PRODUCTION AND

INVENTORY CONTROL:

THEORY AND PRACTICE

By the same authors

AN INTRODUCTION TO PRODUCTION AND INVENTORY CONTROL

Philips Technical Library

PRODUCTION AND INVENTORY CONTROL:

THEORY AND PRACTICE

R. N. VAN HEES

and

W. MONHEMIUS with major contributions by

A. R. W. MUYEN

Macmillan Education

Original Dutch edition © N. V. Philips' Gloeilampenfabrieken, Eindhoven, 1969 English edition© N. V. Philips' G1oeilampenfabrieken, Eindhoven, 1972

Softcover reprint of the hardcover 1st edition 1972

All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission.

First published in English by THE MACMILLAN PRESS LTD

London and Basingstoke Associated companies in New York Toronto Melbourne Dublin Johannesburg and Madras

PHILIPS Trademarks of N. V. Philips' Gloeilampenfabrieken

ISBN 978-1-349-01314-2 ISBN 978-1-349-01312-8 (eBook) DOI 10.1007/978-1-349-01312-8

SBN 333 12125 5

Preface

This book may be regarded as a continuation of 'An Introduction to Production and Inventory Control'. It gives the theoretical background of the topics dis­cussed there. It is intended for specialists in production management and stock control, who should find the discussion given here of use in the development of methods or techniques, in the supervision or execution of practical investigations, or as a basis for courses of instruction for groups of consumers or workers in this field.

The reader will be well aware that, while the subjects dealt with in this book are not simple, the treatment given here is often simpler than the problems encountered in practice. In reality, the following complications are often found, alone or in combination: cascade effects (parallel or series); non-stationary demand; production capacity limitations. These topics are touched on in this book, but not dealt with in depth for the simple reason that the problems involved are still far from being solved. One might ask why, if this is the case, so much space has been devoted to such subjects as the (B, Q) system, the re-order level, Camp's equations and its variants.

The answer is two-fold:

- before dealing with the most difficult problems, we should master the simpler ones. Moreover, we still find that even the simpler approaches are less well known than they deserve to be, and could well be introduced for the solution of many practical problems;

- moreover, formulae for the simplified situations must be regarded as extremely valuable as a reasonable and above all understandable approximation to the solution for more complex problems. This point is so vital that we should like to illustrate it by a number of quotations from the literature.

Ackoff and Sasieni state:

Our experience indicates, that the results obtained from the more elaborate mathematical models seldom justify the additional computational effort that they require.

What is usually wanted in a practical problem is a good approximation that has the merit of simplicity of computation and implementation and which is easy to explain to those who must accept and use it. One must remember that the tacit assumption of fixed and known parameters is often far from realistic and the assumption of a known distribution for demand (let alone deterministic demand) is seldom justified.

vi Preface

In many situations the critical problem is to forecast demand over the lead time. Melese writes:

' ... seules Jes methodes simples fonctionnent bien ... , Toute Ia question est justement de doser habilement Ia complexite des etudes et Ia simplicite des resultats.

Finally, Ackoff and Stafford Beer mention (in the last chapter of No. 16 of the ORSA series, 'The relation between OR and the computer') that their simula­tion showed that:

... the performance of a model depended as much on the accuracy and reliability of estimated values of its parameters as it did on its form. Consequently, in many complex stochastic situations, simple deterministic models performed as well as more complex probabilistic models or even better.

Apart from a correct insight into the desired degree of complexity of the models and methods used, it is of equal importance to consider the training and working pattern of all those who will eventually be involved in the realization and use of the new insights gained by the study of production management and stock con­trol. This means that in each investigation where the investigator and the operator or supervisor are not the same person, training programmes form a very important part of the operational whole.

When new methods or techniques are introduced, a need is often felt for more information; or more information may be produced by the introduction. Further, other aids (for example, computers) may be involved. All these factors mean that the working pattern may be replaced by a new one, or its content may change. Since the 'working pattern' is really the same thing as the 'organization', it is important to include in each investigation a study of how the organization, the functions, the associated responsibilities and competances need to be modified to meet the new conditions.

It goes without saying that it is impossible to deal with all these topics in a single book. In fact, a number of very important aspects of this subject have not been dealt with at all, namely:

-forecasting. Forecasting may be regarded as the foundation of all work in this field, and sensitivity analysis has shown that the total variable costs are very sensitive to the quality of the forecasting; -simulation. This method is coming to be used more and more widely; we expect that combined use of analytical methods and well-chosen simulation will bear rich fruits in the near future; -the role of the computer. A great deal of literature exists on this subject; how­ever, it remains true that one should always have a clear concept of one's aims and have worked out the method to be followed before using a computer. No mention has been made of the available software packages in this book. However,

Preface

the interested reader may be referred to excellent textbooks on the above subjects.

vii

The use of statistical terms in this book may perhaps be judged to be rather careless by mathematicians. However, the fact that this book is largely based on reports and articles from many different sources means that the notation used may differ somewhat from place to place. Some symbols mean different things in different parts of the book. For example, dt generally means the demand during a period oft units of time, while in some sections it is used to mean the demand in period no. t; further, in one particular section di is used to mean the demand for product i during a given period.

We should like to take this opportunity of thanking a number of people who have been associated with the writing of this book:

- Mr Schaafsma: he stimulated us to start writing this book when we worked under him; and later, when we have moved elsewhere, he constantly encouraged us to keep up the good work; -Professor Goudriaan, from whom we have learnt much in public discussions and private correspondence; -the many workers in planning and production control with whom we have co-operated and discussed problems.

We have learnt a great deal from all of them, maybe in particular that an existing system can seldom be called 'wrong'; the most that can be said is that it may be possible to improve it with the aid of modem tools and insights, and a great deal of effort;

-our co-authors Van Ham, VanHouten and Muyen for their friendly co-operation; - Mr Schrakamp, a works economist who wrote a number of the internal reports used in the preparation of this book. Most of the works-economic concepts which we use in this book were worked out by discussion with him; however, any shortcomings in this connection naturally are our responsibility; -Professor Hulshofwho brought to our notice the lecture by Marx.

Finally, we should like to express the hope that this book will help to bridge what R. A. Howard called the 'practicality gap'.

Waalre, R.N. van Hees Geldrop, W. Monhemius

Contents

SECTION I: BACKGROUND

INTRODUCTION

2 GENERAL REMARKS ON PLANNING

2.1 The development of ideas in the planning sector 2.2 Long-term and short-term planning 2.3 Planning and control of production and development 2.4 Flexibility 2.5 Chains; information and stocks 2.6 The application of electronic data processing

SECTION II: STATISTICAL INVENTORY CONTROL

3

9

9 11 14 15 18 19

3 THE IMPORTANCE OF MATHEMATICAL STATISTICS 23

4 STOCHASTIC QUANTITIES, PROBABILITY DISTRIBUTIONS AND MOMENTS 26

5 SOME THEORETICAL DISTRIBUTIONS 29

5.1 Exponential distribution 29 5 .2 The gamma distribution 31

6 FLUCTUATION OF DEMAND PER PRODUCT 33

6.1 Stable situation 33 6.1.1 The Poisson process 33 6.1.2 Pseudo-Poisson process 36 6.1.3 General formula 36 6.1.4 Form of the frequency distribution of the demand 37

6.2 The non-stationary situation 37 6.3 Autocorrelation 39

X Contents

7 NATURAL LAWS AFFECTING A LARGE GROUP OF ARTICLES 43

7.1 Uses of the lognormal distribution 43 7.2 The relationship between average demand and standard deviation

of demand 48

8 THE IDEA OF DYNAMIC PROGRAMMING AS APPLIED TO MULTI-STAGE DECISIONS 49

8.1 The value-determination method 50 8.2 The policy-iteration method 53 8.3 General remarks 56

SECTION III: FORECASTING (PLANS AND PREDICTIONS)

9 INTRODUCTION 59

9.1 Why forecasting is necessary 59 9.2 The reliability of forecasting 61 9.3 The length of the forecast period 62 9.4 Method of forecasting 64 9.5 Choice between extrapolation and explosion 65

10 DISTINCTION BETWEEN CATEGORIES OF CUSTOMERS OR ORDERS 67

SECTION IV: CALCULATIONS ASSOCIATED WITH RE-ORDER SYSTEMS AND PRODUCTION

BATCHES; INTERMITTENT SUPPLY

11 INTRODUCTION

11.1 General survey of this sector 11.2 One stock point: demand known and constant

12 CALCULATION OF THE OPTIMUM BATCH SIZE Q*

12.1 Camp's formula 12.2 Costs increase resulting from deviations from Q*

71

71 72

75

75 78

Contents xi

13 DEFINITION OF THE FACTORS OCCURRING IN CAMPS FORMULA 79

13.1 General introduction 79 13.2 Calculation of the annual programme (D) 80 13.3 General remarks concerning the cost factors 81 13.4 Calculation of the re-order costs 85

13.4.1 Acquisition of goods 85 13.4.2 Optimum batch size in the manufacture of goods 86 13.4.3 The coincidence of order costs of production batch and

order costs of placing an order 89 13.5 Inventory costs 89

13.5.1 Profitability 89 13.5 .2 Costs of space 95 13.5.3 Determination of that component of the product costs

which is sensitive to inventory costs (K) 96

14 VARIANTS OF THE SIMPLE BATCH SIZE FORMULA 102

14.1 Effect of the rate of production (P) 102 14.2 Effect of in process stocks 103 14.3 Substantial risk of obsolescence 106

14.3.1 Theoretical derivation 106 14.3.2 Application 107

14.4 Problem of limited space 112 14.5 Discount on purchased quantities 112 14.6 Tools with limited standing time 117

15 BATCH SIZE IN THE CASE OF PERIODIC RE-ORDERING 122

16 SIMPLE AIDS TO THE CALCULATION OF BATCH SIZE 124

16.1 Table 124 16.2 Nomograms 126 16.3 Slide rules 129 16.4 The chart 129 16.5 Muyen method 131

17 DETERMINATION OF THE RE-ORDER LEVEL 133

17.1 Definitions. A simple example 133

xii Contents

18 FACTORS INVOLVED IN THE DETERMINATION OF THE RE-ORDER LEVEL 136

18.1 Costs 136 18.2 Frequency distribution of usage during the lead time 139

18.2.1 Determination of the lead time 139 18.2.2 Determining the frequency distribution of usage per

time unit or per lead time 141 18.2.3 Practical measurement of lead time 141

19 THE GRAPHICAL-EMPIRICAL METHOD 144

19.1 Principle 144 19.2 Labour saving 148 19.3 Periods of no demand 148 19.4 Tacit assumptions 149 19.5 Goudriaan's and Cahen's classical study 149 19.6 Variants 152

20 ANALYTICAL METHODS 153

20.1 Use of the Poisson distribution 153 20.2 Goudriaan's formula 153 20.3 Determination of second moment by means of correlation

calculation 156 20.3.1 The calculation of mean and standard deviation per

article 167 20.4 Changeover from demand per time unit to demand per lead time 169 20.5 The shape of the frequency distribution of the demand during

the lead time 170

21 STANDARD DEVIATION IN THE LEAD TIME 175

21.1 The need to find a suitable calculation procedure 175 21.2 A general approach 175 21.3 Numerical method 178

22 THE RE-ORDER LEVEL IN THE CASE OF FIXED-INTERVAL RE-ORDERING 180

22.1 A method of approximating sin (s, S) 180 22.2 Determination of s by the numerical method; example 181

Contents xiii

23 CALCULATION OF OPTIMUM BAND Q FOR A (B, Q)SYSTEM I84

23.1 Loss per stockout 23.2 Loss incurred on each product which is late in arriving.

Subsequent delivery permitted 23.3 Sales forfeited, loss 1T per product 23.4 Costs as a function of average negative stock

24 DETERMINATION OF THE LEVELS AND S BY DYNAMIC

I84

I87 I89 I89

PROGRAMMING I90

24.I Definition of the problem I90 24.2 Further analysis I9I 24.3 The strategy iteration method 200

25 ONE ARTICLE; SEVERAL PARALLEL INVENTORY POINTS 203

25 .I General introduction 25.2 Ordering policy 25.3 Delivery from a central warehouse 25.4 Ordering direct from a factory 25.5 Allocation problem

25.5 .I Rush deliveries 25.5.2 No rush deliveries

203 204 204 205 206 206 209

26 ONE ARTICLE; A NUMBER OF STOCK POINTS IN SERIES 2II

26.I Examples 2II 26.2 Methods of combating 'upsweep effect' 2I7

26.2.I The base-stock system 2I8 26.2.2 The fixed-interval re-ordering system 2I9 26.2.3 Corrected calculation of batch size 2I9 26.2.4 Variants such as the 'three-bin' system 2I9

26.3 Where should the stock be located in a base-stock system? 2I9

27 SEVERAL ARTICLES; STOCK POINTS PARALLEL 225

27.I Complex costs pattern 225 27.2 Common limiting factors 23I

27 .2.1 Limited capital 23I 27.2.2 Limited space 233 27 .2.3 Limited number of changeovers 234

xiv Contents

28 NORMS IN INVENTORY CONTROL

28.1 Control 28.2 A practical starting point 28.3 The A.B.C. system of inventory control 28.4 Application of A.B.C. inventory control 28.5 The lognormal distribution and the Lorenz curve 28.6 Stock norms for a group of articles; calculation chart

236

236 237 237 239 240 243

SECTION V: CALCULATION OF PRODUCTION LEVEL (CONTINUOUS SUPPLY)

29 DETERMINATION OF PRODUCTION LEVEL

29.1 Introduction 29.2 The simplified problem 29.3 Applications 29.4 Tables

SECTION VI: CALCULATION OF CAPACITY

30 CALCULATION OF CAPACITY

30.1 Starting point 30.2 Short-term capacity calculations 30.3 Long-term capacity calculations

SECTION VII: SOME EXAMPLES

31 SPARES INVENTORY CONTROL

31.1 Introduction 31.2 The (B, Q) system for spares 31.3 Review of alternatives and refinements 31.4 The Unilever tables

32 FIXING PARTS FOR ASSEMBLY

32.1 Description of the situation 32.2 Analysis of past records of demand 32.3 Forecasting the demand

249

249 250 259 265

273

273 273 274

279

279 279 283 289

291

291 292 294

32.4 The re-ordering system 32.4.1 The lowest level s 32.4.2 The highest level S

32.5 Overall survey 32.6 Results and parameters 32.7 Stock norms

Contents

32.8 Introduction and evaluation

33 PLANNING AND INVENTORY CONTROL IN A WOODWORKING

XV

296 296 298 299 299 304 305

FACTORY 306

33.1 Introduction 306 33.2 Problems 308 33.3 The capacity calculation 308 33.4 Production planning with the aid of cumulative charts 312 33.5 Calculation of materials and components required 313 33.6 Components planning by means of a modified (B, Q) system 314 33.7 Calculation 316

34 EXAMPLE: THE PRODUCTION OF SIMPLE PARTS FOR ELECTRONIC COMPONENTS 317

34.1 Original system 34.2 The new system 34.3 The introduction of the new system 34.4 Advantages of the change

SECTION VIII: APPROACH TO A PROBLEM 35 APPROACH TO A PROJECT

318 320 326 326

331

35.1 How important is a proper approach? 331 35.2 What is really meant by 'the right approach'? 332 35.3 Project analysis in terms of decision levels 337 35.4 Recommendations 338 35.5 Recommendations concerning the technical aspects of the

approach 340 35.5.1 Phases of an investigation 340 35.5.2 Step-by-step approach 340 35.5.3 Appointment of steering committee and work group 343 35.5.4 Preliminary research; introduction and orientation 343 35.5.5 Defining the problem 346

xvi Contents

35.5.6 Constructing the model and collecting data 347 35.5.7 Testing the solution 348

36 SIMULATION AS A METHOD OF INVESTIGATION AND TRAINING 349

APPENDICES

Appendix 1: The normal distribution 351 Appendix 2: Poisson distribution P(x .;;; k) 352 Appendix 3: Table of powers of e 353 Appendix 4: Percentage points of the x2 -distribution 354 Appendix 5: Derivation of the general equation in the quasi-Poisson

process 356 Appendix 6: Calculation of f(e) 357 Appendix 7: Table of iterations 358 Appendix 8: Optimum batch, with due regard to risk of obsolescence 359

BIBLIOGRAPHY 363

INDEX 367