d e l i v e r y s e r v i c e , i t may  be d i f f i c u l t  consequences.  t o reduce the standard without  F o r t h i s reason, the short-term  of s e r v i c e should not he economically maintained  serious standard  s i g n i f i c a n t l y h i g h e r than can be on a longer-term b a s i s .  the longer-term p l a n w i l l be developed  p r i o r to  Ideally, short-term  a n a l y s i s and the d e l i v e r y standards from t h i s p l a n can be used as the upper l i m i t The expressed  f o r short-term d e l i v e r y  d e l i v e r y standards  service.  of the f i r m should be  i n terms of d e l i v e r y d e l a y , eg., the number of  days delay from r e c e i p t of orders to d e l i v e r y at customer's establishments. Market Dimensions An i n i t i a l problem i n e s t a b l i s h i n g the framework f o r s h o r t - t e r m a n a l y s i s i s t h a t of d i v i d i n g the f i r m ' s total  s a l e s f o r e c a s t i n t o the market areas that w i l l  determine the p a t t e r n of t r a f f i c physical distribution  f l o w through p l a n t s and  facilities.  Many f i r m s d i v i d e t h e i r t o t a l market i n t o d e f i n e d g e o g r a p h i c a l r e g i o n s and adopt the p r a c t i c e of s e r v i n g the customers w i t h i n each of these t e r r i t o r i e s from s p e c i f i c d i s t r i b u t i o n points.  A f o u r d i v i s i o n system f o r n a t i o n a l  d i s t r i b u t i o n i n Canada, f o r example, may A t l a n t i c , C e n t r a l , P r a i r i e and  include  P a c i f i c regions  defined  with  d i s t r i b u t i o n warehouses l o c a t e d i n M o n t r e a l , Toronto, Winnipeg and Edmonton.  The  f o r e c a s t i n g task  the whole a n a l y s i s i s much simpler  i f pre-defined  areas f o r warehouses are used as the b a s i s production  This  served from more than  o f the d i s t r i b u t i o n warehouses. To  a v o i d the e x c l u s i o n o f r e l e v a n t  alternatives,  f i r m t h a t s e l l s i t s products to a small number of  l a r g e customers may  be  j u s t i f i e d i n t r e a t i n g each customer  as a separate demand u n i t i n a n a l y s i s . s i t u a t i o n , however, i s where the to a large number of v a r i o u s it  service  overlook s i g n i f i c a n t s a v i n g s i f  some o f the f i r m ' s customers can be  the  as  f o r short-term  and p h y s i c a l d i s t r i b u t i o n p l a n n i n g .  procedure, however, may  one  as w e l l  The  f i r m ' s products are  s i z e customers.  i s d e s i r a b l e t o s i m p l i f y f o r e c a s t i n g and  procedures through a p r e l i m i n a r y customers.  more common sold  In t h i s case analysis  grouping of i n d i v i d u a l  A combination of short-term c o n s t r a i n t s  —  i n c l u d i n g the d e l i v e r y s e r v i c e requirements of customers, and  the  f i x e d l o c a t i o n and  capacity  of d i s t r i b u t i o n ware-  houses  f a c i l i t a t e customer groupings that do. not  eliminate  the r e l e v a n t  alternatives for t r a f f i c  flow.  42 The  first  of these groupings  can be achieved by-  i d e n t i f y i n g the customers or oustomer areas t h a t are withi n the e x o l u s i v e d e l i v e r y range of each warehouse.  distribution  Given the d e l i v e r y s e r v i c e s p e o i f i o a t i o n s and  the a l t e r n a t i v e t r a n s p o r t a t i o n f a c i l i t i e s  and schedules  between stock p o i n t s and customers, i t i s p o s s i b l e t o d e f i n e t h e outer l i m i t s of the g e o g r a p h i c a l area that can be served from eaoh o f the f i n a l  d i s t r i b u t i o n warehouses.  To I l l u s t r a t e , assume that the f i r m ' s products are s o l d w i t h i n the g e o g r a p h i c a l area i n d i c a t e d i n F i g u r e 1.  FIGURE 1 DELIVERY RANGE OF WAREHOUSES A, B, AND C  45. T h i s t o t a l area i s served by three warehouses A, B, and C, whose s e r v i c e areas, based on d e l i v e r y standards, are w i t h i n the boundaries  i n d i c a t e d by the s o l i d l i n e , broken  l i n e and dotted l i n e r e s p e c t i v e l y .  The cross-hatched  s e c t i o n s represent the market areas t h a t are e x c l u s i v e to one o r the other s t o c k p o i n t .  Since these areas can  only be served from one or the other warehouse, the t o t a l customers w i t h i n each can be grouped i n t o s i n g l e demand units f o r planning  purposes.  I f the t o t a l demand t h a t i s generated  by oustomers  w i t h i n these e x c l u s i v e t e r r i t o r e s r e p r e s e n t s the b u l k o f the f i r m ' s s a l e s i t i s reasonable  t o assume that t h i s  demand w i l l d i c t a t e the p a t t e r n o f f l o w through p l a n t s and between p l a n t s and d i s t r i b u t i o n p o i n t s ; and that the demand o f other oustomers, i e . , customers w i t h i n d e l i v e r y range o f two o r more d i s t r i b u t i o n p o i n t s , w i l l merely i n c r e a s e the volume v i a a l t e r n a t i v e routes of t h i s b a s i c pattern.  I n o t h e r words, the p a t t e r n of t r a f f i c  be the same whether o r not the n o n - e x c l u s i v e  flow  delivery  areas are i n c l u d e d i n a n a l y s i s , p r o v i d e d demand w i t h i n these areas i s a s u f f i c i e n t l y s m a l l p r o p o r t i o n o f the total. To i n c l u d e the o v e r l a p p i n g d e l i v e r y areas i n  will  44  a n a l y s i s , one cannot simply s i n g l e demand u n i t , unless  t r e a t each of these as a the t r a n s p o r t a t i o n r a t e i s the  same t o a l l oustomers w i t h i n the area. oost  The a l t e r n a t i v e  of s e r v i n g one o f these customers i n c l u d e s the  d e l i v e r e d product cost at a l t e r n a t i v e d i s t r i b u t i o n p l u s the f i n a l t r a n s p o r t a t i o n c o s t .  points  Where the  t r a n s p o r t a t i o n r a t e d i f f e r s among customers w i t h i n the territory,  i t i s p o s s i b l e that the t o t a l  delivered  product cost t o some of these customers w i l l  favor  d e l i v e r y through one warehouse, w h i l e other customers w i l l be o p t i m a l l y served Since  a great  through an a l t e r n a t i v e stock  point.  d e a l of a d d i t i o n a l work may be i n v o l v e d i f  each of t h e customers w i t h i n overlaps  a r e to be i n c l u d e d  i n a n a l y s i s , i t i s d e s i r a b l e to l i m i t the a n a l y s i s t o the e x c l u s i v e t e r r i t o r i e s whenever demand w i t h i n these areas is sufficient  t o d i c t a t e the p a t t e r n  of t r a f f i c flow; and  whenever the volumes through t h e channels of t h i s are a s u f f i c i e n t  p r o p o r t i o n of the t o t a l to provide  reasonable b a s i s f o r short-term  operating  c o n d i t i o n s w i l l u s u a l l y be s a t i s f i e d d e l i v e r y areas as d e f i n e d major market  pattern  plans.  a  These  i f the e x c l u s i v e  above i n c l u d e a l l o f the f i r m ' s  areas.  I f there are a few l a r g e customers outside  o f the  46 e x c l u s i v e areas, t h e i r i n c l u s i o n i n a n a l y s i s as separate demand u n i t s may provide and p r e c i s i o n .  the d e s i r e d l e v e l o f  confidence  I f not, i t i s d e s i r a b l e t o aohieve a  f u r t h e r grouping r a t h e r than to t r e a t a great  number o f  s m a l l customers as separate demand u n i t s . The  l i m i t e d capacity  of stock p o i n t s  b a s i s f o r a f u r t h e r grouping.  Assuming that  serves  as a  total  c a p a c i t y at f i n a l d i s t r i b u t i o n p o i n t s i s s u f f i c i e n t , but not  s i g n i f i c a n t l y i n excess o f t o t a l a n t i c i p a t e d demand,  a reduction  i n t h e delivery, range o f f i n a l d i s t r i b u t i o n  points to t h e i r handling increase  capacity w i l l  r e s u l t i n an  i n t h e groups o f customers that are t o be  accommodated e x c l u s i v e l y through one or the other d i s t r i b u t i o n warehouse.  To i l l u s t r a t e ,  assume the s e r v i c e  areas of warehouses A and B, based on d e l i v e r y standards, are as shown i n F i g u r e  2.  46  The cross-hatohed section represents the geographi c a l area that can be served from either point insofar as meeting customer delivery requirements i s concerned. We  FIGURE 2 DELIVERY RANGE OF WAREHOUSES A AND B  know, however, that neither warehouse A nor B can accommodate a l l of the customers within this t e r r i t o r y i n addition to the oustomers within t h e i r exclusive range,  47 i e . , the c l e a r area i n F i g u r e 2 . oentre  The c l e a r area i n the  o f F i g u r e 3 r e p r e s e n t s the remaining  o v e r l a p i n the  s e r v i c e t e r r i t o r y o f warehouses A and B a f t e r a r e d u o t i o n i n the d e l i v e r y handling  range of these  two stock p o i n t s to t h e i r  capaoity.  FIGURE 3 THE REDUCTION IN DELIVERY RANGE OF DISTRIBUTION POINTS A AND B TO THEIR HANDLING CAPACITY  48 The cross-hatched s e c t i o n on the r i g h t i s now a part  of the t o t a l market area t o be served e x c l u s i v e l y  from warehouse B. part  The same s e c t i o n on the l e f t  i s now a  of the t o t a l market area t o be served e x c l u s i v e l y  from warehouse A. The extent  of the remaining overlap  i n service  areas depends upon the a n t i c i p a t e d volume of t r a f f i c i n r e l a t i o n t o d i s t r i b u t i o n point the t o t a l handling  capacity  capacities.  In g e n e r a l ,  of a l l of the f i n a l  d i s t r i b u t i o n p o i n t s w i t h i n a system w i l l not be s i g n i f i c a n t l y greater  than the t o t a l  except where warehouse c a p a c i t y  flow of t r a f f i c  has been e s t a b l i s h e d on  the b a s i s of o v e r l y o p t i m i s t i c f o r e c a s t s .  Hence, only a  minor p o r t i o n o f the t o t a l volume of t r a f f i c  i s l i k e l y to  be w i t h i n range of a l t e r n a t i v e d i s t r i b u t i o n p o i n t s the  —  s e r v i c e areas of stock p o i n t s  after  have been reduced t o  t h e i r handling  capacities.  I n t h i s case i t i s reasonable  to assume that  the b u l k of the f i r m ' s volume which has now  been assigned t o one or another d i s t r i b u t i o n point determine the optimum p a t t e r n of t r a f f i c p a t t e r n has been e s t a b l i s h e d ,  flow.  Once t h i s  the marginal cost of  i n c r e a s i n g the flow through a l t e r n a t i v e  will  production-  d i s t r i b u t i o n channels of the p a t t e r n can be used t o  49  determine which of the d i s t r i b u t i o n p o i n t s should customers w i t h i n the remaining  overlaps.  The problem at t h i s stage that can be used to achieve s e r v i c e areas.  serve  i s t o develop a method  t h i s reduction i n overlapping  A f o r e c a s t o f the flow of t r a f f i c  t o the  group of customers w i t h i n the e x c l u s i v e d e l i v e r y range o f a stock p o i n t s u b t r a c t e d from i t s h a n d l i n g  capacity,  i n d i c a t e s the s u r p l u s c a p a c i t y that i s a v a i l a b l e at that p o i n t f o r s e r v i c e to customers w i t h i n d e l i v e r y range of an a l t e r n a t i v e warehouse.  More s p e c i f i c a l l y then, the  problem i s to determine the p a r t i c u l a r customers or customer areas w i t h i n an overlap that should absorb the s u r p l u s c a p a c i t y of a d i s t r i b u t i o n p o i n t , I n the event the optimum p l a n c a l l s f o r the u t i l i z a t i o n of i t s t o t a l handling  capacity. Taking the simple  case o f the o v e r l a p p i n g d e l i v e r y  area f o r the two d i s t r i b u t i o n p o i n t s i n F i g u r e 2, that the volume o f t r a f f i c  that cannot be  we know  accommodated  through warehouse A must be handled through warehouse B. I f the c a p a c i t y of warehouse A i s f u l l y u t i l i z e d , the volume of t r a f f i c that w i l l pass through B i s a l s o f i x e d . Hence, c o s t s that are i n c u r r e d i n the flow o f t r a f f i c p r i o r to f i n a l d i s t r i b u t i o n from warehouse to customer  w i l l be the same r e g a r d l e s s  of the combination o f  customers w i t h i n the overlap f u l l y u t i l i z e d warehouse.  that are s e r v i c e d from the  These c o s t s may be  t h e r e f o r e , i n determining the oapaeity  ignored,  s e r v i o e area o f  d i s t r i b u t i o n points. Since  s h i p p i n g and t r a n s p o r t a t i o n c o s t s are the only  a d d i t i o n a l c o s t s between f i n a l stock p o i n t s and customers, the t o t a l of these c o s t s may be used as the b a s i s f o r a l l o c a t i n g the s u r p l u s c a p a c i t y of a d i s t r i b u t i o n warehouse among customers or customer areas w i t h i n the overlapping t e r r i t o r y .  The o b j e c t i v e i s t o minimize the t o t a l  s h i p p i n g and t r a n s p o r t a t i o n cost t o customers w i t h i n the overlap  —  given that the warehouse i n q u e s t i o n  fully utilized. first  Referring again t o Figure  e s t a b l i s h the c a p a c i t y s e r v i c e area  i s t o be  2, we would o f warehouse A  by m i n i m i z i n g t o t a l s h i p p i n g and t r a n s p o r t a t i o n cost t o a l l customers w i t h i n the o v e r l a p - ~ given t h a t the t o t a l c a p a c i t y o f A i s t o be u t i l i z e d .  The next step would be  to determine the c a p a c i t y s e r v i c e area of warehouse B i n the  same way and assuming that B, and not A, w i l l be  fully  utilized. Where a l a r g e number of customers are i n c l u d e d i n  the o v e r l a p ,  i t i s d e s i r a b l e t o a v o i d a f o r e c a s t of  traffic  f o r each by d i v i d i n g the t e r r i t o r y i n t o  t r a n s p o r t a t i o n r a t e areas.  Each o f these areas s h o u l d  i n c l u d e the group o f customers w i t h the same r e l a t i v e f r e i g h t r a t e from the a l t e r n a t i v e d i s t r i b u t i o n p o i n t s . F o r example, i f one hundred customers can be served from warehouse A at the same f r e i g h t r a t e , but only  f i f t y of  these have the same r a t e from warehouse B, the r a t e would c o n s i s t of the f i f t y  area  customers w i t h the same  r e l a t i v e r a t e from the two warehouses. A forecast  o f demand w i t h i n each of these r a t e  t e r r i t o r i e s oan now be r e l a t e d t o the c a p a c i t y that i s a v a i l a b l e t o the o v e r l a p  from the a l t e r n a t i v e  distribution points. In F i g u r e  4, the o v e r l a p p i n g  d e l i v e r y range o f  warehouses A and B has been d i v i d e d i n t o r a t e areas.  transportation  The f o r e c a s t of s a l e s t o customers w i t h i n  each segment i s shown as w e l l as the c a p a c i t y a v a i l a b l e t o the t o t a l o v e r l a p  that i s  from d i s t r i b u t i o n p o i n t s  A and B. The  problem, then, i s to determine which o f these  segments would be served from A i f A i s used t o c a p a c i t y  i n t h e optimum p l a n ; and, s i m i l a r l y the segments t would be served  from B, i f B i s used t o o a p a c i t y .  FIGURE 4 TRANSPORTATION RATE AREAS WITHIN THE OVERLAPPING DELIVERY RANGE OF WAREHOUSES A AND B  Assuming the sum o f s h i p p i n g and t r a n s p o r t a t i o n c o s t s between warehouses and customers are as shown i n Figure  5, we c a n e s t a b l i s h an order o f s e r v i c e  from each d i s t r i b u t i o n  point.  W  X  Y  Z  1.70  1.80  2.20  1.90  1.30  2.30  1.80  1.40  1.80  .40  -.60  .80  .10  U  V  Warehouse A  1.00  1.70  Warehouse B  1.50  A - B  -.50  Market Areas  preference  0  FIGURE 5 SHIPPING AND TRANSPORTATION COST PER UNIT (D0ILARS) The r e l a t i v e  cost of s e r v i n g the v a r i o u s  territories  from warehouse A, i n d i c a t e s that the cost to t e r r i t o r y W i s seventy cents p e r u n i t higher  than t o t e r r i t o r y U.  know, however, that i f warehouse A has s u f f i c i e n t to serve  We  capacity  only one o f these t e r r i t o r i e s that the other must  54  be served the  from the a l t e r n a t i v e d i s t r i b u t i o n p o i n t .  Hence,  r e l a t i v e cost, of s e r v i n g the two customers from ware-  house B must a l s o be taken i n t o account.  It is clear  that the p e r u n i t saving from A t o U (seventy o f f s e t by the h i g h e r cents).  oost  cents) i s  of s e r v i n g W from B ( e i g h t y  T e r r i t o r y W, t h e r e f o r e , must be served  point A i n preference The s i m p l e r  from  t o t e r r i t o r y U.  comparison i s t h e r e l a t i v e  cost of  s e r v i n g each t e r r i t o r y from the two d i s t r i b u t i o n p o i n t s . The saving  of s i x t y cents p e r u n i t by s e r v i n g  territory  W from A i n s t e a d of B i s g r e a t e r than the s a v i n g of f i f t y cents p e r u n i t i n s e r v i n g U from A. the  same net r e s u l t .  Both methods l e a d t o  The order of p r e f e r e n c e ,  therefore,  can be e s t a b l i s h e d f o r each d i s t r i b u t i o n p o i n t on the b a s i s of the d i f f e r e n c e i n s h i p p i n g cost t o the same customers.  and t r a n s p o r t a t i o n  The order of p r e f e r e n c e f o r  warehouse A i s t e r r i t o r i e s W, U, X, Z, V and Y as i n d i c a t e d by the t h i r d row i n F i g u r e  5.  I f t h e optimum p a t t e r n of t r a f f i c  flow c a l l s f o r  the c a p a c i t y u t i l i z a t i o n o f d i s t r i b u t i o n p o i n t A, the 1000 u n i t s of c a p a c i t y a v a i l a b l e at A must be a l l o c a t e d as shown i n F i g u r e i n a lower t o t a l  6.  cost.  No other a l l o c a t i o n w i l l r e s u l t  55  f e may conclude, t h e r e f o r e , that while  territory  V, X, Y and Z are w i t h i n d e l i v e r y range of d i s t r i b u t i o n point A, the c a p a c i t y of A w i l l not permit d e l i v e r y t o V, Y or Z, and, i f f u l l y u t i l i z e d w i l l meet only s i x t h s of the volume r e q u i r e d i n t e r r i t o r y X. t e r r i t o r i e s V, Y, Z and o n e - s i x t h  five-  Hence,  of X may be excluded  from the c a p a c i t y s e r v i c e area of warehouse A without e l i m i n a t i n g the r e l e v a n t a l t e r n a t i v e s f o r product Market Areas Warehouse A  - V  U 100  Warehouse B Market Demand  Z  100  E00  300  600  200  300  X  400  500  400  600  100  Y  W  500 1  flow.  FIGURE 6 OPTIMUM AlLOCATION OF DISTRIBUTION POINT A'S AVAILABLE CAPACITY The order of p r e f e r e n c e course, the opposite  f o r warehouse B i s , o f  o f A, and the same a n a l y s i s w i l l  i n d i c a t e that t e r r i t o r i e s U, W, excluded from the c a p a c i t y  and o n e - s i x t h  of X may be  s e r v i c e area of warehouse B.  T e r r i t o r i e s excluded from the c a p a c i t y s e r v i c e of one warehouse a u t o m a t i c a l l y market area to be served The r e s u l t  area  become p a r t o f the t o t a l  from the a l t e r n a t i v e stock  point.  i n the above example i s a r e d u c t i o n i n the  56 o v e r l a p of the  s e r v i c e area of warehouses A and B t o  t h i r d s of the a n t i c i p a t e d volume w i t h i n t e r r i t o r y The  volumes of t r a f f i c  X.  to t e r r i t o r i e s that  are  excluded from A's  c a p a c i t y area can be added t o the  volume w i t h i n B's  e x c l u s i v e d e l i v e r y range.  volumes excluded from B's  added t o  e x c l u s i v e d e l i v e r y range.  A n a l y s i s t o determine the optimum flow of t r a f f i c production  the number of demand u n i t s t o the  number of d i s t r i b u t i o n p o i n t s the remaining overlaps ignored  through  and p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s i s thus  s i m p l i f i e d by reducing  be  total  Similarly,  c a p a c i t y area can be  the t o t a l volume w i t h i n A's  two-  (assuming the volumes w i t h i n  are r e l a t i v e l y i n s i g n i f i c a n t  i n formulating  traffic  and  flow a l t e r n a t i v e s . )  can If a  s i g n i f i c a n t p r o p o r t i o n of f o r e c a s t e d volume i s t o customers w i t h i n the remaining overlaps., the number of demand u n i t s for  a n a l y s i s can be  i n c r e a s e d t o i n c l u d e some or a l l of the  t r a n s p o r t a t i o n r a t e areas that are w i t h i n these market segments. It  should be noted that the above procedure f o r  i d e n t i f y i n g segments of the b u t i o n p o i n t s can be s i n g l e product. geographically  overlap with  specific  distri-  used only f o r the d i s t r i b u t i o n of a  T r a n s p o r t a t i o n r a t e s , however, tend t o d i s t r i b u t e d and  there w i l l be a s i m i l a r  r e l a t i o n s h i p , t h e r e f o r e , between the cost from two  ware-  be  houses t o the same customer areas f o r v a r i o u s  commodities.  Hence, the same t r a n s p o r t a t i o n r a t e areas are l i k e l y t o apply  f o r s e v e r a l of the f i r m ' s products and s u f f i c i e n t o f  these can be i n c l u d e d i n a n a l y s i s to provide l e v e l o f confidence Sales  the d e s i r e d  and p r e c i s i o n .  Forecasts According  t o a study sponsored by the C o n t r o l l e r s  I n s t i t u t e Research Foundation, almost a l l manufacturing f i r m s use s a l e s f o r e c a s t s as a primary b a s i s f o r s h o r t o  term p l a n n i n g The  short-term  i n the v a r i o u s  f u n c t i o n s of the b u s i n e s s .  f o r e c a s t g e n e r a l l y o r i g i n a t e s i n the  marketing department.  Following  approval  ment, i t i s passed on to o p e r a t i n g co-ordinate  planning  and budgeting.  by upper manage-  d i v i s i o n s t o guide and The a n t i c i p a t e d  volumes of s a l e s are commonly expressed i n d o l l a r f i g u r e s which a r e t h e n converted by the v a r i o u s u n i t s that are a p p r o p r i a t e  to planning  departments i n t o i n their  respective  areas. I t i s d e s i r a b l e that the approved s a l e s f o r e c a s t be used as the b a s i s f o r p r o d u c t i o n  and p h y s i c a l d i s t r i b u t i o n  Burnard H. Sord, Glenn A. Welsch, B u s i n e s s Budgeting (New York: C o n t r o l l e r s I n s t i t u t e Research Foundation, 1958), p. 133.  58 p l a n n i n g to ensure that the  l e v e l of planned a c t i v i t y  t h i s area i s geared to marketing requirements. f o r e c a s t , however, w i l l r e q u i r e used f o r t h i s purpose. s a l e s w i l l have t o be  This  refinement b e f o r e i t can  be  I n p a r t i c u l a r , the t o t a l volume of divided  the product groups that bution  in  among the t e r r i t o r i e s ,  are r e l e v a n t  for physical  and  into  distri-  planning. . I t i s suggested that the  forecasting  should be  t r a f f i c manager's r o l e i n  l i m i t e d t o d e f i n i n g the market  dimensions and  the product groups that  purposes.  marketing department should then assume the  The  t a s k of a l l o c a t i n g the  a n t i c i p a t e d s a l e s among the  t e r r i t o r i e s a c c o r d i n g to the v a r i o u s underlie  the  approved  II.  are r e l e v a n t  for his  defined  assumptions that  forecast.  FLEXIBILITY IN PRODUCTION  AND  PHYSICAL DISTRIBUTION FACILITIES Production F a c i l i t i e s The the  a l t e r n a t i v e s f o r product flow are l i m i t e d i n  s h o r t - t e r m by  the f i x e d l o c a t i o n of the  p r o d u c t i v e u n i t s and  by the  l i m i t e d capacity  firm's of each of  these u n i t s . " P r o d u c t i o n i s the  r e s u l t of the  flow of work that  59 goes from one t o another o f the fundamental elements,  structural  each o f which i n c l u d e s man, machine, t o o l s ,  m a t e r i a l , and s p e c i f i c a t i o n s . "  3  The maohines and t o o l s  at a p l a n t w i t h which m a t e r i a l s can be transformed  into  products of the d e s i r e d s p e c i f i c a t i o n s are g i v e n i n the short-term. first  The output at a p l a n t , t h e r e f o r e , i s l i m i t e d  o f a l l t o the volume that can be achieved through  the maximum u t i l i z a t i o n o f i t s machines and t o o l s . Expansion o f output t o t h i s l e v e l , however, may be impossible i n the s h o r t - t e r m f o r s e v e r a l reasons. A d d i t i o n a l manpower of the type that i s r e q u i r e d may not be r e a d i l y a v a i l a b l e , or i t may be impossible to adequately t r a i n the a d d i t i o n a l personnel i n the time is available.  that  I f i n c r e a s e d output c a l l s f o r the use o f  overtime, t h i s may c o n f l i c t w i t h e x i s t i n g l a b o r agreements or management p o l i c y .  The p e r i o d may be too short t o  organize and i n t r o d u o e the new o p e r a t i o n s and maintenance procedures that are r e q u i r e d with a h i g h e r u t i l i z a t i o n . These and other c o n s t r a i n t s must be considered i n determining the maximum l e v e l of output t h a t i s r e a l i s t i c f o r each p l a n t i n the short-term.  Raymond V i l l e r s , Dynamic Management i n Industry (Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , I n c . , I960), p. 222.  60 R e i n f e l d and "Vogel employ what i s r e f e r r e d t o as the b o t t l e n e c k concept  i n determining a l t e r n a t i v e  p r o d u c t i o n mix f o r a p l a n t .  4  T h i s concept may a l s o be  used t o s i m p l i f y a study o f output f l e x i b i l i t y . procedure  i s t o i d e n t i f y the least f l e x i b l e  manufacturing processes w i t h i n the p l a n t .  of the T h i s may be a  s p e c i f i c machine o p e r a t i o n , a process r e q u i r i n g labor s k i l l ,  etc.  The  A thorough study of t h i s  special  particular  segment of the t o t a l manufacturing o p e r a t i o n w i l l  reveal  the maximum output that can be achieved, r e g a r d l e s s of flexibility  i n other p r o c e s s e s .  Elements  of s h o r t - t e r m i n f l e x i b i l i t y  t e c h n i c a l problems,  including  p o l i c y and commitments, may a l s o  limit  the extent t o which output at i n d i v i d u a l p l a n t s can be reduced.  A decrease i n the l e v e l of output at a p l a n t  will  g e n e r a l l y i n v o l v e a r e d u c t i o n i n the l a b o r f o r c e and a redistribution among machines.  of work among remaining employees and The t e c h n i c a l i m p l i c a t i o n s of t h i s  may i n c l u d e a change i n p l a n t  action  l a y o u t ; new o p e r a t i o n s and  maintenance p l a n s ; and employee t r a i n i n g where the r e d i s t r i b u t i o n o f work r e q u i r e s the remaining employees  *Nyles V. R e i n f e l d , W i l l i a m R. Y o g e l , Mathematical Programming (Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , I n c . , 1958), p. 210,  t o handle new problems may the  or a d d i t i o n a l t a s k s .  s o l u t i o n to these  w e l l r e q u i r e more time than i s a v a i l a b l e i n  short-term.  plant  The  Commitments that l i m i t  output may  c o n t r a c t s , eg.,  a reduction  in  include r e s t r i c t i v e clauses i n l a b o r guaranteed annual wage c l a u s e s , minimum  work crews, e t c .  The  f i r m may  have entered  into  longer  term purchase agreements w i t h s u p p l i e r s or t r a n s p o r t a t i o n c o n t r a c t s f o r minimum q u a n t i t i e s of m a t e r i a l s to shipped to s p e c i f i c p l a n t s .  be  P o l i c y w i l l o f t e n govern the  more i n t a n g i b l e f a c t o r s that are i n v o l v e d i n r e d u c i n g l e v e l of p l a n t o p e r a t i o n . f o r example, may  Employment s t a b i l i z a t i o n p o l i c y ,  be e x p l i c i t  p u b l i c or employee r e a c t i o n . output r e d u c t i o n s  are  the  i n order to avoid P o l i c y may  adverse  a l s o apply where  l i k e l y to a f f e c t the welfare  of  employees, dependent s u p p l i e r s or the community i n which the p l a n t  i s located.  I n summary, the r e l e v a n t flow  a l t e r n a t i v e s f o r product  are those that c a l l f o r a l e v e l of output at each  p l a n t that i s w i t h i n the f e a s i b l e minimum and maximum range.  T h i s range should be d e f i n e d by  production  p e r s o n n e l who  c o n s t r a i n t s that l i m i t the  business.  responsible  are f a m i l i a r w i t h the  various  f l e x i b i l i t y i n t h i s f u n c t i o n of  62 D i s t r i b u t i o n Warehouses The  constraints that l i m i t  flexibility  i n the  o f flow through each of the f i r m ' s stock p o i n t s s i m i l a r to those that l i m i t Limited materials  storage  handling  the  capacity  facilities;  are  range of output at p l a n t s . and given packing inflexibility  of f a c i l i t i e s due  skills;  shortages of the types of l a b o r that  required to increase  handling,  and  i n the  utilization and  to l a b o r agreements, p o l i c y ,  are  some of the  are  constraints  that must be taken i n t o account l n determining the of t r a f f i c  volumes t h a t can be  rate  range  accommodated through  distribution points. Concentration  on the l e a s t f l e x i b l e of the  procedures at a warehouse w i l l  s i m p l i f y the problem o f  e s t a b l i s h i n g i t s f e a s i b l e handling handling  capacity.  equipment, f o r example, may  that can be accommodated r e g a r d l e s s other warehousing  operations.  Transportation  Handling  and  Although there may  be  limit  Materials  the volume  of f l e x i b i l i t y  in  a great number of a v a i l a b l e  modes of t r a n s p o r t a t i o n between stock p o i n t s and the  handling  a l t e r n a t i v e s that are acceptable  i n the  customers,  short-term  63 are l i m i t e d t o those that w i l l meet the f o l l o w i n g conditions: 1.  A minimum d e l i v e r y s e r v i c e t o customers.  This  may be the e x i s t i n g standard; an approved lower standard; or a l e v e l o f s e r v i c e requested by the customer or the marketing department. 2.  A maximum d e l i v e r y standard.  This  constraint  i s necessary t o prevent the a d o p t i o n o f a l e v e l of s e r v i c e that cannot be maintained on a longer term b a s i s .  The maximum should be t h e standard  c a l l e d f o r i n the longer-term d i s t r i b u t i o n p l a n s . 3.  Transportation  methods that a r e s u i t a b l e f o r the  f i r m ' s p r o d u c t s and that  can be used i n  c o n j u n c t i o n w i t h l o a d i n g and unloading at p l a n t s and warehouses.  I t may be  facilities impossible  i n the short-term, f o r example, t o adapt the p h y s i c a l layout of a p l a n t t o t r u c k l o a d i n g i f the e x i s t i n g arrangement i s intended loading.  F r e i g h t handling  for  rail  or paokaging equip-  ment at a p l a n t or warehouse may be l i m i t e d t o use w i t h a s p e c i f i c method o f t r a n s p o r t a t i o n . 4.  T r a n s p o r t a t i o n methods that customers.  are acceptable t o  I f customers s p e c i f y the method, a l l  other forms of t r a n s p o r t a t i o n are i r r e l e v a n t i n  64 analysis. T r a n s p o r t a t i o n a l t e r n a t i v e s to p l a n t s and between p l a n t s and warehouses are l i m i t e d t o those  that are  s u i t a b l e f o r the f i r m ' s m a t e r i a l s and p r o d u c t s ; and t o those  that can be used i n c o n j u n c t i o n with  existing  l o a d i n g and u n l o a d i n g f a c i l i t i e s at p l a n t s and warehouses. Order-Processing  and Communications  I n a d d i t i o n t o s a t i s f y i n g p h y s i c a l movement r e q u i r e ments, a l t e r n a t i v e s i n the short-term must be f e a s i b l e i n terms of the changes that are necessary p r o c e s s i n g and communications A flow of t r a f f i c  i n order-  procedures.  i s preceded by the flow of paper  work a s s o c i a t e d w i t h the p r e p a r a t i o n and d i s p a t c h of customer orders and supply r e q u i s i t i o n s .  Flexibility in  the u t i l i z a t i o n of c l e r i c a l s t a f f s and o f f i c e equipment must be adequate f o r the p a t t e r n s of d i s t r i b u t i o n b e i n g considered i n a n a l y s i s .  The c o n s t r a i n t s on  short-term  changes i n s t a f f that were d i s c u s s e d i n the p r o d u c t i o n and warehousing s e c t i o n s a l s o apply i n t h i s  area.  Communications f a c i l i t i e s i n the form of m a i l , telephone  and t e l e g r a p h are g e n e r a l l y a v a i l a b l e f o r any  of the ohanges t h a t may be c o n s i d e r e d f o r t r a f f i c  flow.  Some f i r m s , however, employ e l e c t r o n i c systems f o r processing  and communicating orders  from d i s t r i b u t i o n  p o i n t s t o p l a n t s and i n some cases from customers t o distribution points.  I f , i n t h i s case, the f i r m has  abandoned the c o n v e n t i o n a l  s t a f f , equipment and paper  procedures that can be used as an a l t e r n a t i v e t o the system, i t may be i m p r a c t i c a l to c o n s i d e r a l t e r n a t i v e s f o r t r a f f i c flow t h a t do not conform with e s t a b l i s h e d channels o f the communications network.  CHAPTER IV COLLECTION AND PREPARATION OF DATA The method of a n a l y s i s suggested i n Chapter V t o determine the optimum a l l o c a t i o n of output among the f i r m ' s p l a n t s i n v o l v e s a comparison of the v a r i a b l e cost o f the a l t e r n a t i v e routes production-physical  that t r a f f i c may take through the d i s t r i b u t i o n system.  I t i s necessary,  t h e r e f o r e , t o determine the a l t e r n a t i v e t r a f f i c  routes  that  are  a v a i l a b l e to the f i r m i n the short-term  and  r e l a t e the elements o f v a r i a b l e cost that are a s s o c i a t e d  w i t h each of these  and t o i d e n t i f y  routes.  Flow diagrams may be u s e f u l i n i d e n t i f y i n g a l t e r n a t i v e routes involved i n t r a f f i c  and the major processes that are flow.  The p r e p a r a t i o n  diagrams i s d e a l t w i t h i n the f i r s t  of these  s e c t i o n of t h i s  chapter.  The v a r i a b l e c o s t s o f the v a r i o u s processes i n v o l v e d i n traffic  flow and the types of i n f o r m a t i o n that are r e q u i r e d  i n order t o r e l a t e adjacent  processes are d i s c u s s e d  in a  later section. I.  FLOW DIAGRAMS  Magee s t a t e s that , . . an o r g a n i z a t i o n , whatever i t w  may be can be viewed as c o n s i s t i n g of a number of stock p o i n t s and a number of o p e r a t i o n s , t o g e t h e r w i t h a c o n t r o l system.  I n p r i n c i p l e a flow c h a r t can be c o n s t r u c t e d  showing the course of the flow from the sources o f raw m a t e r i a l s through the i n t e r m e d i a t e stock p o i n t s t o customers."  T r a n s p o r t a t i o n i s the connecting  1  link  between adjacent stages i n the flow o f m a t e r i a l s and products and i t s a v a i l a b i l i t y w i l l determine  and s u i t a b i l i t y , t h e r e f o r e ,  the p o t e n t i a l routes that t r a f f i c may  to p l a n t s , between p l a n t s and warehouses and from  take  final  d i s t r i b u t i o n warehouses t o customers. A c h a r t of a l t e r n a t i v e t r a f f i c routes should b e g i n by d e f i n i n g the l o c a t i o n s of raw m a t e r i a l s , p l a n t s and stock p o i n t s .  An e v a l u a t i o n o f t r a n s p o r t a t i o n f a c i l i t i e s  between adjacent stages w i l l then i n d i c a t e the f e a s i b i l i t y of l i n k i n g a g i v e n p l a n t w i t h a p a r t i c u l a r souroe  of raw  m a t e r i a l s , a g i v e n warehouse w i t h a p a r t i c u l a r p l a n t , e t c . D e l i v e r y s e r v i c e i s a prime c o n s i d e r a t i o n i n determining the f e a s i b i l i t y  of l i n k i n g a f i n a l  distribution  p o i n t and a customer through a p a r t i c u l a r mode of t r a n s portation.  D e l i v e r y s e r v i c e , however, i s undefined i n the  ohn F. Magee, P r o d u c t i o n P l a n n i n g and Inventory C o n t r o l (New York, N.Y.: McGraw H i l l Book Company, 1958), p. 16.  68  movement of t r a f f i c  to. p l a n t s and between p l a n t s and  stock  p o i n t s -- except where product p e r i s h a b i l i t y or obsolescence is involved. and  I f t r a n s p o r t a t i o n f a c i l i t i e s are a v a i l a b l e  are t e c h n i c a l l y s u i t a b l e f o r the movement of the  traffic  firm's  through t o a d i s t r i b u t i o n warehouse, the route i s  f e a s i b l e r e g a r d l e s s of movement time.  While s u c c e s s i v e l y  l o n g e r d e l i v e r y time i n c r e a s e s the i n v e n t o r y t h i s a d d i t i o n a l cost may or more of purchasing,  w e l l be o f f s e t by  production,  carrying cost,  savings In  warehousing  one  and  transportation costs. The  technical suitability  p o r t a t i o n must be e v a l u a t e d  of a method of t r a n s -  i n terms of the nature  m a t e r i a l s or products as w e l l as the h a n d l i n g at  p l a n t s and warehouses.  The  be  capable o f accommodating the dimensional  of  requirements  c a r r i e r , f o r example, must size  and  weight of the f i r m ' s m a t e r i a l s or products and must be to p r o v i d e  able  r e f r i g e r a t e d , heated or other s p e c i a l i z e d  equipment where t h i s i s r e q u i r e d .  l o a d i n g and  f a c i l i t i e s at p l a n t s and warehouses must be the requirements of the c a r r i e r .  unloading  adaptable t o  A s t o c k - p i l e of  m a t e r i a l s or products on a r a i l w a y spur, f o r example, be i n a c c e s s i b l e to motor v e h i c l e s . equipment such as oranes and l o c a t i o n and  layout  may  Specialized loading  conveyors, and the  physioal  of the f i r m ' s p l a n t s and warehouses  69  may a l s o l i m i t  i t s a b i l i t y t o adapt to a p a r t i c u l a r mode  of a v a i l a b l e t r a n s p o r t a t i o n .  These and other  c o n s i d e r a t i o n s must be taken i n t o account before i s accepted  as t e c h n i c a l l y f e a s i b l e .  Figure  7 i s a flow diagram of a h y p o t h e t i c a l three  p l a n t , f i v e warehouse system. from f o u r l o c a t i o n s . supply  the route  Raw m a t e r i a l s are a v a i l a b l e  The l i n e s l i n k i n g raw m a t e r i a l s  p o i n t s with p l a n t s , and p l a n t s with warehouses,  i n d i c a t e the f e a s i b l e t r a f f i c  routes  i n s o f a r as t r a n s -  p o r t a t i o n a v a i l a b i l i t y and s u i t a b i l i t y  Raw m a t e r i a l s Locations  i s concerned.  Warehouses  FIGURE 7 FLOW DIAGRAM  The  diagram i n d i c a t e s that  supplies f o r plants A  and B can be shipped from a l l o f the raw m a t e r i a l s l o c a t i o n s , while p l a n t U must r e c e i v e i t s supply p o i n t s 3 and 4.  from p l a n t A ,  Warehouse Y cannot be served  Additional d e t a i l i s included  i n F i g u r e 8 t o i d e n t i f y the  cost elements that are i n v o l v e d i n the p h y s i c a l COST ELEMENTS: 1)  Purchase P r i o e  2)  Transportation  3) a) b) 4) 5)  6) 7)  8)  from  Raw M a t e r i a l s  flow.  Locations  Warehousing Inventory  Production a)  Warehousing  b)  Inventory  Transportation a)  Warehousing  b)  Inventory  A  C  B  Transportation CUSTOMERS FIGURE 8 FLOW DIAGRAM  X  Y  71 The  diagram assumes that customers have been  d i v i d e d among the f i v e warehouses a c c o r d i n g procedure d e s c r i b e d The  i n the p r e v i o u s  t o the  chapter.  advantage of a flow diagram i s that i t s  preparation  a s s i s t s the a n a l y s t  i n h i s understanding o f  the e x i s t i n g system by r e q u i r i n g p r e l i m i n a r y  studies of  the v a r i o u s p r o c e s s e s and t h e i r t e c h n i c a l r e l a t i o n s h i p s . T h i s background i n f o r m a t i o n feasible traffic traffic  routes  i s u s e f u l i n i d e n t i f y i n g the  and the a l t e r n a t i v e s f o r moving  through each of these II. The  routes.  COST SCHEDULES AND OTHER DATA  cost elements shown i n F i g u r e  independent.  8 are not  The d e l i v e r e d cost of raw m a t e r i a l s at p l a n t s  v a r i e s w i t h the sources from which they are r e c e i v e d and the method of t r a n s p o r t a t i o n that i s used f o r t h e i r delivery.  Moreover, the volume of i n v e n t o r y  that must be  c a r r i e d at stock p o i n t s , as w e l l as the volumes i n t r a n s i t , vary w i t h d i f f e r e n c e s i n the d e l i v e r y time of a l t e r n a t i v e carriers.  Handling c o s t s at warehouses may a l s o  differ  w i t h t h e a l t e r n a t i v e methods of r e c e i v i n g and forwarding materials  and p r o d u c t s .  Hence, i n a d d i t i o n t o e s t i m a t e s of cost f o r each  78  segment of the a l t e r n a t i v e t r a f f i c  routes,  the data f o r  a n a l y s i s must i n c l u d e the key parameters that permit a l i n k i n g o f i n d i v i d u a l cost elements i n t o t o t a l route These c o s t s and parameters are d i s c u s s e d sections.  The p r e p a r a t i o n  costs.  i n the f o l l o w i n g  of data i n t o t o t a l route  eosts  i s d e a l t with i n the l a s t p a r t of the chapter. It raw  i s assumed f o r purposes o f t h i s t h e s i s that a l l  materials  are purchased; that these are t r a n s p o r t e d by  public c a r r i e r to processing the p l a n t i n c l u d e storage  p l a n t s ; that f a c i l i t i e s at  space f o r m a t e r i a l s and f i n i s h e d  produots; and that p r o d u c t s are t r a n s p o r t e d  by p u b l i c  c a r r i e r t o company owned f i e l d warehouses f o r d i s t r i b u t i o n t o customers. Raw M a t e r i a l s Data The  purchase p r i c e o f raw m a t e r i a l s  l i s t e d f o r each p o i n t firm.  should be  at which these are a v a i l a b l e t o the  A l t e r n a t i v e p r i c e s should  be shown i f the p r i c e  v a r i e s w i t h the s i z e o f the o r d e r . A review o f the l o c a t i o n s and p r i c e of raw m a t e r i a l s should be undertaken by the f i r m ' s P u r c h a s i n g Agent.  The r e s u l t s of t h i s survey may be prepared i n a  form such as shown i n Table  1.  73 The  last  shipment s i z e .  column has been i n c l u d e d t o i n d i c a t e T h i s may be important i n r e l a t i n g raw  m a t e r i a l s p r i c e and t r a n s p o r t a t i o n a l t e r n a t i v e s , eg., r a i l w a y c a r l o a d and t r u o k - l o a d r a t e s both apply t o a minimum shipment  size. TABLE I PAW MATERIALS DATA  Description  Location  Order Quantity  Price Per Unit  Units Per 100 Lbs.  1 P a r t 101  P a r t 403  Montreal  1000 1001 2001  or less - 2000 o r more  0.50 0.45 0.40  Toronto  2000 or l e s s 2001 o r more  0.55 0.45  Hamilton  No  Discount  5.00  Toronto  No  Discount  4.75  20  £  T r a n s p o r t a t i o n Data In a d d i t i o n to f r e i g h t should  r a t e s , t r a n s p o r t a t i o n data  i n c l u d e the minimum weight and u n i t s of m a t e r i a l s  or products ( i f any) t o which these r a t e s apply as w e l l as the d e l i v e r y time f o r each of the a v a i l a b l e c a r r i e r s . This information  should be c o l l e c t e d and assembled by the  T r a f f i c Manager i n a form such as i s i n d i c a t e d i n Table I I .  74 The d e l i v e r y time i n c l u d e s the  supply  time f o r f i l l i n g the order at  point. TABLE I I TRANSPORTATION DATA Commodity:  Raw M a t e r i a l - P a r t  Rate P e r 100 Lbs.  101  Minimum Units  Minimum Weight  Carrier  From  To  CNR  Mtl.  Wpg.  2.50  None  CNR  Mtl.  Wpg.  1.70  20,000 l b s .  Midland  Mtl.  Wpg.  2.80  None  Midland  Mtl.  Wpg.  2.00  10,000 l b s .  Delivery Time  -  4 Days  4000  6 Days  -  D e l i v e r y time has been i n c l u d e d  3 Days  2000  3 Days  i n Table I I  because of i t s d i r e c t r e l a t i o n s h i p t o t r a n s i t and s a f e t y inventories. rates  Minimum shipment volumes t o which  apply may a l s o r e q u i r e  inventories. discussed  oertain  l a r g e r than normal c y c l e  The nature of these r e l a t i o n s h i p s w i l l be  i n d e t a i l i n a l a t e r s e c t i o n of t h i s  chapter.  P r o d u c t i o n Data The v a r i a b l e p r o c e s s i n g i s manufactured at a p l a n t P r o d u c t i o n Manager.  eost  f o r each product  that  should be estimated by the  These e s t i m a t e s w i l l c o n s i s t  largely  75 of the wages o f some o r a l l of the p l a n t employees and the cost o f o p e r a t i n g machines and equipment.  The cost of raw  m a t e r i a l s w i l l he handled s e p a r a t e l y and should n o t , t h e r e f o r e , be i n c l u d e d , but i n f o r m a t i o n department should  from the p r o d u c t i o n  i n c l u d e t h e types and q u a n t i t i e s of raw  m a t e r i a l s that are r e q u i r e d f o r each product. Given the p e r i o d of time t o be covered i n the a n a l y s i s , the P r o d u c t i o n  Manager w i l l be i n the p o s i t i o n t o  a s c e r t a i n the v a r i a b i l i t y operations.  i n cost of the v a r i o u s  The d e t e r m i n a t i o n  o f c o s t s may be  simple i f the f i r m ' s cost accounting logical  relatively  system p r o v i d e s a  a l l o c a t i o n o f v a r i a b l e c o s t s among  Processing  plant  products.  cost may be presented i n the f o l l o w i n g form: TABLE I I I PROCESSING COST DATA Location  Product  of P l a n t :  Montreal  V a r i a b l e Cost P e r U n i t of Product Labor ' Machines Other  <fe  <fe  Total 1  10D  0.50  0.33  0.08  0.91  6F  0.82  0.54  0.15  1.51  76 In a d d i t i o n to cost i n f o r m a t i o n , the P r o d u c t i o n Manager should determine  the output c a p a c i t y f o r each  p l a n t over the p l a n n i n g p e r i o d . Where o n l y one product i s manufactured,  or when  manufacturing processes f o r each product are independent, c a p a c i t y can he expressed i n " u n i t s of p r o d u c t " . g e n e r a l problem,  however, i s where a p l a n t  The more  manufactures  s e v e r a l products, each of whieh pass through one o r more of the same p r o c e s s e s .  I n t h i s case, the mix of output  that w i l l absorb p l a n t c a p a c i t y cannot be predetermined and i t becomes necessary t o d e f i n e c a p a c i t y i n man-hours, machine-hours o r o t h e r a p p r o p r i a t e common measurement. The o a p a c i t y measurement that should be used depends upon the nature of the manufacturing p r o c e s s that l i m i t s t o t a l output.  P r o d u c t i o n at a f u r n i t u r e p l a n t , f o r example, may  be l i m i t e d  t o the r a t e at which i t s c a r p e n t e r s can assemble  the b a s i c frames. frame assembly capacity•  I n t h i s oase, a v a i l a b l e man-hours i n the  d i v i s i o n i s an a p p r o p r i a t e measurement of  The output of a pipe m i l l ,  may be l i m i t e d  on the o t h e r hand,  t o the c a p a c i t y of i t s welding equipment.  In t h i s event, a v a i l a b l e p r o c e s s i n g time on welding machines i s the c a p a c i t y measurement that in  analysis.  should be used  77 D e f i n i n g maximum c a p a c i t y i n t h i s way, i e . , i n terms of the b o t t l e n e c k o p e r a t i o n , put o f o t h e r manufacturing  i m p l i e s t h a t t h e out-  2  processes at the p l a n t can be  a d j u s t e d t o whatever mix of p r o d u c t i o n i s c a l l e d f o r i n the optimum p l a n .  T h i s assumption  may or may not be v a l i d .  A necessary c o n c l u d i n g step i n a n a l y s i s , t h e r e f o r e , i s t o compare the proposed  output  of a product w i t h the  c a p a c i t y of i t s e x c l u s i v e manufacturing compare combined product  p r o c e s s e s ; and t o  outputs against the c a p a c i t y of  the a p p r o p r i a t e eommon manufacturing  processes.  I n f o r m a t i o n r e l a t e d to p l a n t c a p a c i t i e s should include a l i s t  o f the manufacturing  processes i n the p l a n t ;  the short-term o a p a e i t y f o r each process I n man-hours, machine-hours or o t h e r a p p r o p r i a t e measurement; the products that pass through each of the p r o c e s s e s ; and the q u a n t i t y of process c a p a c i t y t h a t i s r e q u i r e d f o r each u n i t o f product.  Table IV i s an example o f the form i n  which t h i s i n f o r m a t i o n may be p r e s e n t e d .  N y l e s V. H e i n f e l d , W i l l i a m R. V o g e l , Mathematical Programming (Englewood C l i f f s , tf.J.: P r e n t i c e - H a l l Inc., 1958), p. 210. 6  78  TABLE IV PLANT CAPACITY DATA LOCATION:  Process  Capacity  Mat'1 Handling  4480 Man  Lathes Drills  Montreal C a p a c i t y Required Per U n i t  Products  10D 6F  0.10 0,08  Hrs. Hrs,  9500 Machine Hrs,  10D 6F  0.35 0.50  Hrs. Hrs.  1900  10D  0.E0  Hrs.  Hrs,  Machine Hrs.  Warehousing Data The  v a r i a b l e cost of h a n d l i n g m a t e r i a l s or  products at warehouses should be i n charge of these o p e r a t i o n s . m a t e r i a l s may  developed  by the  officer  Warehouses f o r raw  be under the P r o d u c t i o n Manager's  j u r i s d i c t i o n , while product warehouses may  be  the  r e s p o n s i b i l i t y of the S a l e s Manager. V a r i a b l e c o s t s i n t h i s area w i l l c o n s i s t l a r g e l y of the wages of warehouse employees and the c o s t s of o p e r a t i n g m a t e r i a l s h a n d l i n g equipment.  Costs may  d i f f e r , however,  w i t h the method that i s used to t r a n s p o r t goods to and  from  these p o i n t s .  The t r a n s p o r t a t i o n schedule i l l u s t r a t e d i n  a p r e v i o u s s e c t i o n of t h i s chapter i n d i c a t e s the p o t e n t i a l methods f o r the movement of raw m a t e r i a l s and products t o p l a n t warehouses and t o d i s t r i b u t i o n warehouses.  Using  t h i s schedule as a guide, the h a n d l i n g cost p e r u n i t o f m a t e r i a l or product  should be developed f o r each of the  p o t e n t i a l modes o f t r a n s p o r t a t i o n .  T h i s i n f o r m a t i o n may  be presented i n a form such as i s i n d i c a t e d i n Table 7. TABLE V WAREHOUSING DATA LOCATION:  Product  Winnipeg  Method of Transport a t i o n  Handling Cost Per Unit f  10D  Rail CL R a i l - LCL Truck  0.025 0.015 0.010  6F  R a i l - CL R a i l - LCL Truck  0.100 0.125 0.125  The  c a p a c i t y o f d i s t r i b u t i o n warehouses w i l l have  been taken i n t o account i n determining t h e i r g e o g r a p h i c a l 2 service areas. Warehousing space f o r raw m a t e r i a l s and  See Chapter I I I , pp. 41-57.  80 f i n i s h e d product i n v e n t o r i e s at p l a n t s w i l l not be considered  d i r e c t l y i n the p r o d u c t i o n  P r o v i s i o n should  allocation analysis.  be made, however, t o check the space  c a p a c i t y of those p o i n t s at which the volume of i n v e n t o r i e s ( a s suggested i n the a l l o c a t i o n s o l u t i o n ) i s s i g n i f i c a n t l y g r e a t e r than i n the p a s t . Inventory B a t a The inoludes  cost of c a r r y i n g Inventory i n the short-term  the r i s k o f obsolesoenee and d e t e r i o r a t i o n , a s  w e l l as the o p p o r t u n i t y inventories.  cost of having funds i n v e s t e d i n  A cost i s i n v o l v e d i n the use o f storage  space at warehouses only i f the space has a l t e r n a t i v e p r o d u c t i v e use. I t i s assumed f o r purposes o f t h i s t h e s i s that the cost o f c a r r y i n g i n v e n t o r y  i s l a r g e l y the o p p o r t u n i t y  i n v o l v e d i n having funds t i e d up i n m a t e r i a l s T h i s cost should obtained  represent  and p r o d u c t s .  . . . t h e r e t u r n that would be  i f the c a p i t a l were i n v e s t e d otherwise.  making t h i s estimate, liquidity  n  and r i s k  cost  account should  In  be taken of the  involved."^  ^Charles C. H o l t , Franco M o d i g l i a n i , John F. Muth, Herbert A. Simon, P l a n n i n g P r o d u c t i o n . I n v e n t o r i e s and Work Force (Englewood G l i f f s , N.J.: P r e n t i c e - H a l l I n c . , 19"60), p. 71.  81  Trie q u a n t i t y and  value  of i n v e n t o r y  r e q u i r e d f o r each of the t r a f f i c the l a t t e r part of t h i s chapter. sufficient  routes  that w i l l  i s dealt with i n  At t h i s stage i t i s  to define the cost of c a r r y i n g i n v e n t o r y  terms of the percentage r e t u r n that i s r e q u i r e d inventory  in  on  investment.  Order-processing The  and  Communication Data  cost of p l a c i n g an order i n c l u d e s the  time i n v o l v e d i n p r e p a r i n g s t a t i o n a r y , and machines and supply  he  the r e q u i s i t i o n , the cost  the v a r i a b l e cost of u s i n g  equipment.  clerical  Transmitting  of  office  the order to  the  point i n c l u d e s the cost o f p o s t a l , telephone,  t e l e g r a p h and  other f a c i l i t i e s that may  purpose.  cost  The  of p r o c e s s i n g  be  used f o r t h i s  an order r e c e i v e d at a  p l a n t from a d i s t r i b u t i o n p o i n t w i l l i n c l u d e the clerical,  s t a t i o n a r y and  variable  machine c o s t s of i s s u i n g shipment  r e q u i s i t i o n s or other i n s t r u c t i o n s to the  shipping  department. The mission  v a r i a b l e cost of order placement and  should be  developed f o r each of the  combinations of raw The  v a r i a b l e cost  materials  trans-  relevant  supply p o i n t s and  plants.  of order placement, t r a n s m i s s i o n  and  8E receipt  should  be developed f o r each of the p l a n t  warehouse a l t e r n a t i v e s .  T h i s i n f o r m a t i o n may  be  to prepared  as shown i n Table V I . TABLE VI ORDER PROCESSING AND  COMMUNICATION COSTS  V a r i a b l e Cost Per  From  To  Placing Order  I  Receiving Order  Order Order Transmission  t  T o t a l Cost  $  I  Mtl.  Wpg.  10.00  10.00  5.00  25.00  Mtl.  Edmtn. 10.00  7.00  7.00  24.00  The  f o u r t h column w i l l be l e f t blank: f o r orders p l a c e d  the p l a n t s i n c e i t i s assumed that a l l raw m a t e r i a l s purohased from outside III. The  by  are  suppliers. TOTAL ROUTE COST  method of comparing a l t e r n a t i v e s suggested i n  Chapter V r e q u i r e s an estimate of the t o t a l u n i t v a r i a b l e cost i n c u r r e d i n the manufacture and p h y s i c a l ' d i s t r i b u t i o n o f each product to each d i s t r i b u t i o n warehouse and each of the routes that the product may  through  take through the  83  production-distribution The  first  s e c t i o n of t h i s chapter i n d i c a t e d  the p o t e n t i a l t r a f f i c p r o c e s s e s can he flow diagram. a source of raw  system.  r o u t e s and t h e i r major component  i d e n t i f i e d through the p r e p a r a t i o n  Each of the materials,  The  a plant  and  or more methods of  second s e c t i o n d i s c u s s e d  I n d i v i d u a l processes i n v o l v e d  traffic  the  required  alternatives.  the  i n the  types of other i n f o r m a t i o n  to l i n k successive  of  a distribution  cost of the and  of a  a l t e r n a t i v e routes c o n s i s t  warehouse l i n k e d t o g e t h e r by one transportation.  that  variable f l o w of  that may  be  p r o c e s s e s i n t o route  At t h i s stage i t i s necessary t o examine  some of the i m p l i c a t i o n s  of adding t o g e t h e r the  related  c o s t s of adjacent p r o c e s s e s . The  first  part  of t h i s s e c t i o n d e a l s with  problems of r e l a t i n g the v a r i a b l e c o s t s d i s t r i b u t i o n between a p l a n t warehouse. that the  and  of  the  physical  a final distribution  I t i s assumed f o r purposes of t h i s  accumulated v a r i a b l e cost  discussion  of the product up t o  point  at which i t i s a v a i l a b l e f o r d i s t r i b u t i o n at  plant  has  route, and  been determined.  i e . , the purchase and  The  f i r s t h a l f of the  d i s t r i b u t i o n o f raw  the manufacturing p r o c e s s , i s discussed  i n the  the  the traffic  materials latter  84 h a l f of t h i s s e c t i o n . Estimating Warehouse  the Costs of P h y s i c a l D i s t r i b u t i o n from P l a n t t o  The problem at t h i s stage i n a n a l y s i s i s t o determine the minimum cost method of u t i l i z i n g f e a s i b l e p l a n t t o warehouse r o u t e s .  each of the  Taking one route  at a  time, we may proceed by r e l a t i n g each of the c o s t elements to each of the a l t e r n a t i v e methods of t r a n s p o r t a t i o n f o r the r o u t e .  A comparison of the t o t a l c o s t s a s s o c i a t e d  each of the a l t e r n a t i v e s f o r t r a n s p o r t a t i o n w i l l  with  then  i n d i c a t e the minimum cost method of p h y s i c a l d i s t r i b u t i o n f o r the route. To I l l u s t r a t e the procedure, we w i l l assume that the p l a n n i n g  p e r i o d has been d e f i n e d as "the year ending  December 31, 1965" and that the f o l l o w i n g  information  r e l a t i n g t o t h i s p e r i o d has been developed: 1.  Product value  at the P l a n t  (PV) = $10.00 p e r  unit. 2.  Transportation  a l t e r n a t i v e s between the p l a n t  and warehouse and t h e i r r e s p e c t i v e p e r u n i t costs:  85 Transport a t i o n Cost Per Unit |  Minimum Shipping Quantity (Unit .8)  1) R a i l - C L  0.10  1,200  7  2) R a i l - I C L  0.17  -  5  3) Truck-TL  0.14  600  4  4) T r u e k - L T l  0.20  -  3  Alternative  T r a n s i t Time Plant t o Warehouse (Days)  H a n d l i n g c o s t s p e r u n i t at the p l a n t and warehouse, assuming a d i r e c t r e l a t i o n s h i p t o the method of t r a n s p o r t a t i o n t h a t i s used. Method o f Transport at i o n  Handling Cost P e r Unit Total Plant Warehouse * * $  1) R a i l - C L  0.015  0.025  0.040  2) R a i l - L C L  0.015  0.015  0.030  3) Truck-TL  0.010  0.010  0.020  4) Truck-LTL  0.010  0.010  0.020  Order-processing  and communication c o s t s ( S ) :  Cost of p l a c i n g an order at the warehouse #10.00 Cost of r e c e i v i n g and d i s t r i b u t i n g the o r d e r at the p l a n t Cost of e x p e d i t i n g the order T o t a l per order  10.00 5.00 $25.00  Cost o f c a r r y i n g i n v e n t o r y ( I ) : 25 percent of the i n v e n t o r y v a l u e .  86 6,  E s t i m a t e d product demand at the warehouse f o r the p e r i o d 109.6  Transportation  (Y): 40,000 u n i t s , o r an average of  u n i t s p e r day.  and Handling Cost  Given the above data, the t o t a l o f t r a n s p o r t a t i o n and  handling  c o s t s f o r the p e r i o d can be e s t a b l i s h e d f o r  each of the a l t e r n a t i v e s by m u l t i p l y i n g f o r e c a s t e d  demand  by each of combinations of these c o s t s , as f o l l o w s : A l t e r n a t i v e 1:  40,000 (#0.10 + $0.04) = $ 5,600  A l t e r n a t i v e E:  40,000 ($0.17 + $0.03) = $ 8,000  A l t e r n a t i v e 3:  40,000 ($0.13 + $0.02) = $ 6,000  A l t e r n a t i v e 4:  40,000 ($0.20 + $0.02) = $ 8,800  Inventory C a r r y i n g The by  Cost  cost o f c a r r y i n g i n v e n t o r y  a p p l y i n g the percentage r a t e g i v e n  data t o the d o l l a r value the p l a n n i n g  period.  of the v a r i a b l e route flow  i n the f o r e g o i n g  o f the average i n v e n t o r y f o r  The d o l l a r value  i s the summation  c o s t s up to the p o i n t I n the  at which i n v e n t o r y  i s carried.  of i n v e n t o r y i n t r a n s i t w i l l  Inventory value  Hence, the value  i n c l u d e accumulated product  cost at the p l a n t and the handling plant.  can be estimated  cost out o f the  at the warehouse w i l l  accumulated product cost at the p l a n t ,  include  handling  87 cost  out o f the p l a n t  transportation  cost.  and i n t o the warehouse and I n our example, product v a l u e on a  per u n i t b a s i s at the three i n v e n t o r y  l o c a t i o n s i s shown  i n Table V I I . TABLE V I I INVENTORY VALUE PER UNIT At the Plant  At the Warehouse  In Transit  <fle  4fe  *  *  *  Alternative  1:  10.00  10.04  10.14  Alternative  2:  10.00  10.03  10.20  A l t e r n a t i v e 3:  10.00  10.02  10.15  A l t e r n a t i v e 4:  10.00  10.02  10.22  The next step i s t o estimate the volume of inventory  that w i l l be c a r r i e d at each of the three  l o c a t i o n s so that  the value o f the average i n v e n t o r y  can be  established. In e s t i m a t i n g  the volume and value of i n v e n t o r y i t  i s convenient t o d i v i d e the t o t a l i n v e n t o r y component 1.  parts: Transit Inventories, enroute from p l a n t  2.  i n t o i t s three  i e . , the average stocks  t o warehouse.  Cycle Inventory, or the average s t o c k s that are  88  c a r r i e d at the p l a n t and warehouse t o meet normal demand,, 3.  S a f e t y i n v e n t o r y , l e . , stocks that are h e l d at the warehouse t o p r o t e c t against  unanticipated  l n o r e a s e s i n demand between the time  orders  are p l a c e d and r e c e i v e d . These three i n v e n t o r i e s are shown g r a p h i c a l l y l n F i g u r e 9.  Normal r a t e of demand  Maximum reasonable demand over the l e a d time  V  " |  Transit Time T I M  E—=  "rv—  Lead Time •  FIGURE 9 AVERAGE CYCLE, TRANSIT AND SAFETY INVENTORIES  89 The planning  average volume of i n v e n t o r y  p e r i o d i s simply  i n t r a n s i t f o r the  the normal r a t e of demand p e r day  m u l t i p l i e d by the number o f days i t takes t o t r a n s p o r t the product from p l a n t t o warehouse. transit  inventory  The volume and value of  i n our example, t h e r e f o r e , may be  computed as f o l l o w s : TABLE V I I I VOLUME AND VALUE OF TRANSIT  INVENTORY  Normal Average Per Value o f Avge. Demand T r a n s i t T r a n s i t Unit Inventory i n Transit Per Day Time Inventory Value A l t e r n a t i v e 1:  (Units) 109.6  (Days) 7  (Units) 767  10.04  $ 7701  A l t e r n a t i v e £:  109.6  5  547  10.03  5496  A l t e r n a t i v e 3:  109.6  4  436  10.02  4393  A l t e r n a t i v e 4:  109.6  3  328  10.02  3295  In e s t i m a t i n g  the average volume of c y c l e stock  that  w i l l be c a r r i e d w i t h each o f the f o u r a l t e r n a t i v e s , we may employ a m o d i f i c a t i o n of the e q u a t i o n t h a t i s used by  Magee, op., c i t . p. 17. Note that the r e s u l t o f t h i s c a l c u l a t i o n r e p r e s e n t s the average i n v e n t o r y i n t r a n s i t over the p l a n n i n g p e r i o d r a t h e r than the average over the t r a n s i t I n t e r v a l s of the p e r i o d . t  90 Whitin  to determine the optimum purchase The  equation,  before  quantity.  m o d i f i c a t i o n , i s as  follows:  where, Y =  expected y e a r l y s a l e s i n u n i t s '  Q, =  economic purchase q u a n t i t y i n u n i t s  C =  unit  S =  procurement expense i n making  cost  order I =  one  (in dollars)  cost of c a r r y i n g a d o l l a r s worth of inventory  over the p l a n n i n g  T h i s e q u a t i o n recognizes  period.  that the t o t a l v a r i a b l e  cost a s s o c i a t e d w i t h c y c l e stock i n c l u d e s the cost procuring the  the i n v e n t o r y  inventory.  of  as w e l l as the cost of c a r r y i n g  Expressed i n equation form, procurement  cost f o r the p e r i o d becomes Y g and  c a r r y i n g cost becomes  0,0 _ . The d i v i s i o n by two i n the l a t t e r e q u a t i o n 2 suggests t h a t , on the average, one-half of the order q u a n t i t y w i l l be  on hand at the stock p o i n t .  This  assumption i s reasonable when i t i s expected, as i n our  Thornson M. W h i t i n , Management ( P r i n c e t o n , New P r e s s , 1957). p. 33. 6  The Theory of Inventory Jersey: Princeton University  91 example, that demand at the stock p o i n t w i l l tend toward a uniform r a t e over the p e r i o d . Since procurement cost orders w h i l e the reverse inventory  i n c r e a s e s w i t h the number of  r e l a t i o n s h i p holds between  c a r r y i n g cost and the number of o r d e r s , i t  f o l l o w s that the minimum of these oombined c o s t s  occurs  where: C(Q/E) I  a  S(Y/Q)  S o l v i n g f o r 0,, the e q u a t i o n becomes: Q, »  / EYS V IC  Two m o d i f i c a t i o n s before  of t h i s e q u a t i o n are neoessary  i t can be used t o determine the average volume o f  cyole stock that i s optimum with eaeh of the f o u r a l t e r n a t i v e s f o r p l a n t t o warehouse d i s t r i b u t i o n . the  e q u a t i o n as formulated  above assumes that the product  i s purchased from an outside  source and that inventory i s  c a r r i e d only at the warehouse.  I n our problem, warehouse  replenishment orders w i l l be f i l l e d i s on hand at the p l a n t .  out of i n v e n t o r y  Hence, c y c l e i n v e n t o r y  c a r r i e d at both the p l a n t and the warehouse. the e q u a t i o n f o r our problem should per u n i t product cost  Firstly,  that  w i l l be  Seoondly,  r e f l e c t the f a c t  that  at the warehouse i s higher than at  92 the p l a n t by the p e r u n i t handling  and t r a n s p o r t a t i o n  costs. Assuming f o r our purpose that the r a t e o f production  at the p l a n t w i l l be geared t o the normal r a t e  of demand at the warehouse, output at the plant accumulate at the same r a t e as i n v e n t o r y i s depleted.  will  at the warehouse  T o t a l c y c l e stock, t h e r e f o r e , w i l l be e q u a l  t o the s i z e of the warehouse replenishment order — average of one-half  of t h i s quantity being  on hand at eaoh  of the p l a n t and the d i s t r i b u t i o n warehouse. G G  an  I f we l e t  denote the u n i t cost o f the product at the p l a n t and w  the u n i t cost o f the product at the warehouse, the cost  of c a r r y i n g c y c l e stock can be w r i t t e n as?  1(0/2) C  + KQ/2)  p  , o r 1(072) ( G + C ) p  w  Then the t o t a l o f procurement  costs  (order-processing  oommunioations) and i n v e n t o r y  c a r r y i n g c o s t s i s at a  minimum where: KQ/2)  (G  p  + G ) = S(Y/QJ w  S o l v i n g f o r Q,, t h i s equation becomes; Q, =  See  /  2YS  Table V I I , p. 87.  and  T h i s e q u a t i o n may now be a p p l i e d t o determine the optimum volume of c y c l e stock f o r each of the f o u r a l t e r n a t i v e s f o r p h y s i c a l d i s t r i b u t i o n between the p l a n t and warehouse. processing  U s i n g the s a l e s volume ( Y ) , the order-  and communications cost  cost per d o l l a r of inventory the  the  ( I ) given i n the data at  b e g i n n i n g of the s e c t i o n ;  c o s t s at the p l a n t  ( S ) , and the c a r r y i n g  and the per u n i t product  and the warehouse as shown i n Table V I I ,  optimum c y c l e s t o c k s (Q,) f o r each of the a l t e r n a t i v e s  are as f o l l o w s : A l t e r n a t i v e 1: Q = / ,2 (125.00) (40.000) = \/0.25 (flO.OO + $10.14) A l t e r n a t i v e 2: Q =  6  / 2 (125.00) (40,000) = JO.25 (§10.00 + f l O . 2 0 )  A l t e r n a t i v e 3: Q = fz  ($25.00) (40,000)  =  ,25 ($10.00 + --110.15) s/o.r -  A l t e r n a t i v e 4: Q = / 2 ($25.00) (40.000) VO.25 ($10.00 +. 110.22)  =  3  &Z  6  0  9  2  u  n  i t  s  units  0  6 2 9  units  u n  i+  a  R e f e r r i n g back to the data presented at the beginning of t h i s chapter, however, we see t h a t there i s a minimum s h i p p i n g  quantity  transportation  of 1,200 u n i t s a s s o c i a t e d  the  oarload  alternative.  the  above formula suggests an o r d e r q u a n t i t y  Hence, although of 630 u n i t s  f o r a l t e r n a t i v e one, i t i s c l e a r that the order  8  See pp. 85-86.  with  quantity  94 w i l l have t o he 1,200 u n i t s f o r t h i s a l t e r n a t i v e i n order t o o b t a i n the c a r l o a d Since, quantity the  freight rate.  on the average, one-half of the order  w i l l be on hand at each of the p l a n t  and warehouse,,  d o l l a r value o f c y c l e stock may be expressed as  follows: Q/2  ( C ) + Q/2 ( C ) p  w  The r e s u l t o f t h i s c a l c u l a t i o n i s shown i n Table IX f o r each of the a l t e r n a t i v e s i n our example. TABLE IX VOLUME AND VALUE OF CYCLE  INVENTORY  Volume  Value  (units)  I  A l t e r n a t i v e 1:  1200  12,084  A l t e r n a t i v e 2:  629  6,353  A l t e r n a t i v e 3:  630  6,347  A l t e r n a t i v e 4:  629  6,359  Safety  inventory  necessary t o p r o t e c t  at a d i s t r i b u t i o n warehouse i s  against  unpredictable  increases i n  demand over the l e a d time, i e . , over the i n t e r v a l between the  time a replenishment order i s p l a c e d  But  the cost  and r e c e i v e d .  of c a r r y i n g a d d i t i o n a l i n v e n t o r y  to protect  95 against maximum p o s s i b l e demand over these i n t e r v a l s i s usually prohibitive.  I t becomes necessary, t h e r e f o r e , t o  e s t a b l i s h " . . . a reasonable balance between the amount o f e x t r a i n v e n t o r y (and i t s o a p i t a l , storage and o t h e r c o s t s ) and the p r o t e c t i o n obtained against s t o c k exhaustion." To estimate the volume of s a f e t y s t o c k at which t h i s balance i s achieved, Magee s t a t e s that two p i e c e s of i n f o r m a t i o n are r e q u i r e d : 1.  A d i s t r i b u t i o n of d i f f e r e n c e s between f o r e o a s t and  2.  a c t u a l demand over a l e a d  time.  An agreement as t o how o f t e n run-outs may be allowed t o o c c u r . ^  The  f i r s t p a r t of t h i s  i n f o r m a t i o n i n d i c a t e s the  frequency w i t h which stock shortages are l i k e l y at v a r i o u s l e v e l s of s a f e t y Inventory. frequency  t o occur  The permissable  of stook run-outs g i v e n i n the second p a r t the n  i n d i c a t e s the l e v e l of s a f e t y i n v e n t o r y that i s necessary. The  d i s t r i b u t i o n of d i f f e r e n c e s between f o r e c a s t  and a c t u a l demand can be estimated from h i s t o r i c a l experience.  Assume, f o r example, that the l e a d time i s  Magee, op_. c i t . , p. 69. ' i b i d . , p. 7£.  96 twelve days.  Demand over twelve day i n t e r v a l s o f the  previous period  o r p e r i o d s f o r the group of customers t o  he served hy the warehouse can then be examined t o establish: 1.  The average demand from t h i s group over twelve day i n t e r v a l s .  2.  The percentage o f twelve day i n t e r v a l s i n which the l e v e l of demand was at s p e c i f i e d h i g h e r or lower volumes than the average.  When average demand i n the past does not correspond w i t h forecasted  average demand, i t i s d e s i r a b l e t o convert the  h i s t o r i c a l f i g u r e s i n t o percentages as shown i n F i g u r e 10. One hundred percent on the h o r i z o n t a l  scale r e p r e s e n t s  average demand. The d i s t r i b u t i o n of d i f f e r e n c e s between f o r e c a s t and a c t u a l demand can now be determined by a p p l y i n g the percentage f i g u r e s t o f o r e c a s t forecast  volume.  I n our example,  average demand at the warehouse i s 109.6 u n i t s  per day, o r 1,315 u n i t s over a twelve day l e a d time. A p p l y i n g the percentages g i v e n i n F i g u r e 10, we can see that d u r i n g t e n percent o f the twelve day l e a d times there i s l i k e l y t o be a demand of 1,900 u n i t s or more, i e . , forecast  average demand of 1,315 u n i t s m u l t i p l i e d by 145  97 percent; that  during  twenty peroent  of the twelve day l e a d  times there i s l i k e l y i o be a demand of 1,575 u n i t s or more, i e . , f o r e o a s t  average demand of 1,315 u n i t s  m u l t i p l i e d by 120 peroent; e t c .  i  •  1  J  Li_  20 40 60 80 100 120 140 Demand over 12 day l e a d times as a percentage of average 12 day demand  FIGURE 10 DISTRIBUTION OF DEMAND OVER TWELVE DAY INTERVALS  98 To continue w i t h our example, we w i l l assume  that  the l e a d times f o r the f o u r a l t e r n a t i v e s are as shown i n Table X. TABLE X LEAD TIME Alternative  D e s c r i p t i o n of Delays  Days  Days  Days  P l a c i n g the orders at the Warehouse  1  1  1  1  Transmitting the p l a n t  1  1  1  1  1  1  the o r d e r t o  R e c e i v i n g and p r o c e s s i n g o r d e r at the p l a n t  the  F i l l i n g the order  1  Transportation warehouse  7  plant t o  U n l o a d i n g the o r d e r at the warehouse T o t a l l e a d time  We w i l l  1 5  1 12  Days  1 10  4  8  assume f u r t h e r that the d i s t r i b u t i o n of d i f f e r e n c e s  between f o r e c a s t and a c t u a l demand has been estimated f o r each of the a l t e r n a t i v e s as i n d i c a t e d i n F i g u r e broken l i n e s represent  11.  The  f o r e c a s t average demand over each  of the l e a d times.  Since c y c l e inventory  s a t i s f y average demand, s a f e t y inventory volume i n excess of t h i s q u a n t i t y . that  i s required  equivalent that  against  stock  i s intended t o w i l l be the  Hence i f the p r o t e c t i o n  shortages i s set at a l e v e l  t o t e n percent o f the lead times, I t i s apparent  a s a f e t y stook o f 585 u n i t s w i l l be necessary with a  l e a d time o f twelve days (1,900 u n i t s as shown i n F i g u r e  11  at the t e n percent l e v e l l e s s average demand over the l e a d time of 1,315  units).  lead Times  90 80 Percentage of lead times when demand exoeeds the Indicated level  12 10 8 -7  70 60 50 ft  40  Days Days Days Days  \ A  \ i\ '\  I\ i \  !\  \\\  30 20 10 I  600  I  »  ' *  1000  .  I  1500  •  I  2000  Demand over lead times FIGURE 11 DISTRIBUTION  OF DEMAND OVER INDICATED LEAD TIME  100 The next step i n e s t i m a t i n g the volume of s a f e t y inventory  i s t o determine the l e v e l of p r o t e c t i o n that i s  required against  stock  shortage.  T h i s w i l l depend i n part  upon the cost of c a r r y i n g s u c c e s s i v e l y l a r g e r volumes o f s a f e t y stock  and i n p a r t upon opposing f a c t o r s such as  p o s s i b l e l o s s e s i n s a l e s due t o stock  shortages,  d e t e r i o r a t i o n i n r e l a t i o n s w i t h customers as a r e s u l t o f d e l i v e r y delays, e t c . The cost of c a r r y i n g s a f e t y i n v e n t o r y f o r a l t e r n a t i v e l e v e l s of p r o t e c t i o n can be e s t i m a t e d by m u l t i p l y i n g the a p p r o p r i a t e Figure  volumes, as c a l c u l a t e d from  11, by the cost of o a r r y i n g a u n i t of  over the d e f i n e d p l a n n i n g  period.  The extent  inventory and cost o f  s a l e s l o s s e s and d e t e r i o r a t e d r e l a t i o n s w i t h customers as a result  of stock  shortages, however,  i d e n t i f y and t o q u a n t i f y . the  i s d i f f i c u l t to  I n the t y p i o a l case,  therefore,  judgement of experienced management p e r s o n n e l i s l i k e l y  t o play an important r o l e In e s t i m a t i n g balancing  these c o s t s , and i n  the sum of these f a c t o r s against  c a r r y i n g s a f e t y inventory the p e r m i s s i b l e  t o a r r i v e at an agreement as t o  frequency of stock  Continuing  the c o s t s of  run-outs.  with our example, we w i l l assume that an  agreement has been reached t o the e f f e c t that  stock  short-  101 ages should  not occur more f r e q u e n t l y than s i x times  the p l a n n i n g p e r i o d . is permissible  This i s equivalent  during  t o saying that i t  t o have a stock shortage at the warehouse  during s i x o f the t o t a l l e a d times,  s i n c e i t i s only  a l e a d time t h a t the r i s k of run-out occurs.  during  There w i l l be  a t o t a l o f t h i r t y - t h r e e l e a d times over the p e r i o d i f a l t e r n a t i v e one i s used ( t o t a l demand of 40,000 u n i t s f o r the y e a r d i v i d e d by the order q u a n t i t y of 1,200 u n i t s ) . A l t e r n a t i v e s two, three and f o u r each r e q u i r e a t o t a l of s i x t y - f o u r l e a d times over the p e r i o d .  Hence, the l e v e l  of p r o t e c t i o n expressed as a percentage-of-lead-time be e i g h t e e n percent for  each of a l t e r n a t i v e s two, three  stock-outs The  f o r a l t e r n a t i v e one and nine and f o u r  will  percent  (permissible  d i v i d e d by the t o t a l number of l e a d  times).  volume of s a f e t y stock can now be determined from  F i g u r e 11 by t a k i n g the d i f f e r e n c e between the q u a n t i t i e s i n d i c a t e d i n t h i s chart at the e i g h t e e n percent percent and  l e v e l s f o r a l t e r n a t i v e one and at the nine  f i f t y percent  four.  and f i f t y percent  l e v e l s f o r a l t e r n a t i v e s two, three and  F i g u r e 11 has been used i n e s t i m a t i n g the volumes  of s a f e t y stock shown i n Table X I .  102 TABLE XI VOLUME AND VALUE OF SAFETY STOCK ALTERNATIVE 2  3  4  1625  1200  1080  1315  1096  877  767  335  529  323  313  1 Maximum demand over the l e a d time at the 18$ l e v e l o f protection (units)  1650  Maximum demand over the l e a d time at the 9% l e v e l of protection (units) Average demand over the l e a d time ( u n i t s ) Safety  stock  (units)  U n i t produet value at the warehouse  §10.14  110.20  $10.16  $10*22  D o l l a r value o f s a f e t y stock:  |3397  #5396  #3282  $3199  Having e s t i m a t e d the value of t r a n s i t , safety stocks,  the cost o f c a r r y i n g i n v e n t o r y  c y c l e and can now he  e s t i m a t e d f o r each o f the f o u r a l t e r n a t i v e s by a p p l y i n g the c a r r y i n g cost p e r d o l l a r three  inventory  amounts.  of i n v e n t o r y  t o the sum of these  Inventory v a l u e s g i v e n i n Tables  V I I I , IX and XI have been t o t a l l e d  i n Table X I I and the  percentage r a t e has been a p p l i e d t o produce an estimate  103 of  the c o s t of o a r r y i n g i n v e n t o r y over the p l a n n i n g  period. TABLE X I I COST OE CARRYING INVENTORY Total Inventory Value  C a r r y i n g Cost as a fo of I n v e n t o r y Value  Inventory Carrying Cost.  T A l t e r n a t i v e 1:  23,182  A l t e r n a t i v e 2:  17,245  A l t e r n a t i v e 3:  14,022  A l t e r n a t i v e 4:  12,853  5796  25  4311  25  3506  25  3213  25  O r d e r - P r o c e s s i n g and Communications Cost O r d e r - p r o c e s s i n g and communications c o s t has been estimated at t w e n t y - f i v e d o l l a r s p e r o r d e r .  1 1  Dividing  t o t a l demand f o r the p e r i o d by the order q u a n t i t y i n d i c a t e s that t h e r e w i l l be t h i r t y - t h r e e orders p l a c e d over t h e p l a n n i n g p e r i o d w i t h a l t e r n a t i v e one and s i x t y - f o u r orders plaoed over the p e r i o d with each o f a l t e r n a t i v e s two,  three and f o u r .  Order-processing  oost f o r the p e r i o d ,  t h e r e f o r e , w i l l be |825 f o r a l t e r n a t i v e one and |l600 f o r a l t e r n a t i v e s two, three and f o u r .  See  p. 85  104 Total Variable To  Cost  complete the example that we are u s i n g f o r  i l l u s t r a t i o n purposes, i t remains t o t o t a l the i n d i v i d u a l cost elements developed i n the preceding X I I I i s a summary  section.  Table  of these c o s t s and shows the t o t a l and  the p e r u n i t cost o f p h y s i c a l d i s t r i b u t i o n from the p l a n t t o the d i s t r i b u t i o n warehouse f o r each of the f o u r alternatives. TABLE X I I I TOTAL VARIABLE COST OF PHYSICAL DISTRIBUTION PLANT TO WAREHOUSE ALTERNATIVE Cost Elements  1  2  3  4  T r a n s p o r t a t i o n and Handling Inventory Order-processing Communication T o t a l Cost  $ 5,600  | 8,000  #6,000  $ 8,800  5,796  4,311  3,506  3,213  825  1.600  1,600  1.600  12,221  13,911  11,106  13,613  and  Per Unit Cost 0.306 0.348 0.278 0.341 I t i s c l e a r that the t h i r d a l t e r n a t i v e i s the optimum method f o r p h y s i c a l d i s t r i b u t i o n from the p l a n t t o the d i s t r i b u t i o n warehouse used i n t h i s example.  105 To produce an estimate of the t o t a l v a r i a b l e cost for  the whole route we must now  add  the |0.278 per u n i t f o r  p l a n t to warehouse d i s t r i b u t i o n t o the v a r i a b l e cost u n i t f o r the f i r s t h a l f of the route, v a r i a b l e eost  i e . , t o the  of the product up to the p o i n t  per  accumulated  at which i t  becomes a v a i l a b l e f o r d i s t r i b u t i o n at the p l a n t .  In  developing  to ware-  inventory  c a r r y i n g c o s t s f o r the p l a n t  house p o r t i o n of the r o u t e , we v a r i a b l e cost  f o r the f i r s t  assumed that the  h a l f of the route  been estimated at $10.00 per u n i t . for  accumulated  had  already  T o t a l v a r i a b l e cost  the whole route, t h e r e f o r e , would be f l O . 8 8 per u n i t .  T h i s f i g u r e w i l l be the one  that i s compared w i t h  s i m i l a r l y developed u n i t costs r e p r e s e n t i n g routes  to determine the  the f i r m ' s p l a n t s .  alternative  optimum a l l o c a t i o n of output among  T h i s comparison w i l l be d e a l t w i t h i n  chapter V. R e t u r n i n g now  t o the procedure f o r determining  t o t a l v a r i a b l e cost f o r the f i r s t  h a l f of the route,  problem i s t o r e l a t e the processes that are Involved the p h y s i c a l d i s t r i b u t i o n of raw m a t e r i a l s and manufacture i n t o the f i n i s h e d p r o d u c t .  The  the in  in their  objective  i s to determine the minimum p e r u n i t product cost at each of the p l a n t s f o r each of the p o i n t s from which  raw  106 m a t e r i a l s may be r e o e i v e d . Estimating  trie Cost f o r the F i r s t  Dealing  H a l f of a T r a f f i c Route  w i t h one p l a n t at a time, the f i r s t  problem i s t o s p e c i f y the p r o d u c t s that the p l a n t i s equipped t o manufacture and the raw m a t e r i a l s for  each of these p r o d u c t s .  decided  At t h i s p o i n t  requirement  i t should be  i f i t w i l l be worthwhile t o i n v e s t i g a t e the  p h y s i c a l d i s t r i b u t i o n of a l l of the m a t e r i a l s used i n the manufacturing prooess. of one o r two b a s i c m a t e r i a l s  that are  I f the product  consists  and only minimal amounts of  s e v e r a l other r e l a t i v e l y low cost items, an i n v e s t i g a t i o n of the p h y s i c a l d i s t r i b u t i o n of the l a t t e r group i s not likely The  t o b r i n g about a s i g n i f i c a n t change i n produot  cost.  q u a n t i t y , purchase p r i c e and t r a n s p o r t a t i o n cost of  each o f the raw m a t e r i a l s  that are used f o r a product are  the major f a c t o r s that should be considered  i n deciding  which of these should be i n c l u d e d i n the study of raw materials  distribution.  I t may be assumed, f o r purposes of e s t i m a t i n g the p e r u n i t cost o f the excluded group, that these  materials  w i l l be r e c e i v e d from the same source as i n the past; the t r a n s p o r t a t i o n and h a n d l i n g that the same l e v e l of inventory  that  cost w i l l be the same and p e r unit of m a t e r i a l  will  107 apply.  In other words, an approximation based upon  h i s t o r i c a l records the per  should be  adequate f o r an estimate of  u n i t d e l i v e r e d cost f o r t h i s group of  materials.  The  physical  second step  i s to i n v e s t i g a t e the  d i s t r i b u t i o n of each of the raw  materials  selected for further investigation.  The  that  have been  objective i s to  determine the minimum cost method of p h y s i c a l d i s t r i b u t i o n t o the p l a n t from each of the The  a v a i l a b l e sources of  a v a i l a b l e sources are those from which there  s u i t a b l e methods of The  d i s t r i b u t i o n of raw  materials  t r a n s p o r t a t i o n , handling, The  i n the  physical  i n c l u d e the purchase p r i c e ,  order-processing  purchase p r i c e can be  and  The,alternatives  t r a n s p o r t a t i o n and  and  handling  inventory  obtained from  the p u r c h a s i n g department.  be a v a i l a b l e i f the  are  transportation.  c o s t s that are i n v o l v e d  carrying costs.  supply.  for  t h e i r respective  schedules d i s c u s s e d  i n the  costs  will  previous  s e c t i o n of t h i s chapter have been prepared. Inventory and p o r t i o n of the  order-prooessing  costs f o r t h i s  route cannot be e s t a b l i s h e d w i t h the same  degree of p r e c i s i o n as f o r plant to warehouse d i s t r i b u t i o n . I t has been shown that the volume of i n v e n t o r y required  that i s  i s c l o s e l y r e l a t e d t o the r a t e of demand.  The  108 demand f o r a product at a s p e c i f i c p l a n t , however, i s c l e a r l y unknown at t h i s stage s i n c e i t i s the o b j e c t i v e o f a n a l y s i s t o determine how t o t a l demand should be a l l o c a t e d among the f i r m ' s  plants.  F o r purposes of a p r e l i m i n a r y processing  and i n v e n t o r y  estimate o f order-  c a r r y i n g c o s t s , i t may be assumed  t h a t demand f o r raw m a t e r i a l at the p l a n t over the p l a n n i n g p e r i o d w i l l be the same as i n the p a s t . described  The procedure as  above f o r p l a n t t o warehouse d i s t r i b u t i o n may now  be used t o estimate the t o t a l i n v e n t o r y  and  order-processing  cost f o r the p e r i o d f o r each of the a l t e r n a t i v e s f o r t r a n s p o r t a t i o n and h a n d l i n g  between a source of raw  materials  and the p l a n t .  materials  are purchased, t h e r e w i l l be no stocks h e l d at  the  source.  one-half  Cycle  Since  inventory,  t h e r e f o r e , w i l l be equal t o  o f the order q u a n t i t y ,  inventory  equivalent  as compared w i t h a c y c l e  t o t o t a l order quantity f o r plant t o  warehouse d i s t r i b u t i o n .  I t should be noted that the  percentage of i n v e n t o r y value carrying inventory  i t i s assumed that raw  representing  the cost of  w i l l , i n t h i s case, be a p p l i e d t o the  sum of the purchase p r i c e and the cost o f t r a n s p o r t i n g and handling  the m a t e r i a l between i t s source and the p l a n t . The estimate of i n v e n t o r y  and o r d e r - p r o c e s s i n g  cost  109 may now be added t o the r e l a t e d purchase p r i c e , t r a n s p o r t a t i o n and handling  c o s t s t o determine the t o t a l  v a r i a b l e cost o f the raw m a t e r i a l at the p l a n t .  A  comparison of the t o t a l v a r i a b l e cost a s s o c i a t e d w i t h each of the methods of t r a n s p o r t a t i o n and handling  will  then  i n d i c a t e the a l t e r n a t i v e that o f f e r s minimum m a t e r i a l s cost from a given  source.  I t i s assumed i n t h i s t h e s i s that there  i s no l i m i t  to the volume of a raw m a t e r i a l that can be purchased from a s i n g l e source. available  Hence, where there are two o r more  sources of supply  f o r a s p e c i f i c p l a n t , the cost  of m a t e r i a l used i n determining product cost w i l l be the minimum o f a l l of the a l t e r n a t i v e s .  I n other words, a  f i n a l comparison o f t h e minimum m a t e r i a l cost at the p l a n t from each of the sources of supply  w i l l have t o be made t o  ensure that the m a t e r i a l cost used i n a n a l y s i s i s the minimum of the a l t e r n a t i v e s from a l l a v a i l a b l e sources of supply. Given the minimum t o t a l v a r i a b l e cost of raw materials  at the p l a n t , i t remains t o add the cost o f the  q u a n t i t i e s r e q u i r e d by a product t o the p r o c e s s i n g  cost t o  determine the v a r i a b l e cost of the product at the p l a n t . The  types and q u a n t i t i e s of raw m a t e r i a l that are used i n  110 the manufacture of a product, as w e l l as the  processing  cost per u n i t of product, w i l l be a v a i l a b l e from the information provided The  by the p r o d u c t i o n  department.  per u n i t product cost at the p l a n t s  determined through the above procedure may  now  as be used  as  the b a s i s f o r e s t a b l i s h i n g d e l i v e r e d product cost at each of the f i r m ' s d i s t r i b u t i o n p o i n t s .  The  method f o r  determining t o t a l cost f o r the p l a n t t o d i s t r i b u t i o n warehouse p o r t i o n of the route p a r t of t h i s s e c t i o n . d i s t r i b u t i o n was  has been o u t l i n e d i n the  first  Although p l a n t to warehouse  considered  first  i n the  foregoing  d i s c u s s i o n , i t i s necessary, of course, t o develop e s t i m a t e s of product cost at the p l a n t s b e f o r e  the  total  c o s t of the product at f i n a l d i s t r i b u t i o n warehouses be  can  ascertained. In summarizing t h i s chapter i t i s suggested that  a preliminary  study of t r a n s p o r t a t i o n and  handling  a l t e r n a t i v e s w i l l be u s e f u l i n i d e n t i f y i n g a v a i l a b l e a l t e r n a t i v e s between the p l a n t s and  source of raw  between p l a n t s and  G i v e n t h i s framework, e f f o r t  materials  route  and  d i s t r i b u t i o n warehouses. can be  concentrated  i n the  development of c o s t s f o r the v a r i o u s p r o c e s s e s i n v o l v e d i n the r e l e v a n t a l t e r n a t i v e s f o r t r a f f i c  flow.  These  Ill p r o c e s s e s and t h e i r r e s p e c t i v e  c o s t s were d i s c u s s e d  i n the  second s e c t i o n of the c h a p t e r . The  o b j e c t i v e of the l a t t e r s e c t i o n o f the c h a p t e r  was t o o u t l i n e a procedure f o r r e l a t i n g the elements of route cost i n order t o produce u n i t product c o s t s at each d i s t r i b u t i o n warehouse f o r each of the a l t e r n a t i v e routes that t r a f f i c may take t o these p o i n t s .  The way i n which  these u n i t c o s t s w i l l be used t o determine the optimum a l l o c a t i o n of output among the f i r m ' s p l a n t s w i l l be the subject  of the f o l l o w i n g  chapter.  CHAPTER V DETERMINING THE OPTIMUM ALTERNATIVE I t was i n d i c a t e d i n Chapter I I I that  this thesis  w i l l d e a l w i t h two of short-term p h y s i c a l d i s t r i b u t i o n problems. 1.  These two problems were d e f i n e d a s : The day-to-day a l t e r n a t i v e s f o r s a t i s f y i n g customer o r d e r s from output that  i s available  at d i s t r i b u t i o n warehouses, and 2.  The a l t e r n a t i v e s f o r a l l o c a t i n g short-term p r o d u c t i o n among the f i r m s  Having d i s c u s s e d  plants.  the determinants of the  a l t e r n a t i v e s that are a s s o c i a t e d  with each o f these  problems and the prooedure that may be used t o i d e n t i f y a l t e r n a t i v e s and t h e i r c o s t , i t remains t o o u t l i n e the method f o r s e l e c t i n g the optimum i n each case. The number of a l t e r n a t i v e s that must be taken i n t o account i n the t y p i c a l p h y s i c a l d i s t r i b u t i o n problem p r e c l u d e s a n a l y s i s through c o n v e n t i o n a l methods. and  Henderson  S c h l a i f e r make the f o l l o w i n g comment t o i l l u s t r a t e the  need f o r improved methods f o r day-to-day p h y s i c a l distribution  decisions:  113 When there are only a few p o s s i b l e courses of action — f o r example, when a company w i t h only two p l a n t s wants to supply three or f o u r customers at the lowest p o s s i b l e f r e i g h t cost — any competent scheduler can q u i c k l y f i n d the r i g h t answer. However, when the number of v a r i a b l e s becomes l a r g e r — when a company has a dozen f a c t o r i e s and 200 or 300 customers s c a t t e r e d a l l over the country — the man w i t h the job of f i n d i n g the best s h i p p i n g p a t t e r n may w e l l spend many days only to end up with a f r u s t r a t e d f e e l i n g ; though he t h i n k s he i s c l o s e t o the r i g h t answer, he i s not at a l l sure that he has i t . What i s worse, he does not even know how f a r o f f he i s , or whether i t i s worth spending s t i l l more time t r y i n g to improve h i s s c h e d u l e . 1  The  s o l u t i o n t o a p h y s i c a l d i s t r i b u t i o n problem  r e q u i r e s an a l l o c a t i o n of l i m i t e d r e s o u r c e s among competing demands.  I n the case of the day-to-day problem,  there i s u s u a l l y s u f f i c i e n t customer o r d e r s , but  i n v e n t o r y t o meet t o t a l  there are competing orders f o r the  l i m i t e d q u a n t i t y of products  that are a v a i l a b l e at  i n d i v i d u a l d i s t r i b u t i o n warehouses.  S i m i l a r l y , there  are  competing ways i n which the l i m i t e d c a p a c i t y of each p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n f a c i l i t y may  be  utilized  limited  i n the  short-term p l a n n i n g problem.  The  r e s o u r c e s , competing demands c h a r a c t e r i s t i c s p l a c e  these  problems w i t h i n the realm of mathematical s o l u t i o n that  •'•Alexander Henderson and Robert S c h l a i f e r , "Mathematical Programming," Harvard Business Review. May - June, 1954, p. 118.  114 i s generally The  referred  t o as l i n e a r programming.  c h i e f advantage of the l i n e a r programming  technique i s the ease w i t h which i t p r o v i d e s t h e r i g h t answer t o a problem that may i n v o l v e interdependent  a m u l t i t u d e of  alternatives.  What "mathematical" programming does i s t o reduce the whole procedure t o a simple, d e f i n i t e r o u t i n e . There i s a r u l e f o r f i n d i n g a program t o s t a r t w i t h , t h e r e i s a r u l e f o r f i n d i n g the s u c c e s s i v e changes that w i l l i n c r e a s e the p r o f i t s o r lower the c o s t s , and there i s a r u l e f o r f o l l o w i n g through a l l the r e p e r c u s s i o n s of each change. What i s more, i t i s a b s o l u t e l y c e r t a i n that i f these r u l e s are f o l l o w e d , they w i l l l e a d t o the best p o s s i b l e program; and i t w i l l be p e r f e c t l y c l e a r when the best p o s s i b l e program has been found. 2  The  first  section  of t h i s chapter w i l l  illustrate  the  use of the l i n e a r programming technique i n s e l e c t i n g  the  optimum a l t e r n a t i v e  The  l a t t e r part  f o r output a l l o c a t i o n  of the chapter w i l l o u t l i n e  of the technique t o the day-to-day p h y s i c a l  decisions.  the a p p l i c a t i o n distribution  problem. I. FOR  LINEAR PROGRAMMING MODEL OUTPUT ALLOCATION DECISIONS  S e v e r a l methods are a v a i l a b l e programming problems.  2  for solving  linear  Most of these have been developed  I b i d . , p. 119,  115 as a l t e r n a t i v e s t o the general procedure — r e f e r r e d t o as the S i m p l e x .  g  sometimes  The g e n e r a l procedure  will  solve any l i n e a r programming problem, but the work that i s required One  i n the a p p l i c a t i o n o f t h i s method i s t e d i o u s .  of the a l t e r n a t i v e methods that can be used f o r  c e r t a i n types of problems  and "...by f a r the most  frequently  u s e f u l of the s h o r t e r procedures i s the one known as the T r a n s p o r t a t i o n Problem Problems  Procedure".  4  that can be s o l v e d through the Transpor-  t a t i o n Procedure must meet c e r t a i n c o n d i t i o n s —  one of  which i s that demands and c o n s t r a i n t s be expressed i n the same u n i t s .  The output a l l o c a t i o n problem w i t h which  are concerned i n t h i s s e c t i o n does not meet t h i s and cannot, t h e r e f o r e , be formulated through the T r a n s p o r t a t i o n Method. formulated it  we  condition  directly for solution The problem must be  f o r the Simplex, but i n c e r t a i n circumstances  i s p o s s i b l e t o convert  the Simplex t a b l e a u  into a  T r a n s p o r t a t i o n m a t r i x so that the T r a n s p o r t a t i o n Method of s o l u t i o n can be  used.  F o r a d e s c r i p t i o n o f the g e n e r a l procedure see: A. Charnes, W.W. Cooper, and A. Henderson, An I n t r o d u c t i o n t o L i n e a r Programming. (New York, John Wiley and Sons, Inc., 3  19517)  Alexander Henderson and Robert S c h l a i f e r , op_. c i t . , p.  138.  116 The  o b j e c t i v e of t h i s p o r t i o n of the  develop the Simplex t a b l e a u  f o r the output  problem; to demonstrate a c o n v e r s i o n m a t r i x and  to i n d i c a t e the  a transformation  to a  chapter i s t o  allocation Transportation  circumstances under which such  i s acceptable;  and  to i n d i c a t e the method  of s o l u t i o n through the T r a n s p o r t a t i o n Procedure.  The  data that w i l l be used f o r i l l u s t r a t i o n purposes are summarized i n the  following section.  Demands, C o n s t r a i n t s The f o r the  various  and  Costs  types of i n f o r m a t i o n  that are  output a l l o c a t i o n a n a l y s i s were d i s c u s s e d  Chapter IV.  I t i s assumed that the p r e l i m i n a r y  develop t h i s data have been undertaken and of these s t u d i e s have been summarized as 1.  required in  s t u d i e s to  that the  results  follows:  Warehouse demand: 1)  Product  10D  Warehouse at P l a n t A  (AW)  = 40,000 u n i t s  Warehouse at P l a n t B  (BW)  * 30,000 u n i t s  Warehouse at P l a n t  (CW)  = 35,000 u n i t s  Warehouse X  (XW)  20,000 u n i t s  Warehouse Y  (YW)  10,000 u n i t s  (AW)  30,000 u n i t s  Product  C  6F  Warehouse at P l a n t  A  117 Warehouse at P l a n t B  (BW) = 20,000 u n i t s  Warehouse at P l a n t C  (CW) = 15,000 u n i t s  Warehouse X  (XW) = 10,000 u n i t s  Warehouse Y  (YW) =  Plant Capacities:  8,000 u n i t s  280,000 machine minutes f o r  each of P l a n t s A, B and C. Minutes o f time p e r u n i t o f product on c a p a c i t y l i m i t i n g process: Product 10D (Minutes)  Product 6F (Minut e s)  Plant A  2.00  5.50  Plant B  2.20  6.00  Plant C  2.45  6.40  Accumulated  v a r i a b l e cost p e r u n i t of product  at d i s t r i b u t i o n warehouses. 1)  Product  10D: To AW  r  To BW  To CW  To XW  To YW  F  F  From P l a n t A: 3.40  4.20  5.10  3.90  -  From P l a n t B: 4.50  2.90  3.80  3.30  3.50  From P l a n t C: 5.30  5.20  4.00  4.50  4.30  •F  F  118 2)  Product  6?: To AW  T  To BW  To CW  T  T  T  To YW  T  8,id  10.50  11.20  9.20  From P l a n t B: 10.20  8.70  9.50  9.00  9.30  11.80  8.90  9.60  9.20  From P l a n t A:  From P l a n t  G: 12.20  The f i g u r e s shown above represent  the minimum cost  methods of u t i l i z i n g each o f the p o t e n t i a l t r a f f i c A preliminary  To XW  routes.  comparison of a l t e r n a t i v e s f o r d i s t r i b u t i n g  product 10D from P l a n t A t o warehouse G, f o r example, has shown that the minimum d e l i v e r e d product cost v i a t h i s route w i l l be #5.10. The Simplex F o r m u l a t i o n Given the data i n the preceding  s e c t i o n , the f i r s t  step i n s e t t i n g up the Simplex i s t o express the demands and  constraints algebraically.  Standard mathematical  n o t a t i o n may be used as f o l l o w s : 1.  Number the p l a n t s one through  three.  2.  Number the d i s t r i b u t i o n warehouses one through  119 f i v e f o r product 10D; and s i x through t e n f o r product 6F.  (Numbers  one and s i x both r e f e r  t o warehouse A, two and seven both r e f e r t o warehouse B, e t c . ) 3.  Let X j j equal the number o f u n i t s of product s u p p l i e d by p l a n t i t o warehouse j . Then the q u a n t i t i e s of product r e q u i r e d at warehouses can be s t a t e d as  1) 8) 3) 4) 5)  X  *11 x  12  X  l3  81  22  X  32  X  23  •  X  33  X  24  +  X  34  +  U  X  25  X  35  6)  X  16  X  26  X  7)  X  17  X  27  8)  X  18  +  9)  x  19  +  10)  X  ^8 X  29  +  o- = 40,000  31  X  X  *14  follows: 4  5 " 30,000 35,000  *•  U  +  u = 20,000 7  =  8  10,000  36  30,000  x  37  ^10= 20,000  x  38  Ull= 15,000  X  39  U  12-  2,10 + X 3,10 * %3 =  10,000 8,000  The U v a r i a b l e i s added t o each e q u a t i o n i n order to eliminate  the i n e q u a l i t i e s .  The c a p a c i t y c o n s t r a i n t s at each p l a n t are g i v e n by the f o l l o w i n g e q u a t i o n s :  120 11.  2.00 X  i  ;  l  + 5.50 X t U 12.  x  + 2.00 X  + 2.00 X 1 ?  1 3  + 5*50 X  + 2.00 X 1 8  1 4  + 5.50 X  1 9  = 280,000  2.20 X  + 2.20 X  g l  + 6.00 X 2.45  + 5.50 X  1 6  + 2.20 X-  13.  l g  2g  g g  2 g  + 2.20 X  • 6.00 X  2 6  + 6.00 X  g t l 0  X „ T • 2.45  X„  0  g g  + 6.00 X *U  + 2.45  + 2.20 X g 7  g 4  + 6.00 X g  8  = 280,000  2  X„„  Z  + 2.45  rtA  oc, 33 34 • 6.40 X„^ + 6.40 X^„ • 6.40 X„_ CO OD o" oo  ox * 2.45 X „ • 6.40 X  g 9  c  + 6.40 X  3 > 1 0  • U  3  = 280,000  These equations r e c o g n i z e that c a p a c i t i e s are s t a t e d i n terras of minutes  of time t h a t i s a v a i l a b l e i n the b o t t l e -  neck process at each p l a n t .  Henoe, 2.00 minutes o f  c a p a c i t y at p l a n t A i s used f o r every unit o f product 10D that i s manufactured  at that p o i n t ; 5.50 minutes o f  c a p a c i t y f o r every u n i t o f product 6F, e t c . The U v a r i a b l e e l i m i n a t e s the i n e q u a l i t i e s i n the equations and r e p r e s e n t s unused The  capacity.  o b j e c t i v e of a n a l y s i s i s t o minimize  p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n c o s t . a l g e b r a i c a l l y , t h i s o b j e c t i v e becomes:  total  Expressed  121 3.40 X  + 4.50 X  l:L  + 5.30 X  2 1  + 4.20  3 1  + 2.90 X 2  * 5.20 X  • 4.00 X  3 3  * 3.90 X  1 4  + 3.30  X  + 3.50 X  2 5  + 4.30 X  3 6  «r 8.10  X  + 12.20  X  3 6  + 10.50  + 11.20 X  1 8  4.  2  + 9.00 +  U-L  f U  X  9.50  * 9.60  2 9  + U  1 0  1 X  + U  X X  X  * Ug +> Ug +• U  + 5.10 X  3 2  4  + 9.30  X  1 3  =  g 3  + 4.50  X  3 4  2  + 9.20  2 6  7  +  UQ  X X  * 9.20  1 0  + U  X  + 11.80  g 7  3 8  X ^ 6  X  + 10.20  6  + 8.90 X  + Ug + U  f U  1 2  1  1 2  + 3.80  2 4  + 8.70  1 ?  2 8  3 9  1 3  X  +  1  9  Xg U  3 ?  1  Q  9  MINIMUM  The next step l n the f o r m u l a t i o n of the Simplex i s to  set up the v a r i a b l e s and c o e f f i c i e n t s from the above  equations i n m a t r i x f o r m . XIV on page  5  T h i s has been done i n Table  122.  The c o e f f i c i e n t s of the o b j e c t i v e e q u a t i o n have been p l a c e d i n the second row from the t o p .  The  first  f i f t e e n spaces i n t h i s row i n d i c a t e the u n i t v a r i a b l e cost of  product 10D at each warehouse from each of the  native plants.  alter-  Spaces s i x t e e n through t h i r t y i n t h i s  row  5 For a d e s c r i p t i o n of the Simplex m a t r i x see Nyles V. R i e n f e l d , W i l l i a m R. V o g e l , Mathematical Programming, (Englewood C l i f f s , N.J., P r e n t i c e H a l l , Inc., 1958), p. 81.  TABLE X I V SIMPLEX MATRIX  1 COST »  3  2  3.40 4.50  5.30 4.20  103 t o AW 1. .A £ 6 0 , 0 0 0 5  2.  B £80.000  B« 30.000 CW 35,000 I B £0,000 YS 10.000 AH 30,000 B B 20,000 IS.000 'Xt 10.000  £.9(  5.20 5.10  J_  -  10D t o BI  £.00  2.00  9  .10  11 . .12  13  J  17  18  6F t o AX  19  20 . .21  22'  £3  24  2.45  6F t o . CW  6F t o BS-  S.60 2.20  £.£0 £.45  16  £5  26  27.  3^0 4.30 8.10 10.20 12.20 10.50 5.70 LL£0 2120 9.50 6.90 9.20 9.00 9.60  E.OO  £.00  2.4 5  15  10B t o IW  10D t o  2.20  14  if  aso 4.00 3.90 3.30 4.50  2.00  2.45  1 •1  - 6  • i o D t o cvr  2.20  2.20  0 S60.000 Alt 40,000  7  6  4  E.60 6.CO  2.45  5.50 5.00  6.40  TR  6F t o S.50  6.00 6.40  28  29'  U  9.31 3.20  6F  to  30  6.40  32  33 34 36 36  0  0  0  0  0  37  6  0  36 39 40  41 42  43  0  0  0  0  0  0  W 1  5.'50 5.00  31  6.0O  1 6.40  6.40  1.  1 1  1  1  -  1 1  1  1  -  1 -1  1  3  1  -  K  . 1  1  1 1  1  1  1 1 .  1  1  1 1 .  1.  1  1 1  1  1  i 1  T»  8,000  1  .1  1  1  H  ro  123 show the same I n f o r m a t i o n f o r product 6F. one  through f o r t y - t h r e e i n d i c a t e that t h e r e  Spaoes t h i r t y i s no vari able  cost i n v o l v e d i n unused p l a n t c a p a c i t y or u n f i l l e d Note that the l e t t e r M has been entered and twenty-eighth spaces.  Since  demand.  i n the t h i r t e e n t h  i t i s impossible  t o ship  output from p l a n t A t o warehouse Y the M may be i n t e r p r e t e d as a s u f f i c i e n t l y high cost t o preclude t h i s route  i n the s o l u t i o n t o the problem.  Plant  c a p a c i t i e s i n minutes are shown i n the  second column at the l e f t three.  the i n c l u s i o n of  i n rows numbered one through  Warehouse demands f o r product 10D are shown i n  u n i t s o f product i n rows f o u r through eight and warehouse demand f o r product 6F i n rows nine through t h i r t e e n . The  body o f the matrix ( i e . column one through  t h i r t y ) i n c l u d e s the c o e f f i c i e n t s o f the p l a n t  capacity  equations and the c o e f f i c i e n t s of the warehouse demand equations.  The f i g u r e one i n rows numbered f o u r through  t h i r t e e n s i g n i f y that t o t a l p r o d u c t i o n  f o r eaoh warehouse  i s not t o exceed i t s demand, but that demand may be s a t i s f i e d from any one or more of the p l a n t s . The  c o e f f i c i e n t s of the U v a r i a b l e from each of the  aforementioned equations are shown i n the I d e n t i t y p o r t i o n of the m a t r i x ( i e . , column t h i r t y - o n e through f o r t y - t h r e e ) .  These c o e f f i c i e n t s c o n s i s t of the f i g u r e one and i t i s a requirement  i n each  case  of the Simplex matrix that these he  d i a g o n a l l y arranged as shown i n the  table.  I t i s p o s s i b l e to f i n d the minimum cost s o l u t i o n t o t h i s problem by a p p l y i n g Simplex  r u l e s t o the m a t r i x as  formulated i n Table XIV, page 122. i m p r a c t i c a l , however, t o attempt calcualtion.  It i s generally  a s o l u t i o n through hand  I t has been assumed f o r s i m p l i c i t y sake i n  our example that there are only three p l a n t s , f i v e warehouses and two p r o d u c t s . a matrix w i t h 539  spaces.  These assumptions  have  produced  A more t y p i c a l example would  probably i n v o l v e a c o n s i d e r a b l y broader product l i n e perhaps  a d d i t i o n a l p l a n t s and warehouses t o produce  matrix of s e v e r a l thousand  spaces.  suggest that i t would perhaps  a  R i e n f e l d and V o g e l  take from two t o three  months to s o l v e a Simplex m a t r i x w i t h from 800 to spaces.  and  1200  B e a r i n g i n mind that the model i s to be used f o r  short-term p l a n n i n g purposes  and that a great d e a l of time  w i l l have a l r e a d y been spent i n d e v e l o p i n g the data t o be i n c l u d e d i n the a n a l y s i s , a r a p i d s o l u t i o n i s d e s i r a b l e .  6  I b i d , p.  132.  125 Many of the l a r g e r computers have been programmed f o r the Simplex  and t h i s i s the p r e f e r r e d method of s o l u t i o n f o r  the s i z e of m a t r i x that w i l l u s u a l l y be i n v o l v e d i n t h i s type of problem. In  c e r t a i n circumstances, however, the  Simplex  method of s o l u t i o n can be avoided by r e d u c i n g the m a t r i x to  one  that i s s u i t a b l e f o r s o l u t i o n through the Transpor-  t a t i o n Method.  The procedure  f o r r e d u c t i o n and  the  circumstances under which t h i s s i m p l i f i c a t i o n w i l l  produce  an adequate s o l u t i o n are d e s c r i b e d i n the f o l l o w i n g s e c t i o n and have been adapted R i e n f e l d and V o g e l .  from the w r i t i n g s of  7  Conversion of the Simplex  Matrix  A Simplex t a b l e a u can be reduced to a form for  suitable  c o n v e r s i o n i n t o a t r a n s p o r t a t i o n model p r o v i d e d each of  the f i g u r e s contained i n the body of t h i s matrix can be transformed to the f i g u r e one. Table XIV  The body of the m a t r i x i n  c o n s i s t s of rows numbered one  through  up t o and i n c l u d i n g column number t h i r t y .  The  thirteen, following  m a t r i x a l g e b r a r u l e s w i l l be used f o r the r e q u i r e d Simplex  7  I b i d . , p. 137 -  141  transformation: 1.  You can d i v i d e or m u l t i p l y any row i n the m a t r i x by any number other than zero*  8.  You can d i v i d e o r m u l t i p l y any column i n the matrix by any number o t h e r than zero.  I n e i t h e r case, every number i n the row (or column) must be m u l t i p l i e d  ( o r d i v i d e d ) by the number.  The t r a n s f o r m a t i o n with the use of these r u l e s can be achieved i n f o u r s t e p s , as f o l l o w s : 1. .j  D i v i d e rows numbered  one through three by 8.00,  8.20, and 8.45 r e s p e c t i v e l y .  A l l o f the  f i g u r e s i n the body up t o and i n c l u d i n g  column  number f i f t e e n become l ' s . The t a b l e a u a f t e r completion  of t h i s step i s shown i n Table XV,  page 187. 8.  D i v i d e column number s i x t e e n and every  third  column t h e r e a f t e r up t o and i n c l u d i n g column twenty-eight by 8.75. D i v i d e column number seventeen  and every  third  column t h e r e a f t e r up to and i n c l u d i n g column twenty-nine by 8.73. D i v i d e column number e i g h t e e n and every  third  column t h e r e a f t e r up to and i n c l u d i n g column  o O)  *r  o  i-i  o  o  r-l H  o  r-l  o >  o •  O)  c-  w  r  o  «  o o •  tO KJ  .-1  •.. o '  35  8  o  Vi  ifl  o  OJ  0  o  »  ' o • w  O ' to  Ol O ' . M c n  ' (71 « to  '  •' <V  2 •  8 > o '  CO t > *J  m  o o  e\i  . 8  C •O  r-i  3  u5 o  in  • m "  c u • .•. «  «•  !i o  to  i-i  9  o  ••s .  O iO 0  • o  •  in  to  u  t\t > o ri  - • OJ rH lO  c-  O  i-l  CM  Pu,  10  rH  fc "rt  r-t  0  r-i  01 i-i  rt  «  CO  r-i  • ri  o to  • i-i  1-1  •V  o to  0  .  r-H  pj'  ' 'o  0  'o ^1  r-i  r-i  o  o aj c o o  £-  B a • * » 0  r-i  . 1-*  -  • rH  to o  <H  Ui o o > a  • CM •  to  C-Y  •••8:  ,i  -  a  o  ' « .  <£>' r-i*  Hi  r-i  U)  o.  ,B-  >D  ri  c u  d  CD  CO  ' t>  fit  .8  j > ' r-l  .a >  rt  c w  8  O CM  r-1  CM  rt  r-t  o  r-t  0  .' c n  • CM  r-t ri  CO  o  O  • W  • -• m • i-i  .5  ".CT»  *r  H  ta  >  O  w  ri  W  p  o  '3 to o in M*  a CO  S 0 +•  O •r-i  r-t  X -< O O O n  r-i  O O  O  Q  E-t O o  -  r-t  O ' «* r-i  •H  O  G) (M  O  W  O O  O  fj  to  B = rfl  5  B E  f)  O  O O  0 CM  . at  O  0 0  to  ..0  O O  r> CM  0 0 0  a  §  0  cl O O O  EX  L-  al  cn  O  CW 15,000  .  17*  r-  .  O O  b  O  ( O  O  r H  8  R a  128 t h i r t y hy  2.61.  These d i v i s i o n s a l s o apply to the f i g u r e i n the cost  row.  Table XVI  on page 129  shows the  r e s u l t of t h i s t r a n s f o r m a t i o n .  •  D i v i d e rows nine through t h i r t e e n by 0.371, i e . , by the average these rows.  of the t h r e e f i g u r e s i n each of  The  r e s u l t of t h i s step i s shown  i n Table XVII on page  130.  Note i n Table XVII that the f i g u r e s i n the body of the matrix i n each of rows n i n e t h i r t e e n now  approximate  t h i s i s the l a s t  through  the f i g u r e one.  of the steps that  can be  Since taken  t o t r a n s f o r m the body of the m a t r i x , i t must be decided whether or not each of these  figures  are s u f f i c i e n t l y c l o s e t o the f i g u r e one  to  c o n s i d e r the m a t r i x as transformed s u f f i c i e n t l y t o apply the T r a n s p o r t a t i o n Method of s o l u t i o n . I n t h i s p a r t i c u l a r example, the converted f i g u r e s i n d i c a t e that e r r o r of 3.2  t h e r e w i l l be a maximum  percent i n the s o l u t i o n t h a t i s  suggested f o r product 6F through the use of the T r a n s p o r t a t i o n Method.  But there w i l l be  e r r o r i n the s o l u t i o n suggested f o r the p r o d u c t i o n and p h y s i c a l  d i s t r i b u t i o n of  no  TABLE XVI SIMPLEX TABLEAU AFTER STEP 2. 1 COST.$  _ 1.  A 140,000  B* 30,000 CW 36,000 c  7.  xw 20.000 y* IO.OOO  &  aV Ii 3 •>  ;io.  AW 30,000 BW £ 0 . 0 0 0  4  IOC to AW  lOB  1  1 1  C 114,260 AW 40,000  3  6  6  7  8  9  10  11  IS  340 4.60 5.20 4.20 2.90 6. SO 6.10 3.80 4.00 3.90 MO 4;50  S 127,270  ILL  z  to BW  1  1  V  14  16  16  17  19  19  20  21  IOC to IW  l o t to VS.  6r to kV  6F to BW  1  1.  1  1  1  .1 1  1 l"  22  23  ?4  26.  26  27  2.80 4.30 £ . 3 6 3.74 4.67 3.60 5.19 4.E2 4.07 3.45 3.41 3.36 3.30 3.68  102 to CW .  1 1.  13  1  1 1  . 1  .'tr. to .CW 1  1 1  -67 to-  '.'-'• -  1  3.1 0  32 0.  33 34 '£ 36 0  0  0/ 0  S7 0  38 79 0'  0  40 41 42 0  0  43  0  0  to YR  1 1'  1  30  V. 3.41 3.53 ' 6F  1 . 1 '  1  rB  28 . 29  .600 .456  1 1  406 1  1 1  . 1  1  1 1  1  1  1 .1  1  1 1  1  1  1. 364 . 3 5 6 .383  i 1.  .364 .366 .383  1  s  ' 11. CW 15,000 • 12. ZW 10,000 13. T» 8,000  .364 .366 .3S3  1 .364. .366 .583  1 .364 .2 66 .383  1  TABLE XVII SIMPLEX TABLEAU AFTER STEP 3. l | COST t  3  2  1 ? . « O 4 . 5 0 5.30 _ i ... 10D t o AW  A H O , 000  a m u  2.  C  4.  AW 4 0 . 0 0 0  £  BW 307000  1. '• 01 ~* 3 a  CB 2 6 . 0 0 0 X» 2 0 , 0 0 0  a. "  YW 1 0 , 0 0 0  9.  jtSI 80,860  lie.  BUT 6 3 , 9 1 0  t>  K  V s a =  J  CW 4 0 . 4 3 0 11.  ZW 2 6 , 9 6 0  12. 13.  YW 2 1 , 6 6 0  i.?o  I  10D to BW  8  9  30D  tr C(B  1 1  1  0  13  I i t ; i=  10D t r 151  1  14  16  10B t 5 TO '  17  16  .19  1  if  6F t o 1  1  1 1  is  . 20  21  22  2 3 ' 24  26  26 .  £7  M S.50 4.30 2.96 3.74 4 . 6 7 3.60 3.19 4.52 4.07 3 . 4 9 3.41 3.36 3 . 3 0 3.68  3  1 •  J-  1 1  7  z . s o 5.20 5.10 3.SO 4.00 3.90 3.3D 4.60  3  j  C 114.280  6.  u  3 32 7.2 70  I  6 •  <  t o B.W  6F t o  • 1  1  1  6F t o  i  3 1  CF  i  29  i l  30  fe.4lb.63 1  31  32  33  34  3£  36  37  0  0  : 0  0  0  0  0  0  39  40  41  42  43  0  0  0  0  0  6F t o YW  l .i j  M  . 1  :  1 3  73  29  1  1 " 1  i i!  .455  3 1  i  .500  1  1  .406  1  l  1 3  •  1 1  1  1  - 3 1  1  |  1 1  1  1  1  .sei .987 L032  2.70 .961 .987 3-038"  2.70 .981 .967 1.032  J.70  1. 70  .991 .987 1.032 .9.81 .98* 103!  2.70  03 O  131 product 10D since a l l of the f i g u r e s i n t h i s p o r t i o n of the matrix are e x a c t l y ones.  Hence,  the maximum t o t a l e r r o r r e s u l t i n g from the use of the T r a n s p o r t a t i o n  Method i s l i k e l y t o  produce an e r r o r o f l e s s than two p e r c e n t , considering  the r e l a t i o n s h i p s between oonverted  c o s t s and demands of the two p r o d u c t s .  A  p o t e n t i a l e r r o r of t h i s s i z e w i l l u s u a l l y be insignificant  —  p a r t i c u l a r l y since the  estimates that are necessary i n the  formulation  of f o r e c a s t s and product costs are l i k e l y t o c o n t a i n e r r o r s of t h i s s i z e o r l a r g e r . case, the s i z e of e r r o r t h a t be c o n s i d e r e d i n the l i g h t  I n any  i s acceptable must  of the saving i n  time and e f f o r t that i s a v a i l a b l e through the use 4.  of the T r a n s p o r t a t i o n  Method.  The f i n a l step i s to convert the i d e n t i t y p o r t i o n of the m a t r i x .  This  can be  accomplished by m u l t i p l y i n g each of the f i g u r e s contained t h e r e i n by the appropriate  integer to  produce the f i g u r e one. The Simplex m a t r i x has now been converted i n t o the form s u i t a b l e f o r s e t t i n g up the T r a n s p o r t a t i o n  matrix.  138 The  circumstances i n which the r e d u c t i o n t o the Transpor-  t a t i o n Method i s d e s i r a b l e i s , o f course, r e l a t e d t o t h e s i z e o f the e r r o r d i s c u s s e d  under step t h r e e .  The s i z e  of t h i s e r r o r w i l l i n c r e a s e w i t h l a r g e r d i f f e r e n c e s i n the u n i t s of c a p a c i t y u t i l i z e d i n the manufacture of products at a l t e r n a t i v e p l a n t s .  I t i s c l e a r , however, that a few  c a l c u l a t i o n s can be made t o determine the d e s i r a b i l i t y of the T r a n s p o r t a t i o n conversion  Method without performing the complete  as d i s c u s s e d  above.  S o l u t i o n Through the T r a n s p o r t a t i o n To set up the T r a n s p o r t a t i o n  Procedure matrix, the warehouse  requirement f i g u r e s shown i n Table XVII a r e t r e a t e d as product demands; t h e converted a v a i l a b l e minutes a r e taken as t h e p l a n t c a p a c i t i e s ; and the are i n s e r t e d i n the  converted cost  figures  small squares of the T r a n s p o r t a t i o n  m a t r i x (see Table X V I I I ) .  Plant  c a p a c i t y I n t h i s example  exceeds demand f o r the p e r i o d and a dummy warehouse has been added t o t h e matrix t o e l i m i n a t e  this inequality.  There i s no v a r i a b l e cost a s s o c i a t e d with unused as i n d i c a t e d by the zeros  i n the  capacity  s m a l l squares o f the  dummy warehouse eolumn. The  first  step i n s o l u t i o n i s t o i n s p e c t the cost  f i g u r e s i n t h i s m a t r i x and t o take a guess at t h e best  TABLE X V I I I TRANSPORTATION-  MATRIX  DISTRIBUTION WAREHOUSES 10D to AW 3.40  10D to BW  10D to CW  4.20  5.10  10D to XW 3.90  10D to YW  6F to AW M  2.95  6F to BW 3.80  6F to CW 4.07  6F to XW 3.35  6F to YW  Dummy Plant Ware- C a p a c i t y House M  0 140,000  A 4.50  PLANT:  ro  2.90  3.80  3.30  3.50  3.94  3.19  3.48  3.30  3.41  0  B  127,270 5.30  5.20  4.00  4.50  4.30  4.67  4.52  3.41  3.68  3.53  0  C Product Demand 40,000  114,280  30,000 35,000  20,000 10,000  80,860  53,910 40,430  26,950 21,560 22,840 381,550  H  134 assignment of demands a c c o r d i n g at each p l a n t . it  t o the c a p a c i t i e s a v a i l a b l e  S t a r t i n g w i t h the f i r s t  column, f o r example,  appears l i k e l y that the demand f o r product 10D at ware-  house A should  be met from p l a n t A s i n c e t h i s i s the lowest  cost frame i n the column. may be entered  Product demand of 40,000 u n i t s  i n t h i s frame, t h e r e f o r e , and s i m i l a r l y f o r  each succeeding guess u n t i l a l l demands have been s a t i s f i e d . The  c i r c l e d f i g u r e s i n Table XIX represent  guess at the optimum s o l u t i o n .  a completed  Note that the assignment  must be made i n such a way that the c i r c l e d f i g u r e s i n each row  add up t o the f i g u r e s shown i n that  capacity.  row f o r p l a n t  S i m i l a r l y , the c i r c l e d f i g u r e s i n each column  must add up t o the corresponding product demand f i g u r e . The  problem at t h i s stage i s t o determine whether  or not t h i s assignment i s the minimum cost s o l u t i o n .  The  t e s t of o p t i m a l i t y r e q u i r e s an i n v e s t i g a t i o n of the change i n t o t a l cost that would r e s u l t i f the assignment were t o i n c l u d e any one of the excluded r o u t e s , Table XIX i n which there routes must be analyzed appraise  I e . , the frames i n  are no c i r c l e d f i g u r e s . one at a time.  These  It i s sufficient to  the cost of moving one u n i t v i a an unused route t o  determine whether or not i t s u t i l i z a t i o n w i l l improve the assignment.  TABLE XIX TRANSPORTATION MATRIX - INITIAL -ASSIGNMENT  DISTRIBUTION WAREHOUSES lOD to AW 3.40 A  W  B  d  tooog) 4.50  ]..15 5.30  C Product Demand  .1.90  40000  10D to BW 4.20 1.25 2.90  10D to CW 5.10 1.10 3.80  (30000) -0.15 5.20  4.00  10D to XW  10D to YW  3.90 0.55 3.30  M M 3.50  (20000) (^OOOO) 4.50  4.30  6F to AW  6F to BW  6F to CW  6F to XW  2.95  3.80  4.07  3.35  (|0860)  0.56  0.66  (^3590)  3.94  3.19  3.48  3.30  (5391^)  0.12  4.52  3.41  1.04 4.67  2.25  (350^)  1.15  0.75  1.72  30000  35000  20000  10000  80860  1.28  53910  (4043B)  40430  6F to YW M M 3.41  (13360) -0.07 3.68 0.33  26950  3.53  Dummy Warehouse  Plaat Capacity  0 (5550)  140000  0 0.05  127270  0  (21560)  L729^  114280  21560  22840  381550  136 Bearing i n mind that the assignment must always s a t i s f y demand and c a p a c i t y c o n s t r a i n t s , i t i s c l e a r that to p l a c e  a u n i t i n an empty frame r e q u i r e s at l e a s t  adjustments i n the e x i s t i n g assignment. example, that one u n i t l s p l a c e d the f i r s t  row o f Table X I X .  three  Assume, f o r  i n the second frame o f  To reduce the t o t a l  assignment  i n the second column to the r e q u i r e d 30,000 u n i t s i t i s now necessary to s u b t r a c t second row.  one unit from the second frame o f the  But t h i s w i l l r e s u l t i n an unassigned u n i t o f  c a p a c i t y f o r p l a n t B, w h i l e at the same time the t o t a l assignment  i n row one now exceeds p l a n t A's c a p a c i t y by  one u n i t as a r e s u l t of the i n i t i a l s t e p .  The next  adjustment, t h e r e f o r e , must c o r r e c t the assignments i n rows one and two without v i o l a t i n g demand requirements. T h i s can only be done by s u b t r a c t i n g one u n i t from the assignment  i n the n i n t h frame of the f i r s t  t h i s u n i t t o the assignment second row.  These  row and adding  i n the n i n t h frame o f the  adjustments, expressed i n terms o f cost  i n d i c a t e that an a d d i t i o n a l $4.20 would be i n v o l v e d i n a s s i g n i n g one u n i t to the second frame of the f i r s t a s a v i n g o f $2.90 by r e d u c i n g  the assignment  row,  i n the second  frame of the second row by one u n i t ; an a d d i t i o n a l $3.30 for  i n c r e a s i n g the assignment  i n the n i n t h frame of the  13.7 second row;  and  a s a v i n g of $3.35 by reducing  ment i n the n i n t h frame of the use  row.  assign-  In t o t a l ,  of t h i s route would i n v o l v e an a d d i t i o n a l cost  $1.25  per u n i t  f i g u r e has i n Table it  first  the  ($4.20 - $2.90 + $3.30 - $3.35).  been shown i n the XIX .  Since  the  of  This  second frame of the f i r s t  t o t a l cost would be  not  assignment.  A few  simple r u l e s can be used t o q u i c k l y  each of the empty frames. 1.  row  increased,  i s c l e a r that the u t i l i z a t i o n of t h i s route w i l l  improve the  the  These r u l e s are as  S t a r t from an empty frame and  evaluate  follows:  record i t s unit  c os t . 2.  Proceed t o a frame i n the which there unit  3.  same row  i s a c i r c l e d number and  or column i n record i t s  cost as a minus f i g u r e .  Make a r i g h t angle t u r n and proceed t o second c i r c l e d number. (The  the  Record i t s u n i t c o s t .  second move must, of course, be t o a  c i r c l e d number from which the t h i r d move i s possible)• 4.  Make another r i g h t angle t u r n and proceed t o the t h i r d c i r c l e d number. a minus f i g u r e .  (The  Record i t s cost  as  t h i r d move must be made  138 i n such a way that If this circled  the f o u r t h move i s p o s s i b l e ) .  number i s i n the same column or  row as the empty frame, the loop i s oomplete. I f n o t , continue the s e r i e s of r i g h t  angle  moves t o s u c c e s s i v e frames i n which there are circled  numbers ( r e c o r d i n g  the u n i t  cost  a l t e r n a t i v e l y as p o s i t i v e and n e g a t i v e ) u n t i l the  circled  f i g u r e t o which a move i s made i s  i n the same column o r row as the s t a r t i n g point. 5.  T o t a l the u n i t c o s t s and e n t e r the f i g u r e i n the  Examples  empty frame. o f the a p p l i c a t i o n of these r u l e s are  shown i n F i g u r e s 12 and 13. the  Both f i g u r e s are s e c t i o n s o f  body o f the m a t r i x shown i n Table XIX,  139  FIGURE 12 DETERMINING THE COST OF AN UNUSED TRAFFIC ROUTE F o l l o w i n g the arrows; c o s t s would he recorded Start Step 1 2 3 4 5  ^3.48  -#3.41  0 3.35 6.83  as f o l l o w s :  0 - 3.30 - 6.71  The net ohange i n t o t a l oost, i f the f i r s t  frame of the  middle row i n F i g u r e  12 i s i n c l u d e d  i n the assignment,  would be an a d d i t i o n a l ' $0.12 p e r u n i t .  FIGURE 13 DETERMINING THE COST OF AN UNUSED TRAFFIC ROUTE In t h i s example, changes i n cost are as f o l l o w s : Start Step 1 2 3 4 5 The net change  $3.41 0 3.35 6.76  -3.53 0 -3.30 -6.83  i n t o t a l c o s t , i f the second frame i n tr  141 middle row would be  of F i g u r e 13 i s i n c l u d e d i n the  a saving The  assignment,  of $0.07 per u n i t . .  above procedure has been c a r r i e d out  in  e v a l u a t i n g the per u n i t cost a s s o c i a t e d w i t h the u t i l i z a t i o n of each o f the routes from the assignment. frames i n Table XIX The  negative  The  that have been excluded  numbers i n each of the  are the r e s u l t  of these  evaluations.  f i g u r e s appearing i n the t h i r d and  frames of the  second row  i n d i c a t e t h a t the  o r i g i n a l l y formulated, i s not  optimum.  unused  tenth  assignment,  There i s a  p o t e n t i a l r e d u c t i o n i n t o t a l assignment c o s t of $0.15 u n i t f o r every u n i t that can be p l a c e d  The  routes.  used to evaluate  the  frame i n which the  negative  number appears.  The  evaluate  frame t e n of the  second row  path t h a t was  used,to  i s shown i n F i g u r e  w i l l be used, t h e r e f o r e , t o i l l u s t r a t e t h i s  Normally, however, the f i r s t the  tenth  procedure f o r t h i s step i s t o f o l l o w the same  path that was  and  i n the  next step, t h e r e f o r e , i s t o change the  assignment t o i n c l u d e these The  per  i n the t h i r d frame,  and $0.07 f o r every u n i t that can be p l a c e d frame*  as  change would be  frame i n which the l a r g e s t negative  to  step. include  number appears.  13  148 Referring to Figure  13, the f i r s t  step i n  a d j u s t i n g the assignment i s t o determine the maximum number of u n i t s that Following  can he p l a c e d  the arrows, we  see that we w i l l have to subtract  the u n i t s that are p l a c e d c i r c l e d numbers —  i n the s t a r t i n g frame.  i n t h i s frame from three  21,560, 5,550 and 13,360.  of the  Since the  d i s t r i b u t i o n from p l a n t t o warehouse must be e i t h e r zero or a p o s i t i v e q u a n t i t y , i t i s c l e a r that 5,560 i s the maximum number of u n i t s that can be p l a c e d frame.  i n the s t a r t i n g  The t o t a l adjustment through the i n c l u s i o n of  5,550 u n i t s i n the s t a r t i n g frame and subtractions  and a d d i t i o n s of the same amount t o the  c i r c l e d numbers i n F i g u r e  13, i s shown i n Table  The next step i s t o recompute u t i l i z i n g each of the routes i n the new  successive  assignment.  the cost o f  that have not "been i n c l u d e d  The r e s u l t of t h i s c a l c u l a t i o n i s  shown i n each of the frames of Table XX l n which numbers do not appear.  XX.  The negative  circled  number i n the t h i r d  frame of the second row i n d i c a t e s that the s o l u t i o n i s s t i l l not optimum.  The same procedure as o u t l i n e d above  w i l l I n d i c a t e that the 5,550 u n i t s that has j u s t been placed  i n the t e n t h frame of the second row, must now  p l a c e d i n the t h i r d frame of that row, w i t h a  be  TABLE XX TRANSPORTATION MATRIX - FIRST ADJUSTMENT  DISTRIBUTION WAREHOUSES 10D to AW 3.40 A  (^oooS) 4.50  co  10D to BW 4.20 1.85 2.90  10D to CW 5.1C 1.17 3.8C  10D to XW  10D to YW  3.90 0.55 3.30  M M 3.50  6F to AW 2.95  6F to BW 3 . 80  <|086(^  0.56  3.94  3.19  6F to CW 4.07 (),73 3.48  6F to XW  6F to YW  !3.35 (^9149) 3.30  M U  Dummy Warehouse  Plant Capacity  0 0.07  3.41  140000  0  E-I  ih  B  1..15 5.30  C Product Demand  1.83  40000  (3000^) 5.20  -0.08 <2000§) C^OOOO) 4.0C  4.50  2.18  (3500^  1.08  30000  35000  20000  4.30 0.68  10000  1.04 4.67 1 e 65  80860  <^391§) 0.19 4.52  3.41  1.21 < £ 0 4 3 ^  53910  40430  <7810) (^555^) (3.68  3.53  127270  0.12 0  0.26 <^601§} ^2284^  114280  22840  381550  26950  21560  H  corresponding s u b t r a c t i o n and a d d i t i o n r e s p e c t i v e l y i n the t h i r d and t e n t h frames of the t h i r d row.  The ehange i n  assignment as a r e s u l t o f t h i s adjustment i s shown i n Table XXI. The  recomputed cost of u t i l i z i n g each of the routes  that have been excluded from the new•assignment are a l s o shown i n Table XXI. now p o s i t i v e .  Note t h a t  T h i s means that  a l l of these f i g u r e s are i t i s impossible  to  rearrange the assignment t o produce a lower t o t a l The  solution, therefore, As a point  cost.  i s optimum.  of i n t e r e s t , the t o t a l cost  of the  assignments i n each of T a b l e s XIX, XX and XXI has been e s t a b l i s h e d by summing the product of each of the c i r c l e d f i g u r e s and t h e i r a p p r o p r i a t e  u n i t cost  #3.40 + 80,860 x $2.95 + , e t c . ) .  (eg., 40,000 x  The r e s u l t of these  c a l c u l a t i o n s are as f o l l o w s : Table XIX  The  fl,178,098  Table XX  1,177,709  (Improvement $389,)  Table XXI  1,177,265  (improvement $444.)  s a v i n g through re-assignment In Table XX can be  e s t a b l i s h e d by simply m u l t i p l y i n g the s a v i n g p e r u n i t  that  was shown t o be a v a i l a b l e i n frame t e n o f the second row i n Table XIX by the number of u n i t s assigned t o that i n Table XX, i e . , $0.07 x 5,550 = $389.  frame  S i m i l a r l y , the  TABLE XXI TRANSPORTATION MATRIX - OPTIMUM SOLUTION  DISTRIBUTION WAREHOUSES lOD to AW 3.40  PLANTS  A  (40000). 4.50  B  Produot Demand  4.20 1.25 2.90  1.15 (3OOO9) 5.30  C  10D to BW  5.20  10D to CW  10D to XW  5.10  3.90  1.25  0.55  M  3.80  3.30  3.50  (Wo)  10D to YW M  (20000) (lOOO^)  4.00  4.50 1.00  O06Q  20000  10000  1.75  2.10  (Slio)  40000  30000  35000  4.30  6F to AW  6F to BW  6F to CW  2.95  3.80  4.07  (§0860) 3.94  1.04 4.67 1«£7  80860  0.56 3.19 (53910) 4.52  0.81 3.48 0.27 3.41  6F to XW  6F to YW  3.35 (19143) 3.30 (7810) 3.68  1.13  (40430)  0.18  53910  40430  2 5950  K M 3.41 0.08 3.53  Dummy Warehouse 0 0.15  140000  0 0.20  127270  0  (2156^) (22840)  21560  Plant Capacity  22840  114280  381550  146 saving through re-assignment i n Table XXI  can be  computed  by m u l t i p l y i n g the saving per u n i t shown i n the t h i r d frame of the  second row  assigned $444.  of Table XX by the  to that frame i n Table XXI,  These savings  the t o t a l c o s t .  number of u n i t s i e . , $0.08 x 5,550 =  are r e l a t i v e l y s m a l l i n comparison t o  I t should be remembered, however, that  have l i m i t e d the number of p l a n t s , warehouses and  we  products  i n these i l l u s t r a t i o n s i n order to s i m p l i f y the  discussion.  As a r e s u l t , we  were able to come c l o s e r t o the  optimum  s o l u t i o n on the  first  possible  t r y than would u s u a l l y be  i n the p r a c t i c a l s i t u a t i o n where the a n a l y s t would be working with a matrix that i s made up  of a s u b s t a n t i a l l y  l a r g e r product l i n e and perhaps a d d i t i o n a l p l a n t s warehouses.  I t i s c l e a r , however, that the  organization  of data i n t o a T r a n s p o r t a t i o n m a t r i x i n i t s e l f the b a s i s f o r a more i n t e l l i g e n t  and  guess at the  provides optimum  solution.  I n t e r p r e t a t i o n of the Optimum The f o r the  r e d u c t i o n of the  formulation  i n a transformation  Simplex t o a form s u i t a b l e  of the T r a n s p o r t a t i o n of some of the  s o l u t i o n that has been provided  matrix r e s u l t e d  o r i g i n a l data.  through the  The  Transportation  Method i s , of course, i n terms of t h i s t r a n s f o r m a t i o n  and  147 must now be converted back t o the o r i g i n a l  data.  Product c o s t s , demand f o r e c a s t s and p l a n t c a p a c i t i e s are g i v e n  i n the o r i g i n a l data and there  need, t h e r e f o r e , t o convert  these f i g u r e s .  i s no  Furthermore,  the warehouse requirements of product 10D were not changed i n the t r a n s f o r m a t i o n  process and are s t a t e d , t h e r e f o r e , i n  a c t u a l p h y s i c a l q u a n t i t i e s i n the T r a n s p o r t a t i o n The  only c o n v e r s i o n  that i s necessary i s that r e q u i r e d t o  e s t a b l i s h the p h y s i c a l q u a n t i t y assigned  solution.  t o each p l a n t  o f product 6F that has been  i n the optimum s o l u t i o n .  In transforming  the Simplex, the warehouse r e q u i r e -  ments of product 6F were d i v i d e d by the number 0.371 (see step 3 of the c o n v e r s i o n  p r o c e s s on page 128).  These  converted o r normalized f i g u r e s were then t r a n s f e r r e d t o the T r a n s p o r t a t i o n  matrix.  The p h y s i c a l q u a n t i t i e s o f  product 6F, t h e r e f o r e , w i l l be 37.1 percent shown i n the T r a n s p o r t a t i o n Taking 37.1 percent  of the f i g u r e s  solution. of the sum of the c i r c l e d  f i g u r e s f o r product 6F i n each row of Table XXI, we see that the output of t h i s product that w i l l be r e q u i r e d at each plant  i s as f o l l o w s :  P l a n t A = 37*100 u n i t s (37.1$ of 80,860 + 19,140) P l a n t B • 22,900 u n i t s (37.1$ of 53,910 +  7,810)  P l a n t C = 23,000 u n i t s '(37.1$ o f 40,430 + 21,560)  148 The  output of product 10D that w i l l he r e q u i r e d at each  plant —  taken d i r e c t l y from Table XXI —  i s as f o l l o w s :  P l a n t A - 40,000 u n i t s P l a n t B - 65i550 u n i t s P l a n t 0 = 39,450 u n i t s The  t o t a l c a p a c i t y that w i l l he absorbed by the above  combination of output at each p l a n t  i s shown i n Table XXII.  TABLE XXII PLANT CAPACITY ABSORBED IN THE TRANSPORTATION SOLUTION  Plant  Product  Units  Production Time Per Unit  A  10D 61  40,000 37,100  2.00 5.50  80,000 204.000 284,000  2.20 6.00  144,200 137,400 281,600  2.45 6.40  72,200 147*200 219,400  Absorbed Capacity B  C  at A  10D 65,550 6F 22,900 Absorbed Capacity at B 10D 6F  29,450 23,000  Absorbed Capacity  Total Production Time  at C  We have s t a t e d i n the o r i g i n a l data that there be  will  280,000 minutes o f c a p a c i t y time a v a i l a b l e at each p l a n t *  Absorbed time at p l a n t C i s , of course, below  this  149 c o n s t r a i n t because the  s o l u t i o n has  f i r m ' s excess productive point.  c a p a c i t y be  T h i s has  that  the  concentrated  Absorbed time at p l a n t s A and  the c a p a c i t y c o n s t r a i n t . the  provided  at t h i s  B i s s l i g h t l y above  occurred  as a r e s u l t  of  assumption that each of the converted f i g u r e s i n the  Simplex matrix were s u f f i c i e n t l y c l o s e t o the f i g u r e one  to  8 permit the f o r m u l a t i o n recognized,  of a T r a n s p o r t a t i o n model.  however, that there would be  of l e s s than two  percent  t h e r e f o r e , t h a t the  was  a potential error  i n the T r a n s p o r t a t i o n  a r e s u l t of t h i s assumption.  It  s o l u t i o n as  I t i s not s u r p r i s i n g ,  s o l u t i o n suggests a combination of  output that exceeds the' c a p a c i t y c o n s t r a i n t at plant A 1.4  and at p l a n t B by 0 . 6 percent.  percent  An  i n the assignment t o conform w i t h a p p r o p r i a t e  by  adjustment reductions  i n the c a p a c i t y c o n s t r a i n t s of both p l a n t s A and B w i l l , course, be necessary i f i t i s impossible increase  some f l e x i b i l i t y  I t w i l l be  The  advisable, light  pp.  however, there w i l l  shown that one 128  and  131.  t h e r e f o r e , to  of the  s o l u t i o n should be  r e - e v a l u a t i o n has See  In g e n e r a l ,  be  i n the c a p a c i t y e s t i m a t e s that are used i n  these estimates i n the provided.  to accommodate the  i n output that would be r e q u i r e d w i t h the s o l u t i o n  as g i v e n i n Table XXI.  analysis.  of  re-evaluate  s o l u t i o n that has  been  r e j e c t e d only when t h i s or more p l a n t s w i l l  be  150 unable to adapt t o the suggested l e v e l of output. Demand c o n s t r a i n t s f o r product 10D have, of course, been met by the s o l u t i o n s i n c e there was no c o n v e r s i o n i n t r a n s f e r r i n g these f i g u r e s t o t h e . T r a n s p o r t a t i o n  matrix.  To show that these c o n s t r a i n t s have a l s o been s a t i s f i e d f o r product 6F, the c i r c l e d f i g u r e s i n the a p p r o p r i a t e columns of Table XXI should be m u l t i p l i e d by 37.1 percent, as  follows: Warehouse A -  80,860 x 37,1$ = 30,000 u n i t s  Warehouse B = 53,910 x 37.1$ = 20,000 u n i t s Warehouse G = 40,430 x 37.1$ = 15,000 u n i t s Warehouse X = 26,950 x 37.1$ = 10,000 u n i t s Warehouse Y = 21,560 x 37.1$ = The  8,000 u n i t s "  r e s u l t s of these c a l c u l a t i o n s correspond with demand  f i g u r e s shown i n the o r i g i n a l Solution  data.  Implications The  method that has been d e s c r i b e d  i n the f o r e g o i n g  was based upon bottleneck: c a p a c i t y at each p l a n t , and a predetermined product cost at d i s t r i b u t i o n warehouses v i a alternative t r a f f i c  routes.  The v a l i d i t y of the  assumptions that u n d e r l i e these two parameters must now be evaluated implicit  i n the l i g h t of the t r a f f i c  flow that i s  i n the output a l l o c a t i o n s o l u t i o n .  151 Plant capacity*  I t was  i n d i c a t e d i n Chapter IV  that p l a n t c a p a c i t y d e f i n e d i n terms of the operation  i m p l i e s that the  output of other  processes at the p l a n t can be a d j u s t e d of p r o d u c t i o n  bottleneck manufacturing  to whatever  i s c a l l e d f o r i n the optimum p l a n .  mix In  words, while the output a l l o c a t i o n s o l u t i o n w i l l be the it  c a p a c i t y l i m i t s of the assumed b o t t l e n e c k i s p o s s i b l e that the p a r t i c u l a r mix  i n other p l a n t  within  operation,  of output that  would be r e q u i r e d by t h i s s o l u t i o n w i l l cause an bottleneck  other  unforeseen  operations.  I t i s necessary, t h e r e f o r e , t o check the  capacity  of each of the manufacturing processes i n the plant i n the l i g h t  of the mix  solution.  The  short-term  planning  of output that i s c a l l e d f o r i n the  s o l u t i o n w i l l be  an adequate b a s i s f o r  only i f the mix  l i m i t s of a l l of the p r o d u c t i o n  i s w i t h i n the  processes i n each p l a n t .  Product Cost E s t i m a t e s .  In estimating  oosts at d i s t r i b u t i o n warehouses, i t was assume a c e r t a i n flow of t r a f f i c  method and  cost  product  necessary t o  through a route  to approximate c e r t a i n of the cost The  in  order  elements.  of t r a n s p o r t a t i o n , f o r example,  assumed that t o t a l demand at a warehouse would be through one  capacity  or another t r a f f i c  routes.  I f we  met  look at  the  152 optimum s o l u t i o n as shown i n Table XXI, we see. that the demand f o r product 6F at warehouse X i s t o be s a t i s f i e d through two r o u t e s .  The q u e s t i o n then a r i s e s as t o  whether or not the s p l i t  i n demand among the two  routes  w i l l a f f e c t the method of t r a n s p o r t a t i o n that w i l l be used. If  the r a i l c a r l o a d r a t e was used i n c o s t i n g the p l a n t B  t o warehouse X movement, f o r example, w i l l the much lower volume through t h i s route preclude If  a r a i l c a r l o a d movement?  so, Is the change i n t r a n s p o r t a t i o n r a t e  significant?  Inventory c a r r y i n g c o s t s and order p r o c e s s i n g at  costs  d i s t r i b u t i o n warehouses were based i n part upon the  assumed method of t r a n s p o r t a t i o n .  It i s possible,  t h e r e f o r e , that these c o s t s w i l l change i f the t r a n s p o r t a t i o n method d i f f e r s from that assumed i n the cost The t r a n s p o r t a t i o n and i n v e n t o r y materials  estimates.  cost estimates f o r raw  a l s o assumed a c e r t a i n minimum flow.  The  v a l i d i t y of t h i s assumption may a l s o be questionable light  i n the  of the mix of output that i s suggested i n the optimum  solution. It  i s d e s i r a b l e , t h e r e f o r e , t o ensure that the  p a t t e r n of t r a f f i c flow that i s i m p l i c i t a l l o c a t i o n s o l u t i o n w i l l not r e s u l t  i n the output  i n significantly  different  unit c o s t s from those that were used i n the  analysis.  T h i s may be done by re-computing the u n i t  costs  153 for  each of the t r a f f i c  solution —  routes  u s i n g the t r a f f i c  that are i n c l u d e d i n the f l o w from t h i s s o l u t i o n as  the b a s i s f o r the new e s t i m a t e s .  I f i t i s found that  there  i s a d i f f e r e n c e between the o r i g i n a l and the new estimate for  a p a r t i c u l a r r o u t e , put t h e new estimate through the  Simplex conversion appropriate  and t r a n s f e r the r e s u l t t o the  frame i n the T r a n s p o r t a t i o n  matrix.  It will  then be apparent whether o r not the d i f f e r e n c e i s s i g n i f i c a n t enough t o r e q u i r e an adjustment i n the output allocation solution. II.  LINEAR PROGRAMMING MODEL FOR DAY-TO-DAY PHYSICAL DISTRIBUTION DECISIONS  It was suggested i n Chapter I I I that s h i p p i n g and t r a n s p o r t a t i o n from d i s t r i b u t i o n warehouses t o customers i s the only a d d i t i o n a l cost i n the p h y s i c a l d i s t r i b u t i o n process, final  once the f i r m ' s output becomes a v a i l a b l e at i t s  stock p o i n t s .  One of the t r a f f i c manager's t a s k s ,  t h e r e f o r e , i s t o minimize the s h i p p i n g cost  infilling  customers orders  and t r a n s p o r t a t i o n  out of the g i v e n  quantities  of products that are a v a i l a b l e f o r d i s t r i b u t i o n at f i n a l warehouses-  I t i s assumed that customer orders are  r e c e i v e d at a c e n t r a l l o c a t i o n and that the t r a f f i c  manager  a l l o c a t e s these among d i s t r i b u t i o n warehouses on a d a i l y basis.  154 The  q u a n t i t y of products  that are a v a i l a b l e f o r  d i s t r i b u t i o n on any p a r t i c u l a r day clarification.  r e q u i r e s some  I f i t i s assumed that a l l of the  that i s on hand at a stock p o i n t may  be used f o r immediate  customer orders, there i s a danger of To i l l u s t r a t e ,  c o n s i d e r the simple  inventory  sub-optimization.  case of two  A and B, and two  customers, Y and Z.  u n i t s of product  on hand at warehouse A.  warehouses,  There are only Shipping  500  and  t r a n s p o r t a t i o n cost per u n i t t o Y and Z are as f o l l o w s :  On the f i r s t  A to Y  $1.00  and  A to Z  $3.00  B to Y  $4.00  and  B to Z  $5.00  day  an order i s r e c e i v e d from Z f o r 500 u n i t s .  Since the s h i p p i n g and t r a n s p o r t a t i o n cost from A i s l e s s than from B, the order i s f i l l e d  from A at a cost of $1500.  On the f o l l o w i n g day,  i n v e n t o r y at A can be  and before  plenished,, an order i s r e c e i v e d from Y f o r 500 order must be f i l l e d  This  from warehouse B at a cost of $2000.  T o t a l cost f o r the two  orders i s $3500.  been r e c e i v e d on the same day,  Had  or i n reverse  would have been s u p p l i e d from A and cost f o r the two  units.  re-  both  orders  order, Y  Z from B at a t o t a l  orders of only $3000.  To a v o i d t h i s kind of s u b - o p t i m i z a t i o n  it is  d e s i r a b l e to l i m i t the day-to-day d i s t r i b u t i o n from each warehouse to what may  be termed s u r p l u s Inventory.  A  155 p o r t i o n o f the t o t a l i n v e n t o r y at each warehouse i s intended t o p r o t e c t against a maximum demand from a s p e c i f i c group of customers over a l e a d time, l e . , between the time a replenishment  order i s p l a c e d and r e c e i v e d .  I f day-to-day  d i s t r i b u t i o n i s l i m i t e d t o the i n v e n t o r y i n excess of t h i s portion, sub-optimization  i s not l i k e l y t o occur.  l i m i t may change from one day t o the next — upon whether or not a replenishment and,  This  depending  order has been p l a c e d  i f so, the time that w i l l elapse b e f o r e r e c e i p t o f  the order.  To i l l u s t r a t e , c o n s i d e r a s i t u a t i o n i n which  the l e v e l of i n v e n t o r y at a warehouse i s based upon a group of customers with a maximum demand of t e n u n i t s per day. I f i t takes t e n days t o r e c e i v e a replenishment  order from  the p l a n t , d i s t r i b u t i o n from the warehouse on any day before  an order I s p l a c e d should be l i m i t e d to the q u a n t i t y  on hand i n excess of one hundred u n i t s .  If a  replenishment  order has been p l a c e d , however, any q u a n t i t y i n excess o f ten u n i t s m u l t i p l i e d by the remaining should be considered  days of l e a d time  as a v a i l a b l e f o r d i s t r i b u t i o n .  A p e r p e t u a l r e c o r d of i n v e n t o r y a v a i l a b i l i t y and d i s t r i b u t i o n at each warehouse w i l l s i m p l i f y the f o r m u l a t i o n of a day-to-day p h y s i c a l d i s t r i b u t i o n model. Table XXIII i s an example o f the way i n which t h i s i n f o r m a t i o n may be recorded.  156 TABLE XXIII INVENTORY AVAILABILITY AND DISTRIBUTION RECORD PRODUCT: lOD  DATE: June 1 Available  Shipped  Balance On Hand  400  600  100  900  200  100  100  70  130  C  400  200  200  120  280  X  1*000  400  600  80  920  Y  800  300  500  80  720  Warehouse  On Hand  A  1,000  B  To be Retained  The balance on hand a f t e r shipments have been made on June first  are shown i n t h e l a s t column.  The f i g u r e s from t h i s  column may now be t r a n s f e r r e d t o a second copy of the form to r e c o r d inventory  t r a n s a c t i o n s f o r the f o l l o w i n g day*  T h i s has been done i n Table XXIV. Note that the q u a n t i t y  t o be r e t a i n e d at warehouse  B has been reduced t o 50 u n i t s i n Table XXIV. reduction and  This  shows that a replenishment order has been p l a c e d  that the order w i l l be r e c e i v e d at B on June 3*  (Units t o be r e t a i n e d at B on June 2 d i v i d e d by a maximum demand p e r day of f i f t y  units).  I t i s a l s o apparent  from  Table XXIV t h a t a replenishment order has been plaoed f o r warehouse C.  157 TABLE XXIV INVENTORY AVAILABILITY AND DISTRIBUTION RECORD PRODUCT: 10D  DATE: June 2  Ware ho us e  On Hand  To be Retained  Available  A  900  400  500  B  ISO  50  80  C  £80  150  130  X  9£0  400  5£0  Y  7£0  300  420  The  Shipped  Balance On Hand  f i g u r e s i n the a v a i l a b l e column of Table XXIV  may now be used as the c a p a c i t y c o n s t r a i n t s I n a l i n e a r programming model t o determine the minimum cost method of meeting customer orders on June 2* In a d d i t i o n t o product a v a i l a b i l i t y , the model f o r day-to-day p h y s i c a l d i s t r i b u t i o n d e c i s i o n s must customer demands and the s h i p p i n g  inolude  and t r a n s p o r t a t i o n cost  to each customer from a l t e r n a t i v e warehouses. I t i s assumed f o r i l l u s t r a t i o n purposes that customer orders f o r June 2 are as shown i n Table XXV.  158 TABLE XX? CUSTOMER ORDERS Order Quantity  To he D e l i v e r e d by  Gust omer  Location  1.  Adams  Ottawa  30  Wednesday  A.M.  2.  Wilson  Montreal  50  Wednesday  A.M.  3.  Brown  Toronto  140  Wednesday  A.M.  4.  White  Hamilton  100  Thursday  A.M.  5.  Smith  Winnipeg  60  Friday  A.M. ,  6.  Jones  Edmont on  20  Friday  A.M.  Shipping  and t r a n s p o r t a t i o n cost p e r unit of  product between each warehouse and customer i s shown I n Table XXVI.  I t i s assumed that a comparison of the  a l t e r n a t i v e methods of t r a n s p o r t a t i o n t o each customer from each warehouse has been made and that the c o s t s shown represent  t h e minimum cost a l t e r n a t i v e f o r each warehouse-  customer combination -- g i v e n the s i z e o f the orders and the d e l i v e r y requirements. impossible  shipping  route.  The l e t t e r M i n d i c a t e s an  169 TABLE XXVI SHIPPING AND TRANSPORTATION COST (IN DOLLARS PER UNIT OF PRODUCT)  \ v  To  CUSTOMERS  1  2  3  4  5  6  A  .32  .20  .60  .52  .65  M  B  .45  .15  .12  .30  .60  .76  G  .40  .30  .22  .25  M  M  X  .38  .58  .53  .69  .16  .36  y  M.  M  .59  .61  .20  .12  From  The data as o u t l i n e d above may now be t r a n s f e r r e d d i r e o t l y t o a Transportation matrix. i n Table XXVII.  T h i s has been done  The procedure f o r s o l v i n g the Trans-  p o r t a t i o n matrix has a l r e a d y been described' l n the p r e c e d i n g s e c t i o n of t h i s chapter. it  Using t h i s same method,  i s found that the minimum cost s h i p p i n g p a t t e r n f o r  June 2 i s as i n d i c a t e d by the o i r c l e d numbers i n Table XXVII.  160 TABLE XXVII TRANSPORTATION MATRIX  CUSTOMERS  To  1  From \.  2 20  32  ©©  A  45  15  B 40  CO  W  50  12  5  6  Dummy  65  ©  52  M  0 500  (390)  30  60  76  0  ^8oJ)  CO  o  4  3  Available Quantity  30  C  22  (6cT) 38  58  53  80 25  ©  59  X M  M  59  61  . M  30  50  140  100  0 130  16  ©  20  Y  Customer Demand  M  60  35  0 520  (^60) 12  © 20  0 (400)  420  1250  1650  Once again, the. minimum cost s o l u t i o n i s r a t h e r obvious  i n t h i s case through  p o r t a t i o n matrix.,  an i n s p e c t i o n of th« Trans-  I n the p r a c t i c a l s i t u a t i o n ,  however,  the s e l e c t i o n of the optimum w i l l u s u a l l y be complicated by a f a r g r e a t e r number of customer orders than has been  used i n t h i s i l l u s t r a t i o n .  But even then, the Trans-  p o r t a t i o n Method w i l l p r o v i d e the optimum s o l u t i o n i n few simple s t e p s .  CHAPTER. VI SUMMARY AND CONCLUSIONS I. The  SUMMARY  p h y s i c a l d i s t r i b u t i o n concept i s concerned  w i t h the group of i n t e r r e l a t e d processes that are i n v o l v e d i n the p h y s i c a l flow of t r a f f i c  from the source of raw  materials to production  and from p r o d u c t i o n  distribution f a c i l i t i e s  t o customers.  include transportation, materials order-processing  through  These p r o c e s s e s  handling,  warehousing,  and communications.  There i s an i n c r e a s i n g volume of l i t e r a t u r e emphasizing the f a c t that  i t i s the t o t a l oost o f the  p h y s i c a l d i s t r i b u t i o n processes r a t h e r than cost of i n d i v i d u a l processes that must be taken i n t o account i n problems r e l a t e d d i r e o t l y or i n d i r e c t l y t o the p h y s i c a l movement of m a t e r i a l s  and p r o d u c t s .  however, tends t o concentrate  This  literature,  on one or the other o f the  s e v e r a l problems to which the p h y s i c a l d i s t r i b u t i o n concept may be a p p l i e d .  There a l s o tends t o be a l a c k of  a t t e n t i o n i n the area o f procedures t h a t by the f i r m i n the f o r m u l a t i o n  can be f o l l o w e d  and comparison o f p h y s i c a l  distribution alternatives. Chapter two of t h i s t h e s i s attempted t o i d e n t i f y  163 the major a p p l i c a t i o n s of the p h y s i c a l concept and the  distribution  to i s o l a t e those a p p l i c a t i o n s that are  scope of the t r a f f i c manager's sphere of  Chapters three  to f i v e developed the  procedures that may applying  responsibility.  step-by-step  be u s e f u l to the t r a f f i c  manager i n  the p h y s i c a l d i s t r i b u t i o n concept t o  that f a l l w i t h i n h i s j u r i s d i c t i o n a l Maj.or A p p l i c a t i o n s The  decisions  area.  of the P h y s i c a l D i s t r i b u t i o n Concept  scope of the problem to which the  physical  d i s t r i b u t i o n concept should be a p p l i e d tends t o w i t h the time p e r i o d . must be met  out  should be  increase  In day-to-day o p e r a t i o n s ,  demand  of i n v e n t o r i e s that are on hand at  distribution points. l i m i t e d to the  within  The  a p p l i c a t i o n i n t h i s case i s  d e t e r m i n a t i o n of which customer orders  f i l l e d from which d i s t r i b u t i o n p o i n t ,  and  the  methods of t r a n s p o r t a t i o n that should be used between stock p o i n t s and  customers.  Considering  s u c c e s s i v e l y longer planning  the problem over  i n t e r v a l s , however, i t  becomes c l e a r that a l t e r n a t i v e s of p r o g r e s s i v e l y  greater  scope emerge w i t h the e x p i r a t i o n of present c o n s t r a i n t s i n the form of c a p i t a l shortage, c o n t r a c t s commitments.  T y p i c a l l y , the  distribution will  increase  and  other  current  alternatives for physical  i n scope i n the f o l l o w i n g  order  164 as the p l a n n i n g p e r i o d 1.  i s extended f u r t h e r i n t o the  A l t e r n a t i v e u t i l i z a t i o n of e x i s t i n g p h y s i c a l distribution  2.  facilities.  A l t e r n a t i v e systems of p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s w i t h present p r o d u c t i o n and  3.  future:  locations  capacities.  A l t e r n a t i v e systems of p h y s i c a l d i s t r i b u t i o n i n combination w i t h a l t e r n a t i v e s p a t i a l allocations f o r production capacities.  A study of the p h y s i c a l d i s t r i b u t i o n f u n c t i o n , should provide f o r an e v a l u a t i o n  of each o f these groups  of a l t e r n a t i v e s i f the t o t a l b e n e f i t the  that  i s envisaged i n  concept i s to be r e a l i z e d . Since the three groups of a l t e r n a t i v e s l i s t e d  emerge at s u c c e s s i v e be  Intervals  i n the  f u t u r e , the  d i v i d e d i n t o t h r e e separate a n a l y s i s .  exercised,  however, In d e f i n i n g the  a n a l y s i s i n order to avoid d i s t r i b u t i o n planning.  be  f o r each  sub-optimization i n physical  u t i l i z a t i o n o f present  are developed f o r a p e r i o d  f e a s i b l e to introduce  can  S u b - o p t i m i z a t i o n w i l l occur, f o r  example, i f plans f o r the facilities  study  Care must  time p e r i o d  above  a more e f f i c i e n t  distribution facilities.  during  which i t i s  system of  physical  S i m i l a r l y , planned changes i n  165 system f a c i l i t i e s w i l l be sub-optimum i f the time i n t e r v a l that has been used i n the development beyond the p o i n t  of t h i s p l a n  extends  i n time at which a change i n the s p a t i a l  a l l o c a t i o n of p l a n t s Increasing  should be  flexibility  introduced. over time i n the form of  c a p i t a l a v a i l a b i l i t y and freedom from present p o l i c y , contracts  and o t h e r commitments w i l l  successively,  the p o i n t s  p r a c t i c a l to c o n s i d e r changes i n p l a n t  determine,  i n time at which i t becomes  changes  locations.  i n system f a c i l i t i e s  An a n a l y s i s of long-term  a l t e r n a t i v e s w i l l t h e n determine the p o i n t becomes d e s i r a b l e T h i s point  at which i t  t o adopt a change i n p l a n t  locations.  i n time marks the end of the p e r i o d  a l t e r n a t i v e s are l i m i t e d by e x i s t i n g p l a n t hence, d e f i n e s  and  during  locations  which and,  the s h o r t e r - t e r m i n t e r v a l of time over which  a n a l y s i s should be concerned w i t h p o t e n t i a l changes system of p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s .  i n the  S i m i l a r l y , an  a n a l y s i s of changes i n p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s (assuming present p l a n t  locations) w i l l  i n time at which the f i r s t desirable.  change i n system becomes  The p e r i o d p r i o r to t h i s date i s the  i n t e r v a l f o r an a n a l y s i s the present  i d e n t i f y the p o i n t  appropriate  of the a l t e r n a t i v e s f o r u t i l i z i n g  system of p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s .  166 In a d d i t i o n to the need to avoid p r o p e r l y d e f i n e d time p e r i o d s formulation  sub-optimization,  are necessary t o  the  of r e l e v a n t p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s .  P h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s are adequate or inadequate depending upon the volumes of t r a f f i c ,  the  l o c a t i o n of raw m a t e r i a l s , p l a n t s and markets and  the  standards of d e l i v e r y s e r v i c e , or the a l t e r n a t i v e s of these s p e c i f i c a t i o n s . A l t e r n a t i v e s are f e a s i b l e only i f they are w i t h i n the c o n f i n e s of o p e r a t i n g c o n s t r a i n t s , i n c l u d i n g c a p i t a l shortages, commitments, and  the  unexpired  c a p a c i t y and  of f i x e d f a c i l i t i e s ( i f any). requirements and  c o n t r a c t s and  other  other o p e r a t i n g l i m i t a t i o n s  Physical distribution  o p e r a t i n g c o n s t r a i n t s are both subject  change over time and  to  i t i s only when the time p e r i o d i s  c l e a r l y d e f i n e d that these elements of the framework can be  identified. It  i s apparent, t h e r e f o r e , that a study of  p h y s i c a l d i s t r i b u t i o n f u n c t i o n should progress  the  from a long-  term a n a l y s i s to an I n v e s t i g a t i o n of the a l t e r n a t i v e s f o r successively shorter-term period.  i n t e r v a l s of the f u t u r e time  T h i s procedure w i l l a v o i d s u b - o p t i m i z a t i o n  p h y s i c a l d i s t r i b u t i o n planning development of an a p p r o p r i a t e  and w i l l f a c i l i t a t e framework f o r each of  In the the  167 three The  a p p l i c a t i o n s of the p h y s i c a l d i s t r i b u t i o n ooncept.  T r a f f i c Manager's Role The  of the  three  concept.  t r a f f i c manager p l a y s an important r o l e i n each a p p l i c a t i o n s of the p h y s i c a l d i s t r i b u t i o n  His role i s usually advisory,  d e c i s i o n s r e l a t e d to a change i n p l a n t  however, i n l o c a t i o n or a  change i n p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s . decisions  generally  departments, eg.,  a f f e c t operations  i n several functional  marketing, p r o d u c t i o n  cannot, t h e r e f o r e , be p r o p e r l y f u n c t i o n a l department heads.  p a r t i c i p a t i o n of the t r a f f i c ,  and  evaluated Decisions  r e q u i r e top l e v e l d i r e c t i o n and  These  by  finance, any  one  and of  the  of t h i s nature  co-ordination with  the  marketing, p r o d u c t i o n  and  o t h e r i n t e r e s t e d departments. Shorter-term a p p l i c a t i o n s are d e f i n e d  in this  t h e s i s as those In which a l t e r n a t i v e s are l i m i t e d t o u t i l i z a t i o n of e x i s t i n g f a c i l i t i e s .  the  These a p p l i c a t i o n s  range from the day-to-day problem o f d i s t r i b u t i o n t o customers from a v a i l a b l e i n v e n t o r i e s , to the problem of planning  the s h o r t - t e r m a l l o c a t i o n of output among the  firm's plants.  The  day-to-day d e c i s i o n i s e n t i r e l y w i t h i n  the t r a f f i c manager's sphere of r e s p o n s i b i l i t y s i n c e a l t e r n a t i v e s i n t h i s case are l i m i t e d t o the methods f o r shipping  and  transportation —  operations  that  are  traditional traffic The  department r e s p o n s i b i l i t i e s .  output a l l o c a t i o n d e c i s i o n has  t r a d i t i o n a l l y associated responsibility.  been  with the p r o d u c t i o n manager's  I t i s c l e a r , however, that  physical  d i s t r i b u t i o n p r i n c i p l e s should be used i n making t h i s d e c i s i o n t o ensure that the product i s d e l i v e r e d to market at minimum t o t a l c o s t . should be  This decision,  a j o i n t u n d e r t a k i n g by the t r a f f i c  p r o d u c t i o n managers who  therefore, and  out  the  are f a m i l i a r r e s p e c t i v e l y  p h y s i c a l movement and p r o d u c t i o n a l t e r n a t i v e s . be p o i n t e d  the  with  ( I t should  that marketing s p e c i f i c a t i o n s i n the  term are u s u a l l y f i x e d by  longer-term p l a n s and  short-  policy.  Short-term p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s must meet these requirements and  t h e r e i s no danger, t h e r e f o r e ,  marketing a c t i v i t y w i l l be  adversely  a f f e c t e d by  that  the  short-term p r o d u c t i o n a l l o c a t i o n d e c i s i o n ) . Since i t i s only the  short-term a p p l i c a t i o n s  of  the p h y s i c a l d i s t r i b u t i o n concept i n which p h y s i c a l d i s t r i b u t i o n decisions t h i s t h e s i s has  w i l l be made by the  of the p h y s i c a l d i s t r i b u t i o n  applications for t h i s period the  manager,  been l i m i t e d t o the development of a  method of a n a l y s i s f o r two  and  traffic  —  the  output a l l o c a t i o n problem.  day-to-day problem  169 The s o l u t i o n to both of these problems r e q u i r e s an a l l o c a t i o n of l i m i t e d resources among competing demands. In  the day-to-day problem, there are competing customer  orders f o r the l i m i t e d q u a n t i t y of i n v e n t o r y that i s a v a i l a b l e at i n d i v i d u a l d i s t r i b u t i o n warehouses.  In the  output a l l o c a t i o n problem, there are competing ways l n which the l i m i t e d c a p a c i t y of each p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n f a c i l i t y can be u t i l i z e d .  The  limited  resources, competing demands c h a r a c t e r i s t i c s p l a c e the s o l u t i o n t o these problems w i t h i n the scope of the l i n e a r programming technique. the  T h i s t h e s i s attempts t o set down  step-by-step procedures that can be f o l l o w e d i n  developing the p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s i n t o a form s u i t a b l e f o r s o l u t i o n through t h i s t e c h n i q u e . The Day-to-day Problem In  the day-to-day problem, customer o r d e r s must be  s a t i s f i e d out of i n v e n t o r i e s that are on hand at f i n a l d i s t r i b u t i o n warehouses.  The o b j e c t i v e of a n a l y s i s i s t o  determine which customer orders should be f i l l e d  from  which warehouse i n order t o minimize the t o t a l cost of filling the  the day's o r d e r s .  S h i p p i n g and t r a n s p o r t a t i o n i s  only a d d i t i o n a l p h y s i o a l d i s t r i b u t i o n c o s t , once the  product becomes a v a i l a b l e f o r d i s t r i b u t i o n at the f i n a l  170 distribution points. day  The optimum s o l u t i o n t o the day-to-  problem, t h e r e f o r e , w i l l be the one that minimizes the  t o t a l of these c o s t s f o r the day's The a list and  orders.  l i n e a r programming model i n t h i s case  of the customers from whom orders  the s i z e o f t h e i r r e s p e c t i v e  orders;  requires  have been r e c e i v e d a list  of the  d i s t r i b u t i o n warehouses and the u n i t s of product that are a v a i l a b l e f o r d i s t r i b u t i o n at each o f these p o i n t s ; and the minimum s h i p p i n g  and t r a n s p o r t a t i o n cost per u n i t of  product to each customer from a l t e r n a t i v e d i s t r i b u t i o n points. The  list  of customers and t h e i r order  quantities  can be taken d i r e c t l y from the day's s a l e s o r d e r s , o r from shipping r e q u i s i t i o n s r e c e i v e d from the s a l e s department.  The u n i t s of product t h a t are a v a i l a b l e f o r  d i s t r i b u t i o n at each warehouse can be c a l c u l a t e d from warehouse inventory at  records  —  the a v a i l a b l e  inventory  a warehouse being the d i f f e r e n c e between the q u a n t i t y  on hand and the q u a n t i t y that i s expected t o be r e q u i r e d over the p e r i o d p r i o r t o r e c e i p t of a replenishment  order  to s a t i s f y a predetermined maximum reasonable demand from customers that are normally served The  from that  point.  minimum s h i p p i n g and t r a n s p o r t a t i o n c o s t s p e r  171 unit  of product w i l l have t o he e s t a b l i s h e d through a  comparison of the a l t e r n a t i v e s o f these processes f o r each of the f e a s i b l e warehouse-customer combinations. house-customer combination i s f e a s i b l e i f there  A wareis a suit-  able method or s u i t a b l e methods of t r a n s p o r t a t i o n that s a t i s f y d e l i v e r y s e r v i c e s p e c i f i c a t i o n s . The d e l i v e r y s e r v i c e f o r each order may  be  will  required  s p e c i f i e d i n the  shipping r e q u i s i t i o n , or by the marketing department.  In  other  of  i n s t a n c e s , the  a n a l y s t may  s e r v i c e that has been p r o v i d e d  assume that the l e v e l  i n the past  i s adequate.  Having e s t a b l i s h e d the minimum per u n i t cost shipping  and  t r a n s p o r t a t i o n between each of the f e a s i b l e  warehouse-customer combinations, t h i s i n f o r m a t i o n w i t h i n d i v i d u a l customer orders inventory  for  and the  quantity  together of  that i s a v a i l a b l e f o r d i s t r i b u t i o n at each ware-  house, oan be  Inserted  i n a l i n e a r programming m a t r i x .  optimum method of p h y s i c a l d i s t r i b u t i o n can now e s t a b l i s h e d from t h i s matrix by a p p l y i n g the  be  linear  programming method of s o l u t i o n commonly r e f e r r e d to as T r a n s p o r t a t i o n Method.  The  T h i s method i s d e s c r i b e d  the  in detail  i n Chapter V. The  Output A l l o c a t i o n Problem In the  output a l l o c a t i o n problem, the  objective  of  172 a n a l y s i s i s t o determine the optimum a l l o c a t i o n o f f o r e c a s t short-term  demand among the f i r m ' s p l a n t s .  The optimum i s  the a l t e r n a t i v e t h a t w i l l minimize the t o t a l of production  short-term  and p h y s i c a l d i s t r i b u t i o n c o s t s .  The  l i n e a r programming model f o r t h i s problem  r e q u i r e s a f o r e c a s t of product demand at each o f the d i s t r i b u t i o n warehouses; a d e f i n i t i o n o f the p r o d u c t i o n c a p a c i t y o f each p l a n t ; and an estimate of the t o t a l u n i t v a r i a b l e cost that would be i n c u r r e d i n the manufacture and p h y s i c a l d i s t r i b u t i o n of each product t o each d i s t r i b u t i o n warehouse and through each of the routes  that  t r a f f i c may take through the p r o d u c t i o n - d i s t r i b u t i o n system. In f o r e c a s t i n g the u n i t s of product that w i l l pass through each warehouse d u r i n g the p e r i o d , the f i r s t i s to define  the market areas that w i l l be served  each p o i n t .  T h i s can be accomplished i n two s t e p s .  first  step i s t o i d e n t i f y the g e o g r a p h i c a l  t o t a l market that can be served warehouse.  step  from The  segments o f the  from each d i s t r i b u t i o n  The procedure i s t o r e l a t e d e l i v e r y s e r v i c e  requirements i n the v a r i o u s  customer areas w i t h  transpor-  t a t i o n a v a i l a b i l i t y to determine whether or not i t i s f e a s i b l e t o serve  a s p e c i f i c customer l o c a t i o n from a  173 g i v e n warehouse.  The  seoond step i s t o reduce the s i z e  of  the market a r e a that can he served from a warehouse to i t s h a n d l i n g c a p a c i t y by e l i m i n a t i n g the demand of those customers t h a t can be served from an a l t e r n a t i v e warehouse at a lower  s h i p p i n g and t r a n s p o r t a t i o n c o s t .  S a l e s f o r e c a s t s and d e f i n e d d e l i v e r y standards necessary  i n the above procedures.  Since the  department I s l i k e l y to be f a m i l i a r w i t h the  are  marketing territorial  breakdown of the t o t a l s a l e s f o r e c a s t , t h i s department should be c a l l e d upon t o a l l o c a t e f o r e c a s t demand i n u n i t s of product  among g e o g r a p h i c a l areas as d e f i n e d by  t r a f f i c manager.  D e l i v e r y s e r v i c e s p e c i f i c a t i o n s f o r the  v a r i o u s customer areas may marketing  the  be d e f i n e d e x p l i c i t l y by  department, or may  have t o be developed  t r a f f i c manager through a review of p o l i c y , p l a n s or h i s t o r i c a l s e r v i c e r e c o r d s .  The  by  the the  longer-term  delivery  standards used i n a n a l y s i s should not be h i g h e r than that w i l l be provided i n the longer-term and  those  should not  be  lower than i n the p a s t , u n l e s s approval has been obtained from the marketing  department.  Having e s t a b l i s h e d the f o r e c a s t of demand at each d i s t r i b u t i o n warehouse, the next  step i n a n a l y s i s i s t o  define the output c a p a c i t y of each of the f i r m ' s p l a n t s  174 over the short-term  period.  The output of a plant  . t h i s p e r i o d i s l i m i t e d by t e c h n i c a l c o n s i d e r a t i o n s  during i n the  u t i l i z a t i o n of f a c i l i t i e s , p o l i c y , o r g a n i z a t i o n a l problems and  other c o n s t r a i n t s t h a t c o n t r i b u t e toward  inflexibility.  The p r o d u c t i o n  production  manager should  examine  these c o n s t r a i n t s w i t h a view t o d e f i n i n g the minimum and maximum output t h a t defined i n t e r v a l .  i s f e a s i b l e f o r each p l a n t over the The maximum output f i g u r e s w i l l be used  i n t h e l i n e a r programming model.  Minimum output f i g u r e s  w i l l not be used d i r e c t l y i n the model but r a t h e r as a check on the s o l u t i o n t o ensure t h a t the output that i s o a l l e d f o r at each p l a n t i s not below the f e a s i b l e minimum. When two or more o f the products that are manufactured at a p l a n t pass through one or more of the same processes,  the mix of output that w i l l absorb  capacity  cannot be predetermined and i t becomes necessary t o express c a p a c i t y i n terms o f man-hours, machine-hours or other common measurement. operations  I n t h i s case, the v a r i o u s  i n t h e p l a n t should  be examined to determine the  common process that l i m i t s t o t a l output. p r o c e s s i s a manual o p e r a t i o n ,  manufacturing  plant  I f this  bottleneck  c a p a c i t y should be  d e f i n e d i n terms o f a v a i l a b l e man-hours i n t h i s process f o r the p e r i o d .  S i m i l a r l y , i f the b o t t l e n e c k  machine o p e r a t i o n ,  process i s a  t o t a l a v a i l a b l e hours i n t h i s p r o c e s s  175 for  the p e r i o d would he the a p p r o p r i a t e  ment.  The  production  manager should  c a p a c i t y measure-  also define  the  p o r t i o n of bottleneck: c a p a c i t y t h a t w i l l be absorbed i n the manufacture of a u n i t of each of the f i r m ' s products so that the combinations of product volumes that absorb t o t a l c a p a c i t y at the p l a n t  can be  will  identified.  Given the demand f o r e c a s t f o r each warehouse, the  and  output c a p a c i t y of each p l a n t , i t remains t o complete  the data f o r the  l i n e a r programming model by  the t o t a l per unit v a r i a b l e cost  estimating  of each product at each  of the d i s t r i b u t i o n warehouses and through each of routes that t r a f f i c  may  take through the  the  production-  p h y s i c a l d i s t r i b u t i o n system. A traffic of raw  materials  route  c o n s i s t s of a source o r sources  f o r the, product, a p l a n t at which the  product can be manufactured and l i n k e d together The  first  by  one  a d i s t r i b u t i o n warehouse,  or more methods of t r a n s p o r t a t i o n .  step i s to d e f i n e the f e a s i b l e t r a f f i c  by determining whether or not there  is a suitable  routes and  a v a i l a b l e method of t r a n s p o r t a t i o n between each source raw  materials  and  each p l a n t , and between each p l a n t  each d i s t r i b u t i o n warehouse. i n v e s t i g a t i o n can be  The  r e s u l t of  this  shown i n a flow diagram.  of  and  176 The second step  i s t o i d e n t i f y the v a r i a b l e cost  of each of the p r o d u c t i o n  and p h y s i c a l d i s t r i b u t i o n  processes and the key parameters that w i l l permit a l i n k i n g of the i n d i v i d u a l process c o s t s i n t o t o t a l cost*  The u n i t v a r i a b l e cost f o r a route w i l l  the purchase p r i c e of raw m a t e r i a l s  route  include  used i n the produot,  the cost of s h i p p i n g and t r a n s p o r t a t i o n between the source of raw m a t e r i a l s  and the p l a n t , the cost of  manufacturing, the cost of s h i p p i n g  and t r a n s p o r t a t i o n  between the p l a n t and . d i s t r i b u t i o n warehouse, the cost of c a r r y i n g raw m a t e r i a l s and f i n i s h e d product  inventories  at the p l a n t , the cost of c a r r y i n g product i n v e n t o r y at the warehouse and the cost  of o r d e r - p r o c e s s i n g  and  communication procedures. Schedules f o r each o f these c o s t s and the procedures t o be f o l l o w e d  i n estimating  and r e l a t i n g  i n d i v i d u a l process c o s t s i n t o t o t a l route described  c o s t s are  i n d e t a i l i n Chapter IV.  When there are a l t e r n a t i v e s f o r t r a n s p o r t a t i o n between the source of raw m a t e r i a l s  and the p l a n t or  between the p l a n t and warehouse p o r t i o n s of a route, the t o t a l v a r i a b l e cost that would be i n c u r r e d w i t h each method of t r a n s p o r t a t i o n must be developed.  A comparison  of the t o t a l v a r i a b l e c o s t s a s s o c i a t e d w i t h a l t e r n a t i v e  177 methods of t r a n s p o r t a t i o n must then be made i n order  to  i d e n t i f y the a l t e r n a t i v e that o f f e r s minimum per u n i t product cost f o r the one  route.  T h i s cost f i g u r e w i l l be  the  that i s used i n the l i n e a r programming model'. Having e s t a b l i s h e d the minimum v a r i a b l e cost  u n i t f o r each product and traffic  routes,  f o r each of the f e a s i b l e  t h i s information,  together with  the  demand at each d i s t r i b u t i o n warehouse; the c a p a c i t y each p l a n t and  per  the c a p a c i t y  that w i l l be  of  absorbed at  each plant by a u n i t of each product, should be  inserted  i n a l i n e a r programming matrix of the type that i s commonly r e f e r r e d t o as the Simplex M a t r i x . cost s o l u t i o n to the p r o d u c t i o n determined by matrix.  The  minimum  a l l o c a t i o n problem can  be  a p p l y i n g p r e s c r i b e d Simplex r u l e s to t h i s  I t i s g e n e r a l l y i m p r a c t i c a l , however, to.attempt  a s o l u t i o n through hand c a l c u l a t i o n because of the volume of work that of the  i s involved i n applying  these r u l e s .  Many  l a r g e r computers have been programmed f o r the  Simplex and t h i s i s the p r e f e r r e d method of s o l u t i o n when t h i s equipment i s a v a i l a b l e . In c e r t a i n circumstances, however, the matrix can be for  Simplex  transformed i n t o a matrix that i s s u i t a b l e  s o l u t i o n through the r e l a t i v e l y simple  Transporta-  178 t i o n Method.  The p a r t i c u l a r circumstances i n which t h i s  transformation  i s acceptable  procedure to be f o l l o w e d a Transportation Matrix V of t h i s  i s described  from a Simplex t o  i n d e t a i l i n Chapter  CONCLUSIONS  p h y s i c a l d i s t r i b u t i o n concept emphasizes the  interrelationship processing,  i n converting  thesis. II.  The  and the step-by-step  between t r a n s p o r t a t i o n , handling,  order-  warehousing and the other p r o c e s s e s that a r e  i n v o l v e d i n the p h y s i c a l flow  of t r a f f i c from the source  of raw m a t e r i a l s t o p l a n t s and from p l a n t s through distribution f a c i l i t i e s  t o customers.  The essence of the  concept i s that i t i s the t o t a l cost of the s e v e r a l p r o c e s s e s r a t h e r than the cost of i n d i v i d u a l  processes  that should be taken i n t o account i n d e c i s i o n s that are related  d i r e c t l y or i n d i r e c t l y t o the p h y s i c a l movement of  m a t e r i a l s and products. (  The b u s i n e s s d e c i s i o n s i n which p h y s i c a l  d i s t r i b u t i o n cost i s an important element i n c l u d e the l o n g term s p a t i a l a l l o c a t i o n o f p r o d u c t i o n intermediate-term  f a c i l i t i e s ; the  changes i n the system o f p h y s i c a l  distribution facilities; e x i s t i n g production  the short-term  u t i l i z a t i o n of  and p h y s i c a l d i s t r i b u t i o n  facilities;  179 and  the day-to-day d i s t r i b u t i o n of a v a i l a b l e output. In making these d e c i s i o n s , i t i s important t o  recognize  that p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s  (except  day-to-day a l t e r n a t i v e s ) are u s u a l l y i n t e r r e l a t e d w i t h a l t e r n a t i v e s i n one or more of the purchasing, and marketing f u n c t i o n s o f the e n t e r p r i s e .  production  This  inter-  r e l a t i o n s h i p i s not s u r p r i s i n g s i n c e p h y s i c a l d i s t r i b u t i o n i s the connecting  l i n k between p u r c h a s i n g and p r o d u c t i o n  and between p r o d u c t i o n  and marketing o p e r a t i o n s .  of raw m a t e r i a l s  at a p l a n t , f o r example, i n c l u d e s  input  the p r i c e of raw m a t e r i a l s  as w e l l as the cost of p h y s i c a l  d i s t r i b u t i o n from t h e i r source t o the p l a n t . there  The cost  Hence, when  are a l t e r n a t i v e sources of raw m a t e r i a l s , the  purchase d e c i s i o n and the p h y s i c a l d i s t r i b u t i o n d e c i s i o n cannot be made independently. product at a d i s t r i b u t i o n point  S i m i l a r l y , the cost o f the i n c l u d e s the cost  of the  manufactured product at a p l a n t as w e l l as the cost of p h y s i c a l d i s t r i b u t i o n from plant t o warehouse.  Hence,  when d i s t r i b u t i o n warehouses can r e c e i v e the product from a l t e r n a t i v e p l a n t s and when f u t u r e demand i s not expected t o absorb t o t a l p r o d u c t i o n  c a p a c i t y , there must be an  i n t e g r a t i o n o f the d e c i s i o n s that w i l l govern the r a t e of output at each o f the f i r m ' s p l a n t s and the methods of  180 p h y s i c a l d i s t r i b u t i o n between p l a n t s and d i s t r i b u t i o n warehouses. Considered sufficient  i n the longer-term, there w i l l be  c a p i t a l and o p e r a t i n g f l e x i b i l i t y to introduce  changes i n the system of p h y s i c a l d i s t r i b u t i o n  facilities,  some of which w i l l e i t h e r extend the g e o g r a p h i c a l t e r r i t o r y that the f i r m w i l l be able t o accommodate, i n c r e a s e the e f f i c i e n c y i n terms of cost or d e l i v e r y  service  with which the e x i s t i n g markets can be served or change the r e l a t i v e e f f i c i e n c y with which the product  can be d e l i v e r e d  to s p e c i f i c segments of the present market. words, marketing  In other  i m p l i c a t i o n s are a s s o c i a t e d w i t h p h y s i c a l  d i s t r i b u t i o n a l t e r n a t i v e s and d e c i s i o n s i n the .two areas are t h e r e f o r e interdependent.  In the v e r y  long-term,  f l e x i b i l i t y w i l l be s u f f i c i e n t  to permit the f i r m t o  c o n s i d e r a r e l o c a t i o n of p r o d u c t i o n c a p a c i t i e s t o g e t h e r with a change i n the system of p h y s i c a l d i s t r i b u t i o n .  It  i s imperative, of course, that each of the a l t e r n a t i v e combinations  of markets that are a v a i l a b l e t o the f i r m i n  the very long-term be e v a l u a t e d i n the l i g h t d e l i v e r e d product  cost through a l t e r n a t i v e  of t o t a l  spatial  a l l o c a t i o n s of p r o d u c t i o n c a p a c i t i e s and a l t e r n a t i v e systems of p h y s i c a l d i s t r i b u t i o n  facilities.  181 I n view of these i n t e r r e l a t i o n s h i p s , i t i s c l e a r that p h y s i c a l d i s t r i b u t i o n a n a l y s i s , i e . , the and  formulation  comparison o f p h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s , i s  u s u a l l y only a part of the physioal  o v e r a l l a n a l y s i s i n which  d i s t r i b u t i o n a l t e r n a t i v e s are  integrated  with  a l t e r n a t i v e s i n other areas of o p e r a t i o n s to determine the  optimum course of a c t i o n f o r the  i s the  firm.  An  exception  day-to-day problem of s a t i s f y i n g customer orders  from output that  i s a v a i l a b l e at f i n a l  d i s t r i b u t i o n points*  P h y s i c a l d i s t r i b u t i o n a l t e r n a t i v e s In t h i s case must s a t i s f y i n f l e x i b l e marketing requirements (given orders and  delivery service).  operations are u n a f f e c t e d customer p h y s i c a l movement  by the  day-to-day warehouse t o  i n physical distribution  sphere of r e s p o n s i b i l i t y that i s  u s u a l l y assigned to the t r a f f i c however, that  production  decisions.  Day-to-day d e c i s i o n s appear t o f a l l w i t h i n the  P u r c h a s i n g and  customer  manager.  longer-term d e c i s i o n s  It i s c l e a r ,  i n which i t i s  necessary t o i n t e g r a t e a l t e r n a t i v e s f o r p h y s i c a l  distri-  b u t i o n w i t h a l t e r n a t i v e s i n other areas of o p e r a t i o n s , beyond the  soope of the d e c i s i o n s  t r a f f i c manager of the few  firm's  that  can be made by  t y p i c a l organization  structure.  are the A  have appointed p h y s i c a l d i s t r i b u t i o n managers.  T h i s t i t l e , however, appears to he f u n c t i o n a l l y o r i e n t e d if  i t i s intended t h a t these o f f i c e r s are to i n t e g r a t e  marketing, p r o d u c t i o n and p h y s i c a l d i s t r i b u t i o n alternatives. I n the author's o p i n i o n , p h y s i c a l d i s t r i b u t i o n d e c i s i o n s f o r the longer-term,  i e . , changes i n the  of p h y s i c a l d i s t r i b u t i o n f a c i l i t i e s and i n the  system  spatial  a l l o c a t i o n of p r o d u c t i o n c a p a c i t i e s , i s an i n t e g r a l p a r t of the development of o v e r a l l corporate p l a n s .  The  corporate p l a n n i n g f u n c t i o n i s u s u a l l y undertaken by a p l a n n i n g u n i t that r e p o r t s d i r e c t l y to the  chief  e x e c u t i v e , or by a r e s e a r c h and development It would seem t h a t t h i s i s where the  department.  interrelationship  between the longer-term p h y s i c a l d i s t r i b u t i o n  alternatives  and other o p e r a t i o n s can be p r o p e r l y e v a l u a t e d .  The  role  of the t r a f f i c department and other o p e r a t i n g departments should be t o c o n t r i b u t e t o the o v e r a l l p l a n n i n g process  by  p r o v i d i n g cost and other i n f o r m a t i o n r e l a t e d t o alternatives within t h e i r respective f i e l d s . While the t r a f f i c manager's r o l e i s a d v i s o r y i n p l a n n i n g f o r the longer-term,  i t would seem that t h i s  o f f i c e r i s i n a p o s i t i o n to d i r e c t and a n a l y s i s that i s necessary  co-ordinate  the  f o r short-term operating plans  183 i n which m a t e r i a l s and product d i s t r i b u t i o n i s i n v o l v e d * Marketing requirements d u r i n g t h i s p e r i o d  are  usually  f i x e d s i n c e the f i r m w i l l have committed i t s e l f , longer-term plans and a c e r t a i n standard markets.  p o l i c y , to c e r t a i n markets and  and d i s t r i b u t i o n f a c i l i t i e s are  f i x e d during t h i s p e r i o d , but  achieved  to  of s e r v i c e w i t h i n each of these  Production  flexibility  through  i n the mix  there w i l l u s u a l l y be some  and the  at each p l a n t , and  also  r a t e of output that can  be  i n the methods of p h y s i c a l  d i s t r i b u t i o n that can be employed w i t h g i v e n  facilities.  Marketing requirements, the l o c a t i o n and p r i c e of raw  m a t e r i a l s , and  the cost and  at each p l a n t can be  f l e x i b i l i t y of  production  d e f i n e d f o r a n a l y s i s purposes by  marketing, p u r c h a s i n g and p r o d u c t i o n framework w i l l permit the  traffic  a l t e r n a t i v e s f o r short-term  departments.  flow through  p r o d u c t i o n - d i s t r i b u t i o n system; t o determine the cost of p r o d u c t i o n  and  This  manager to develop  traffic  the  the  the total  p h y s i c a l d i s t r i b u t i o n f o r each of  the flow a l t e r n a t i v e s ; and t o s e l e c t the a l t e r n a t i v e t h a t o f f e r s minimum t o t a l d e l i v e r e d product cost f o r the period. the  The' p a t t e r n of t r a f f i c  flow that i s i m p l i c i t  s o l u t i o n to t h i s problem w i l l  from which m a t e r i a l s  i n d i c a t e the  are to be purchased and  in  locations  the mix  and  184 volume of t r a f f i c  that each of the p r o d u c t i o n  d i s t r i b u t i o n f a c i l i t i e s w i l l be The  physical  r e q u i r e d t o accommodate.  s o l u t i o n , then, w i l l p r o v i d e the b a s i s f o r d e t a i l e d  operating and  and  plans w i t h i n each of the p u r c h a s i n g ,  p h y s i c a l d i s t r i b u t i o n areas of b u s i n e s s Mathematical programming i n general  production  operations. and  linear  programming i n p a r t i c u l a r appear t o have promise as methods i n which the  the  complex i n t e r r e l a t i o n s h i p s that  are  usually associated with physical d i s t r i b u t i o n applications can be r e s o l v e d .  The  problems f o r which mathematical  programming i s i d e a l l y s u i t e d are those i n which there  are  s e v e r a l p o s s i b l e courses of a c t i o n ; c e r t a i n c o n d i t i o n s that must be met must not be  (demands); and  c e r t a i n l i m i t a t i o n s that  exceeded ( c o n s t r a i n t s ) .  Physical distribution  a p p l i c a t i o n s f a l l w i t h i n t h i s group of problems. short-term p l a n n i n g  problem, f o r example, there  s e v e r a l ways i n which f u t u r e demand may the  f i r m ' s p l a n t s , but  and  the  are  a l l o c a t e d among  a l t e r n a t i v e a l l o c a t i o n s must  s a t i s f y warehouse demands and of p r o d u c t i o n  be  In  must not  exceed the  capacity  physical distribution f a c i l i t i e s .  The  advantages of the mathematical programming technique that  i t r e q u i r e s a mathematical f o r m u l a t i o n  of the  and,  hence, r e q u i r e s an organized procedure f o r the  are  problem  185 formulation  of a l t e r n a t i v e s ; i t p e r m i t s a l l of  q u a n t i f i a b l e deciands and  constraints  the  that are r e l e v a n t  the problem to be taken i n t o account; and  i t provides  best s o l u t i o n out  solutions  of the  through a simple and  several possible  to the  a d e f i n i t e routine.  I n view of these imposing advantages and  the  fact  that the c h a r a c t e r i s t i c s of p h y s i c a l d i s t r i b u t i o n applications place  these problems w i t h i n the  technique, i t i s s u r p r i s i n g that  few  of the  realm of t h i s proponents of  the p h y s i c a l d i s t r i b u t i o n concept have emphasized  the  p o t e n t i a l of mathematical programming i n p h y s i c a l  distri-  bution  analyses.  i n t o the  There i s a need f o r f u r t h e r  development of l i n e a r programming,  programming and  research non-linear  other mathematical models as the t o o l s f o r  physical d i s t r i b u t i o n analysis. T h i s t h e s i s has the  not  dealt  obvious problems that are  i n d e t a i l w i t h some of  l i k e l y t o a r i s e i n the  development of data f o r the p l a n n i n g model. handling c o s t s and  order-processing  and  c o s t s per order, f o r example, are not a v a i l a b l e from accounting and maintained by the  firm —  t i v e s t o present methods.  The  l i k e l y t o be  p a r t i c u l a r l y f o r the be  unit  communications  other r e c o r d s that  I t may  per  necessary,  readily  are  alternatherefore,  186 t o employ work study procedures, r e g r e s s i o n a n a l y s i s , engineering  s t u d i e s or other methods to develop s u i t a b l e  estimates of i n d i v i d u a l p r o c e s s c o s t s .  A second  short-  coming of t h i s t h e s i s i s that the assumed r e l a t i o n s h i p s between p h y s i c a l d i s t r i b u t i o n p r o c e s s e s that have been used i n the  i l l u s t r a t e d example may  Handling c o s t s , f o r example, may congestion  at the  stock point  be  vary  overly s i m p l i f i e d . with the degree of  as w e l l as w i t h the method  of t r a n s p o r t a t i o n that i s used.  Order-processing  communication c o s t s , which i n c l u d e the cost an order through the  system, may  of  and  expediting  v a r y with the point  from  which m a t e r i a l s are r e c e i v e d or w i t h the method of t r a n s p o r t a t i o n that  i s used.  I t i s e s s e n t i a l , of course,  that a l l of the r e l a t i o n s h i p s between p h y s i c a l d i s t r i b u t i o n processes be i d e n t i f i e d i n order t o produce r e l i a b l e estimates of route  costs.  In p r a c t i c e , the p l a n n i n g complicated  by  problem may  be  s e v e r a l f a c t o r s that have not been taken  i n t o account i n the h y p o t h e t i c a l problem that has been described  i n this thesis.  The  m a t e r i a l s , f o r example, may  purchase p r i c e of  v a r y with order  p o s s i b l e to combine v a r i o u s m a t e r i a l s shipping purposes; i t may  s i z e ; i t may  or products f o r  be p o s s i b l e t o achieve  output at p l a n t s through the use  raw  higher  of overtime; e t c .  be  187 A procedure f o r the alternative  systems of p h y s i c a l  and  alternative  was  beyond the  of the  f o r m u l a t i o n and  comparison of  distribution facilities  s p a t i a l a l l o c a t i o n s f o r plant scope of t h i s t h e s i s .  These  capacities applications  p h y s i c a l d i s t r i b u t i o n concept have been d i s c u s s e d  i n some of the p u b l i s h e d l i t e r a t u r e , most of which dwelt upon the  development of a l t e r n a t i v e s w i t h i n  framework of given marketing s p e c i f i c a t i o n s . be and  emphasized however, that the  the markets that  standards of s e r v i c e  with alternative f a c i l i t i e s and  that  can be  systems of p h y s i c a l  with alternative  production capacities.  w i l l be  can be  served vary  distribution for  I f marketing s p e c i f i c a t i o n s  are  that  contribution  an o p p o r t u n i t y t o serve a opportunity  from e x i s t i n g markets,  overlooked. A review of the  physical  I t should  o f f e r e d may  more p r o f i t a b l e combination of markets, or an net  the  spatial allocations  predefined, i t i s possible  to improve the  has  l i t e r a t u r e dealing  d i s t r i b u t i o n concept suggests the  additional  case h i s t o r i e s of s u c c e s s f u l  These case s t u d i e s permit the 1.  should be  with  the  need f o r  applications*  s u f f i c i e n t l y detailed  to  readers to e v a l u a t e : The  f a c t o r s that  have been taken i n t o account  188 i n e s t a b l i s h i n g the  objectives  and  the  frame-  work f o r a n a l y s e s . Ei  The  procedures that have been used i n the  development of p h y s i c a l d i s t r i b u t i o n alternatives. 3.  The  procedures that have been employed i n  e s t a b l i s h i n g the cost  i n t e r r e l a t i o n s h i p between the  of i n d i v i d u a l p h y s i c a l d i s t r i b u t i o n  processes. 4.  The  p r o v i s i o n that has  been made f o r r e l a t i n g  physical d i s t r i b u t i o n a l t e r n a t i v e s with a l t e r n a t i v e s i n other areas of 5.  The  method that has  the  optimum a l t e r n a t i v e .  In c o n c l u s i o n ,  operations.  been used i n s e l e c t i n g  i t appears that t h e r e i s a need at  t h i s time f o r a b r i d g e between p h y s i c a l d i s t r i b u t i o n theory and studies  physical distribution practice.  More  are necessary before management w i l l be  empirical able  to  grasp the e s s e n t i a l s of p h y s i c a l d i s t r i b u t i o n a n a l y s i s the procedures f o r a n a l y s i s that w i l l i n d i v i d u a l requirements.  satisfy their  and  189  BIBLIOGRAPHY 1.  BOOKS Aminer, Dean S. M a t e r i a l s Management. Homewood, I l l i n o i s : R i c h a r d D. Irwin Inc., 1962. Baumol, W i l l i a m J . Economic Theory and Operations A n a l y s i s . Englewood C l i f f s , New J e r s e y : P r e n t i c e H a l l Inc., 1961. Bock, Robert H., and W i l l i a m K. H o l s t e i n . Production P l a n n i n g and C o n t r o l : Text and Readings. Columbus, Ohio: Charles E . M e r r i l l Books Inc., 1963. Bowman, Edward H., and Robert B. F e t t e r . A n a l y s i s f o r P r o d u c t i o n Management. Homewood, I l l i n o i s : R i c h a r d D. I r w i n Inc., 1957* Brown, R.G. S t a t i s t i c a l F o r e c a s t i n g f o r Inventory Control. New York: McGraw-Hill Book Company Inc., 1959. Charnes, A., W.W. Cooper, and A. Henderson. An I n t r o d u c t i o n t o L i n e a r Programming. New York: John Wiley and Sons Inc., 1953. Churchman, C. West, R u s s e l l L. A c k o f f , and Leonard E . Arnoff. I n t r o d u c t i o n t o Operations Research. New York: John Wiley and Sons Inc., 1957. Dorfman, R., P.A. Samuelson, and R.M* Solow. Linear Programming and Economic Analysis.' New York: McGraw-Hill Book Company Inc., 1958. F r e d e r i c k , John F. Using P u b l i c Warehouses. P h i l a d e l p h i a : C h i l t o n Company Inc., 1957. Greenhut, M e l v i n L. P l a n t L o c a t i o n i n Theory and i n Practice. Chapel H i l l , North C a r o l i n a : The U n i v e r s i t y of North C a r o l i n a P r e s s , 1956. H o l t , Charles C., et a l . P l a n n i n g P r o d u c t i o n , I n v e n t o r i e s . and Work F o r c e . Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l l Inc., 1960.  190 I s a r d , Walter. L o c a t i o n and Space-Economy. John Wiley and Sons Inc., 1956.  New  York:  Lewis, Howard T., and James W. C u l l i t o n . The Role of Air Freight i n Physical Distribution. Boston: The A l p i n e P r e s s Inc., 1956. Magee, John F. P r o d u c t i o n P l a n n i n g and Inventory C o n t r o l . - New York: McGraw-Hill Book Company Inc., 1958. R e i n f e l d , V., and W i l l i a m R. V o g e l . Mathematical Programming. Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l l Inc., 1958. S a s i e n i , Maurice, A r t h u r Yaspan, and Lawrence Operations Research-Methods and Problems. New York: John Wiley and Sons Inc., 1959.  Friedman.  Smykay, Edward ¥., Donald J . Bowersox, and Frank Mossman. P h y s i c a l D i s t r i b u t i o n Management. New York: The M a c M i l l a n Company, 1961.  H.  Sord, Burnard H., and Glenn A. f/elsch. Business Budgeting. New York: C o n t r o l l e r s I n s t i t u t e Research Foundation, 1958. T a f f , C h a r l e s A., T r a f f i c Management P r i n c i p l e s and P r a c t i c e s . . Homewood, I l l i n o i s : R i c h a r d D. I r w i n Inc., 1959. Y a z s o n y i , Andrew. and Industry* 1958.  S c i e n t i f i c Programming In B u s i n e s s New York: John Wiley and Sons Inc.,  V i l l e r s , Raymond. Dynamic Management i n I n d u s t r y . Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l l Inc., 1960. Welch, W. E v e r t . Tested S c i e n t i f i c Inventory C o n t r o l . Greenwich, C o n n e c t i c u t : Management P u b l i s h i n g C o r p o r a t i o n , 1956. Whit In j Thomson M. The Theory of Inventory Management. P r i n c e t o n , New J e r s e y : P r i n c e t o n U n i v e r s i t y P r e s s , 1957.  191 2.  PERIODICALS Baer, John W. " P i n p o i n t i n g T r a n s p o r t ' s Hidden Costs," D i s t r i b u t i o n Age, LIX, No. 7 ( J u l y , 1960), pp. 36, 37 and 70.. Baumol, W i l l i a m J . , and P h i l i p Wolfe. "A Warehouse L o c a t i o n Problem," -Operations Research. V I , 1958, pp. 25S-63. D i l l o n , John D. " G e o g r a p h i c a l D i s t r i b u t i o n of Production i n , M u l t i p l e Plant Operations," Management S c i e n c e , I I , No. 1 (October, 1955), pp. 353-65. . Eneborg, C.G. "How t o P l o t the I d e a l L o c a t i o n f o r a Warehouse,"- Management Methods, X I I I (January* 1958), pp..52-55. F o r r e s t e r , Jay W. " I n d u s t r i a l Dynamics: A Major Breakthrough f o r D e c i s i o n Makers," Harvard B u s i n e s s Review, XXXVI, No. 4 (July-August, 1958), pp. 37-66. Granger, C h a r l e s H. "Best L a i d P l a n s , " (August, 1962), pp. 42-45. Greene, A.W. "The DM, New Man D i s t r i b u t i o n Age, LIX, No. pp. 37-38.  The  Controller.  On I n d u s t r y ' s Top Team," 3 (March, 1960),  Henderson, Alexander, and Robert S c h l a i f e r . "Mathematical Programming, B e t t e r I n f o r m a t i o n f o r B e t t e r D e c i s i o n Making," Harvard Business Review, XXXII, No. 3 (May-June,.. 1954), pp. 117^44. Heskett, J.L. "Ferment i n Marketing's Oldest A r e a , J o u r n a l of Marketing, XXVI, No. 4 (October, 1962), pp. 40-45. n  H o l t , C.C., F. M o d i g l i a n i , and H.A. Simon. "A L i n e a r D e c i s i o n Rule f o r P r o d u c t i o n and Employment Scheduling," Management S c i e n c e , I I , No. 1 (October, 1955), pp. 1-30.  192 "Keys t o Warehouse S e l e c t i o n , " D i s t r i b u t i o n Age, IX, No. 2 (February, 1961), pp. 30-31. L a n d i s , Eugene. " D i s t r i b u t i o n Management. How t o Set Up Your Department," D i s t r i b u t i o n Age. LX, No. 11 (November, 1961), pp. 34-36. Lazer, W i l l i a m . " D i s t r i b u t i o n and M a r k e t i n g Mix," T r a n s p o r t a t i o n and D i s t r i b u t i o n Management. I I , No. 12 (December, 1962), pp. 12-17. Magee, John F. "Guides t o Inventory P o l i c y , " Harvard Business Review, XXXIV, No. 1 (January-February, 1956), pp. 49-60; XXXIV, No. 2 ( M a r c h - A p r i l , 1956), pp. 103-16. . "The l o g i s t l o s of D i s t r i b u t i o n , " Harvard Business Review. XXXVIII, No. 4 (July-^ August, 1960), pp. 89-101. "Mathematics i n Management," P l a n t A d m i n i s t r a t i o n and E n g i n e e r i n g , XXII* No. 11 (November, 1962), pp. 53-72. M o d i g l i a n i , F., and F.E. Hohn. "Planning over Time, w i t h Some C o n c l u s i o n s About the Nature of the E x p e c t a t i o n and P l a n n i n g H o r i z o n , " Econometrica. XXIII (January, 1955), pp. 46-66.. " P i t t Seminar Analyses T o t a l Costs i n D i s t r i b u t i o n Management," Railway Age, CL, No. 9 (February 27, 1961), pp. 40-41. Rapoport, Leo A., and W i l l i a m P. Drews. "Mathematical Approach to Long-Range P l a n n i n g , " Harvard B u s i n e s s Review. XL, No. 3 (May-June, 1962), pp. 75-87. Schorr, J e r r y . "Product Glut and Start-Up I n v e n t o r y , " T r a n s p o r t a t i o n and D i s t r i b u t i o n Management. I l l , . No. 4 ( A p r i l , 1963), pp. 24-26. Shycon, Harvey N., and R i c h a r d B. M a f f i e . "Simulation: T o o l f o r B e t t e r D i s t r i b u t i o n , " Harvard- Bus ine s s Review. XXXVIII, No. 6 (November-December, I960)-, pp. 65-75.  193 Smykay, Edward W. " P h y s i c a l D i s t r i b u t i o n Management," T r a f f i c World. CVII, No. 7 (February 18. 1961), pp. 75-81; CVII, No. 15 ( A p r i l 15, 1961), pp. 64-6 Snyder, R i c h a r d E. " P h y s i c a l D i s t r i b u t i o n Costs," D i s t r i b u t i o n Age. LXI, No. 1 (January/ 1962), pp. 44-51. .".Putting the P h y s i c a l D i s t r i b u t i o n Cost Survey (March, 1962), p. 35; LXI, No. 4 T A p r i l ,  1962), p. 37.  Sweeney, R i c h a r d J . "How to Determine the Number and L o c a t i o n of Warehouses," Modern M a t e r i a l s H a n d l i n g , XVII* No. 1 (January, 1962). pp. 76-79. "Warehouse X - I t s P r o f i t a b l e S h i p p i n g Area," D i s t r i b u t i o n Age. IX, No. 2 (February, 1961), pp. 32-33. PUBLICATIONS OF THE GOVERNMENT AID OTHER ORGANISATIONS Beckmann, M., and T. Marschak. "An A c t i v i t y A n a l y s i s Approach to L o c a t i o n Theory," Proceedings of the Second Symposium i n L i n e a r Programming* pp. 331-79. Washington: N a t i o n a l Bureau of Standards, U.S. Department of Commerce, 1955. F l a k s , M a r v i n . T o t a l Cost Approach t o P h y s i c a l D i s t r i b u t i o n . BMC Report Number 3. Greenwich, C o n n e c t i c u t : B u s i n e s s Management C o u n c i l I n c . , 1963. P h y s i c a l D i s t r i b u t i o n Management. AMA Management Report No. 49. New York: American Management A s s o c i a t i o n Inc., 1960. Smykay, Edward W. ( E d ) . Essays on P h y s i c a l D i s t r i b u t i o n Management. Washington: The T r a f f i c S e r v i c e -Corporation, 1961.  UNPUBLISHED MATERIALS R o b e r t s j M e r r i l l J . "Transport Dynamics and D i s t r i b u t i o n Management." Paper read at the P h y s i c a l D i s t r i b u t i o n Management Seminar, U n i v e r s i t y of P i t t s b u r g h , February 3, 1961. Thompson, John T. "Unimarket, An I n t e g r a t e d D i s t r i b u t i o n System." Paper read at the D i s t r i b u t i o n Management Conference sponsored by the American Management A s s o c i a t i o n Inc., San F r a n c i s c o , C a l i f o r n i a , A p r i l 13, 1960.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0102392/manifest

Comment

Related Items