inventory control in the retail sector: a · pdf filemodel for a periodic review system with a...
TRANSCRIPT
I N V E N T O R Y C O N T R O L IN T H E R E T A I L S E C T O R : A C A S E STUDY O F C A N A D I A N TIRE PACIFIC ASSOCIATES
by
BRIAN A N T H O N Y K A P A L K A
B.Sc.(C.E.), The University of Manitoba, 1992 B.Sc., The University of Manitoba, 1992
A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF
T H E REQUIREMENTS FOR T H E D E G R E E OF
MASTER OF SCIENCE (BUSINESS ADMINISTRATION)
in
T H E F A C U L T Y OF G R A D U A T E STUDIES
(Department of Commerce and Business Administration)
We accept this thesis as conforming to the required standard
T H E UNIVERSITY OF BRITISH COLUMBIA
April 1995
Brian Anthony Kapalka, 1995
In presenting t h i s thesis i n p a r t i a l f u l f i l l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or pub l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission.
Department of Cotv^errg- ftni)> ^osmecs AAnmn\a-WoA\or' The University of B r i t i s h Columbia Vancouver, Canada
Date ZS A y r A \ 9 9 5
Abstract
Canadian Tire Pacific Associates owns and operates 21 retail stores in the lower
mainland of British Columbia and a central warehouse in Burnaby. In this thesis, we formulate
a single-product, single-location model of its inventory system as a first step in developing an
integrated, interactive inventory control system. Specifically, we formulate a Markov chain
model for a periodic review system with a deterministic lead time and lost sales. The model
utilizes empirical demand data to calculate the long-run average cost of inventory for a given
(s,S) policy. We then develop a heuristic that locates a "near" optimal policy quickly. The
heuristic incorporates a constraint on the customer service level, makes use of an updating
technique for the transition probability matrix, and is based on assumptions regarding the
properties of the solution space. Next, we create a prototype of the interface that enables
managers to use the model interactively. Finally, we compare the existing inventory policy to
the optimal policy for each of 420 products sold at one of the stores. This thesis finds that
Canadian Tire Pacific Associates is currently holding excessively large in-store inventory and
that it could reduce its cost of inventory by approximately 40% to 50%. We estimate that
implementing optimal inventory control in the stores would result in annual savings of between
$5.5 and $7 million.
ii
Table of Contents
Abstract ii
Table of Contents iii
List of Tables v
List of Figures vi
Acknowledgement vii
I. INTRODUCTION 1
II. T H E INVENTORY SYSTEM A T CANADIAN TIRE PACIFIC ASSOCIATES . . . . 8 A. Background 8 B. The Problem .11 C. The Project 15 D. The Demand Data 17 E . The Cost Data 18
III. M O D E L FORMULATION 20 A. Terminology 20 B. Assumptions 21 C. A Markov Chain Model 22 D. The Transition Probability Matrix 25 E . The Steady State Probabilities 27 F. The Cost of Inventory . 29 G. The Customer Service Level 31 H . A Methodology for Evaluating an (s,S) Policy 34
IV. A N ALGORITHM FOR OBTAINING T H E OPTIMAL (s,S) POLICY 35 A. Introduction 35 B. A Grid Search 36 C. A Technique for Updating the Transition Probability Matrix 41
A new policy (s+m,S) 41 A new policy (s,S+m) 42 The modified algorithm 43
D. A Lower Bound on S . . . 45 E . A Heuristic Search 48
V . T H E INTERFACE 52
iii
VI. RESULTS A N D SENSITIVITY ANALYSIS 55 A. Comparison of Current Policies to Optimal Policies 55 B. Sensitivity Analysis on the Ordering Cost and Holding Rate 62 C. Sensitivity Analysis on the Demand Probability Mass Function 65
VII. CONCLUSION 70
Afterword 73
Bibliography 74
Appendix A: A Portion of the "Sales" File for Product 200001, a 30-amp
Inline Fuse 76
Appendix B: Sample "Distribution" Files 77
Appendix C: A Proof that the Limiting Distribution is Independent of the
Initial State 79
Appendix D: A Measure for the Steady State Customer Service Level 83
Appendix E: The Calculation of the Conditional Expected Demand Not Satisfied
During a Period of T Consecutive Days 86
Appendix F: Justification of the Updating Technique for the New Policy (s+m,S) . . . . 87
Appendix G: Justification of the Updating Technique for the New Policy (s,S+m) . . . . 92
Appendix H: A Hypothetical Consultation 97
Appendix I: The Source Code for the "Interface" Module 104
Appendix J: The Source Code for the "Main" Module 119
Appendix K: Current and Optimal Policies for Product Category 20 at Store 6 131
iv
List o f Tables
Table 1. Location and particulars of the 21 stores 10
Table 2. Execution times of the algorithms for product 200001, a 30-amp inline fuse 39
Table 3. Execution times of the algorithms for product 206917, a 6%
solder connector 40
Table 4. Products with insufficient existing policies 56
Table 5. Products with the largest potential absolute savings 60
Table 6. A comparison of "optimal" policies to "true optimal" policies 63
Table 7. The cost of existing policies and the relative savings of the "optimal" policies under various scenarios .64
Table 8. "True optimal" and "optimal" policies for each demand scenario 66
v
List of Figures
Figure 1. A typical sample path of the process with a 4-day review period
and a 2-day lead time 24
Figure 2. The flow chart of the grid search algorithm 38
Figure 3. The flow chart of the grid search algorithm utilizing the updating
technique for the transition probability matrix 44
Figure 4. An evaluation of the lower bound, Sm i n 47
Figure 5. The flow chart of the heuristic algorithm 50
Figure 6. The distribution of savings of optimal policies in (a) dollars and
(b) percentage of current cost 59
Figure A-1. The title screen 97
Figure A-2. The main menu 98
Figure A-3. Calculating the optimal policy and evaluating the current policy 99
Figure A-4. Displaying the results 100
Figure A-5. Entering an alternate policy 101
Figure A-6. The particulars of the alternate policy 102
Figure A-7. The main menu revisited 103
vi
Acknowledgement
The completion of this thesis was made possible by the encouragement and assistance
of a number of people.
I would like to express my sincere appreciation to my thesis supervisor, Professor
Martin Puterman, for all of his many efforts on my behalf. His help, advice, patience, charity,
and tolerance were very much appreciated.
I would like to acknowledge Professor Hong Chen and Professor Garland Chow for their
time and input as members of my thesis committee. In addition, I must acknowledge the
assistance of Ph.D. student Kaan Katircioglu for his insight and help on this project.
I offer many thanks to Professor Tom Ross for his kindness and friendship during the
past few years, especially during the writing of this work. I must also thank his family for
"adopting" me on many holidays. I still owe thanks to Professor Slobodan Simonovic at the
University of Manitoba for influencing me to attend graduate school in the first place and for
helping me to obtain funding.
I cannot thank my parents enough for their never-ending support, both emotional and
financial. Also, to my friends, especially Cathy, Dave, Lisa, Steve, and the "Philbuds": thanks
for giving me a life off campus and for picking up many a tab - the next one is on me.
I would like to give special thanks to my good friend and fellow M.Sc. student, Paul
Crookshanks, for allowing me to bounce ideas off of him and for being such a procrastinator
that, despite my finishing a year late, I only "lost" by two days.
Financial assistance received from the Natural Science and Engineering Research
Council (NSERC) and from Canadian Tire Pacific Associates was greatly appreciated.
vii
I. INTRODUCTION
The importance of inventory management has grown significantly over the years,
especially since the turn of this century. In colonial times, large inventories were viewed as
signs of wealth, and, therefore, merchants and policy makers were not overly concerned with
controlling inventory. However, during the economic collapse of the 1930s, managers began
to perceive the risks associated with holding large inventories. As a result, managers
emphasized rapid rates of inventory turnover (Silver and Peterson, 1985). Following the
Second World War, Arrow, Harris, and Marschak (1951) and Dvoretzky, Kiefer, and
Wolfowitz (1952a,b) laid the basis for future developments in mathematical inventory theory.
Shortly thereafter, new inventory control methodologies were widely applied in the private
manufacturing sector. More recently, when inflation and interest rates soared during the 1970s,
many organizations were forced to rethink their inventory strategies yet again. Today, the
control of inventory is a problem common to all org