A Guide to Operational Research A Guide to Operational Research W.E. DUCKWORTH Managing Director. Fulmer Research Institute A.E. GEAR Associate Professor in Management Studies .. Deputy Dean. Faculty of Commerce, University of Auckland, New Zealand A.G. LOCKETT Senior Lecturer in Management Science .. Dean. Faculty of Business Administration. Manchester University LONDON NEW YORK CHAPMAN AND HALL First published 1962 by Methuen & Co. Ltd Third edition 1977 published by Chapman and Hall Ltd, 11 New Fetter Lane, London EC4P 4EE Published in the USA by Chapman and Hall 733 Third Avenue, New York NYlO017 Reprinted 1978, 1982 © 1977 W. E. Duckworth, A. E. Gear, A. G. Lockett Softcover reprint of the hardcover 1s t edition 1977 ISBN-13: 978-0-412-13500-2 e-ISBN-13: 978-94-011-6910-3 DOl: 10.1007/978-94-011-6910-3 This paperback edition is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publisher. Contents Preface by W.E. Duckworth page vii What operational research is and does 2 Measuring uncertainty 16 3 Queuing problems 32 4 Business forecasting 40 5 Simulation and Monte Carlo Methods 61 6 Stock and production control models 84 7 Resource allocation 105 8 Planning projects 127 9 Analysing decisions 150 10 Operational gaming 167 11 Other operational research techniques 180 12 Conclusions 193 Name Index 201 General Index 203 Preface There is nothing more difficult to take in hand. more perilous to conduct. or more uncertain in its success. than to take the lead in the introduction of a new order of things. because the innovator has for enemies all those who have done well under the old conditions. and lukewarm defenders in those who may do well under the new. Machiavelli. The Prince When this book was first written in 1959 I was myself a practising operational research worker in charge of a small group at the Glacier Metal Company, concerned with using Operational Research philosophy and techniques to help solve some of the managerial problems inside the company. About that time Operational Research was beginning to attract attention in industrial circles. Many quite large research groups were being founded. The advertisement columns of the Sunday press and certain daily newspapers were full of advertisements for Operational Research practitioners, at then quite attractive salaries. This interest by industrialists in Operational Research appeared to be based upon faith and expectation rather than upon experience. Many of the classical examples of successful Operational Research being used in the many text-books beginning to appear were still based upon the war-time experiences recently amplified in the newly released and long classified book by Waddington. * The First International Conference on Operational Research held in 1957 attempted to restore the balance by summarizing industrial experience since the War. Even in that publication, however, many of the case studies were still incomplete, the outcomes had not yet been fully evaluated, and the many different types and levels of experience described in the proceedings of that conference did not produce a sufficiently coherent impression of post-war Operational Research practice to satisfy the busy manager, seeking a ready appreciation for his own purposes, as to whether he should seek the assistance of Operational Research. The need for such a ready appreciation was described by the late Oscar Brandt in an editorial in his magazine Metal Treatment in April 1958, and it was in response to his appeal that I wrote two articles for Metal Treatment which appeared in September and October of that year. These subsequently * References are given in alphabetical order of first author at the end of each chapter. vii viii Preface formed the basis of the first edition of A Guide to Operational Research in 1962. This achieved substantially more success than I had expected, or even dreamed of, because it did provide a relatively simple coherent account by one individual of successful Operational Research being practised, albeit at a rather specialized level and not on too grand a scale, in one company. Most of the examples were written from first-hand experience, so they possessed both an immediacy and a clarity of exposition that appeared to be lacking from many other accounts which were at second, third, and some- times even fourth hand. There appears little doubt that the formula has been successful because after thirteen years the book was still being reprinted, it is still selling in several languages, and it has also reached the reading list of many universities and schools of management. To be on this reading list has, in recent years, been causing me great concern because many of the illustrations of Operational Research techniques had become out of date. The book also did not describe several more modern techniques. When the book first appeared it was quite rightly criticized as providing a rather selective view of Operational Research, and as the years have gone by this criticism has become more justified. If the book was serving a valuable purpose, as several other reviews then and subsequently have indicated, in acquainting busy managers in a readily assimilable fashion of the virtues of Operational Research, then it did seem to be a dereliction of duty to let the book die and cease publication, because there did not appear to be another book available that provided for quite the same purpose. Equally, it appeared wrong to let it continue to get more and more out of date. The present version of the book is an attempt to resolve the dilemma with the aid of two collaborators, Tony Gear and Geoff Lockett. I did not feel capable of rewriting the book in quite the same way as sixteen years earlier because I have long ceased to be as closely connected with Operational Research practice as I was in the late 1950s. Tony Gear and Geoff Lockett are, however, such practitioners. They both benefited from reading the book in the early days. Being university teachers as well, they have a personal and a professional interest in seeing it adequately up-to-date. We have tried in this up-dating to preserve the coherency of style that has been such a feature of the earlier book's success. However, the need for a more detailed exposition of Operational Research Techniques for the purposes of student teaching has necessitated a more mathematical, and hence more sophisticated approach to the subject. Despite this, we have endeavoured to preserve sufficient readability to enable the busy business manager to gain relatively painlessly, an understanding of what Operational Research is about. Whether or not we have succeeded is now up to you to judge. Preface ix I have taken the liberty of writing the first chapter from my own personal experience as a manager using Operational Research techniques, in the hope that it will encourage other managers to follow suit. The other chapters have been written, in the main, by one of us and then revised by the others. W.E. Duckworth Fulmer Research Institute Limited, Stoke Poges May, 1976 REFERENCES Duckworth, W.E., A Guide to Operational Research, Methuen, 1962. First International Conference on Operational Research, E.U.P., 1957. Waddington, C.H., Operational Research in World War II. Operational Research against the V-Boat, Elek Science, 1973. ACKNOWLEDGEMENTS Much of the material used in the earlier book which was reproduced from various publications has been reprinted, and permission for its use is grate- fully acknowledged. New material from Technological Forecasting in Pers- pective by Jansch, the Open University and The Limits to Growth by Meadows and colleagues has been incorporated and permission for its inclusion is also gratefully acknowledged. Many thanks are also due to many colleagues, especially D.G.S. Davies, who read the manuscript critically and helpfully and contributed to Chapter 8, and to Mr. R.F. Flint who helped to prepare the index. Finally, but by no means minimally, we owe much gratitude to Mrs. Joan Tarrant who typed an incredible number of scripts with patience and fortitude. 1 What Operational Research Is and Does Operational Research is the art of winning wars without actuallv fighting. Arthur Clarke What Operational Research is Operational Research (O.R.) has never been an easy subject to define, comprising as it does the application of several scientific disciplines to the solving of complex problems in the management of human affairs. The Operational Research Society of the United Kingdom have the following official definition: 'Operational Research is the application of the methods of science to complex problems arising in the direction and management of large systems of men, machines, materials, and money in industry, business, government, and defence. The distinctive approach is to develop a scientific model of the system, incorporating measurements of factors such as chance and risk, with which to predict and compare the outcomes of alternative decisions, strategies, or controls. The purpose is to help manage- ment determine its policy and actions scientifically'. At the time of producing this definition there were some 38 others which all have merit, and no doubt there have been many more produced since. I myself prefer to regard Opera- tional Research as the study of administrative systems pursued in the same scientific manner in which systems in physics, chemistry, and biology are studied in the natural sciences. The problem of definition really arises because language is a classification process and the more complex a process becomes the less easy it is to define it in language which can convey a roughly similar meaning to all its readers. The more precise such a definition is in describing particular attributes of Operational Research the more it can be resented by the physicist, the mathematician, the economist, the sociologist, the work-study man, etc. as encroaching on their particular preserve. It is quite true that O.R. does encroach on these preserves but if it is any consolation to the gamekeepers it is a poacher that treats many such preserves with the same indifference to plunder and ought to continue to do so. 1 2 A guide to operational research A further problem of definition is that, while it is often easy to describe a profession or trade in terms of the tools used (there is for instance little problem in understanding the role of the electron microscopist or the X-ray crystallographer), any definition which so illuminates Operational Research tends to give the impression that it isjust a rag-bag of techniques. It is, of course, more than this but every discipline must have techniques to implement its means of operation, and to describe Operational Research without describing techniques would be to attempt to describe a scent without ever having experienced one. A third major problem of definition is that, since Operational Research covers a very wide embracing field of human management, it is sometimes hard to attempt to describe it in these terms without appearing to usurp the function of management itself. This is one of the major problems which Operational Research implementation has had to face since its inception. It seemed at one time that the exigencies of war had helped to solve this problem, and those responsible for executing decisions had a close rapport with those responsible for understanding and analysing the decisions to be implemented. Waddington's recent book, referenced in the Preface, suggests however that, even under the pressure of survival against the U-boat, the problems of relationships between the managers and operational research workers were just as difficult as they have been ever since. It is very important for the health of industry that this problem of relationships should be solved. This is one of the main motivating forces behind the rewriting of this book. It is a very understandable problem. The decision maker has to make the decisions. If some other agent analyses, inter- prets, and resolves them into components and alternatives, what is there still left for the decision maker to do? There is a great deal. The analysis of decisions by even the most skilled practitioners who have not the responsibi- lity for making them and for 'carrying the can' still lacks some indefinable quality; let us call it judgement. It is this judgement that finally makes the decision viable or otherwise. It is this judgement for which people are paid high salaries. They are not paid for the quantity of work they do. They are not paid high salaries for the amount of time and effort they put into their decisions. They are paid, as Elliot Jaques has shown, for the quality of their decisions and for the length of time which has to elapse before the validity of these decisions can be demonstrated. It is therefore surely more important that the decision maker should have the most valuable aids to his decision making that he can obtain. The manager does not however just want masses and masses of information. It is a standard joke among the uninitiated in management practice to jibe at the manager who says 'I must make a decision, do not confuse me with facts'. Unfortunately, too many managers do mistake facts for analysis and find that they are faced with a completely undigestible volume of information. What operational research is and does 3 This makes it almost impossible for them to make a proper decision because, although they may consider by using their judgement that a parti- cular course of action is the right one, they feel that it is inappropriate to take that course of action until they have checked it against the available information. Because this is too big a task to undertake in the time, they remain like hypnotized rabbits until the effective time for a decision has passed and circumstances take over. What Operational Research can do is to analyse the available information, not just from the point of view of the economist, or the physicist, or the management scientlst, or the production engineer but, with true scientific objectivity, to sort out which information is relevant, to sort out which information from past experience has a causal relationship with the situation being examined, to identify where information does not exist so that at least its absence can be noted if it cannot be rectified, and then to attempt to illustrate the likely outcomes of certain courses of action based upon the information analysed, and only on the information analysed. The objective of the study is to gain understanding of administrative systems so that they may be more readily controlled, just as systems in the natural sciences are more readily controlled than they were and can in fact be harnessed to man's uses. Incidentally, the word 'control' is used throughout this book in the regulative and not the restrictive sense. We can now switch on an electric light with a good degree of probability that the bulb will light up. We can spray crops against certain diseases with a strong expectation that protection will be assured without the occurrence of unforeseen side-effects. But can the average manager be as sure of the workings of his administrative system? Can a manager reduce his stocks to a particular level and be sure that he will not endanger his productive processes or let his customers down? Can he change his distributive outlets and know that he will be better off? Can he in fact introduce changes in routine and procedure without considerable uncertainty as to their results? Does a manager know very often whether a change is necessary or even desirable? Modern industry is so complex that the optimum point of opera- tion of many of its systems is no longer within the intuitive comprehension of individuals. To enable this intuition, this imaginative judgement, which is at the core of management to hold its rightful place in the controlling of such systems is the function of O. R. Its job is to study these systems and to understand how they may be controlled by simple rules. Managers often feel that scientific methods are a threat to their intuition, but I hope to show that the opposite is true. If you doubt the ability of simple rules to handle complex situations, consider how the simple rule 'drive on the left' prevented chaos on the roads