Methods of Operations Research

Methods of Operations Research

by Philip M. Morse, George E. Kimball

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Operations research originated during World War II with the military's need for a scientific method of providing executive departments with a quantitative decision-making basis. This volume — co-written by the father of operations research — explores strategical kinematics, tactical analysis, gunnery and bombardment problems, organizational and procedural…  See more details below


Operations research originated during World War II with the military's need for a scientific method of providing executive departments with a quantitative decision-making basis. This volume — co-written by the father of operations research — explores strategical kinematics, tactical analysis, gunnery and bombardment problems, organizational and procedural problems, more. Includes 51 figures and 31 tables.

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Methods of Operations Research

By Philip M. Morse, George E. Kimball

Dover Publications, Inc.

Copyright © 2003 Dover Publications, Inc.
All rights reserved.
ISBN: 978-0-486-15445-9



Operations research is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. It first developed as a recognized activity in response to the military needs of World War II where it was sometimes known as operations analysis or evaluation (or in one case weapons systems evaluation). Although its techniques and methods of approach have earlier been used sporadically in industrial, governmental, and military activities, sometimes under different names, its systematic applications have to date been predominantly military. However, as the definition suggests, as the examples in this book will indicate, and as experience since the war has shown, the techniques and approach of operations research can be of help in arriving at executive decisions concerning operations in any field, industrial and governmental as well as military. After four years of war experience and four subsequent years of peacetime experience most experts in the field have agreed on the definition given in the first sentence, with all its implications and generality.


Let us first point out some of the more obvious implications of the definition given in the first sentence above; we will then mention a few examples of the methods used and devote the rest of the first chapter to a discussion of techniques, organization, and personnel. First of all operations research is a scientific method. It is an organized activity with a more or less definite methodology of attacking new problems and finding definite solutions. Executives have often in the past used some of the techniques to be explained herein to help themselves arrive at decisions; military staffs have used some of its techniques, and "efficiency experts" have exploited some of its methods. But the term "scientific method" implies more than sporadic application and occasional use of a certain methodology; it implies recognized and organized activity amenable to application to a variety of problems and capable of being taught.

1.1.1 An Applied Science

Next we see that operations research is of service to executive departments: the commanding general of a military force, the vice-president in charge of operations in an industry, or the director of some governmental activity. Operations research, therefore, is an applied science utilizing all known scientific techniques as tools in solving a specific problem, in this case providing a basis for decisions by an executive department. As we shall see, operations research uses mathematics, but it is not a branch of mathematics. It utilizes the results of time and motion studies, but it is not efficiency engineering. It often helps in the introduction of new equipment but it is not an adjunct of a development laboratory. Just as civil engineering uses the results of science in order to build a bridge, so operations research utilizes these various techniques as tools to help the executive. It is likely, however, that operations research should not be classed as a branch of engineering. For the branches of engineering recognized at present are involved in the construction or production of equipment whereas operations research is involved in their use. The engineer is the consultant to the builder, the producer of equipment, whereas the operations research worker is the consultant to the user of equipment.

The next important word in the definition is "quantitative." It is to some extent implied in the earlier phrase "scientific method," but it is worth the iteration. Certain aspects of practically every operation can be measured and compared quantitatively with similar aspects of other operations. It is these aspects which can be studied scientifically.

The phrase "basis for decisions" implies that these quantitative aspects are not the whole story in most executive decisions. Many other aspects can enter: politics, morale, tradition, items often important but impossible to express in numbers. It is the prerogative and responsibility of the executive officer to add these factors to the quantitative basis provided by the operations research group, to reach the final decision. The task of the operations research worker is to present the quantitative aspects in intelligible form and to point out, if possible, some of the non-quantitative aspects that may need consideration by the executive before he reaches his decisions. But the operations research worker does not and should not make the decision.

1.1.2 Separation of Operations Research from Executive Decision

This separation of the duties and activities of the operations research worker and the executive officer is important; the experience of the past ten years has only emphasized this importance. Experience has shown, for instance, that a person with operations research training, when placed in an executive position, loses a great deal of his usefulness as an operations research worker (though he may become an excellent executive). The requirement that the executive reach a decision concerning an operation is to some extent antagonistic to the requirement that he look at it scientifically and impersonally, as would be required in operations research. The proper use of an operations research group by an executive department implies a sort of symbiosis, requiring, on the part of each, trust in the other's activities and respect of the other's prerogatives.

Since operations research is to provide the executive with a quantitative basis for decision, it is easy to see that the techniques of presentation of a result are very important parts of the activity. All scientific method implies the imparting of scientific results to other workers. In this work however the results are usually to be imparted to nonscientists, and no project in this field can be considered completed until the findings obtained by the scientist are imparted to the executive in a manner that will aid the latter to make his decisions.

The word "operations," in the definition, itself requires definition. Its use in military terminology is quite specific, but this usage differs somewhat from that current in industrial or other governmental activities. A specific definition will not be attempted this early in the text, though several implications of the usually understood meanings of the word should be pointed out. The term "operation" implies to some extent a repetition of some action or some parts of an action. This has come to be more and more true as operations of modern times have come to involve machinery as well as men. The repetitive factor in the usual operation is of course the factor that makes it amenable to scientific attack. Often the repetition, the similarity between parts of different operations, is not at all obvious. A standard task of any scientific research is to find similarity between apparently different things and to isolate these similarities so that they can be studied quantitatively. Such techniques are all-important in operations research.

The last phrase "under their control" emphasizes again that this is an applied science, concerned chiefly with the problems of immediate importance to the executive department. An operations research group should not report to the research department of a military service or of an industrial organization, for example. It must have direct and personal contact with the officer who makes the executive decisions, so that the group can know from him what are the important questions requiring decision and so that he can hear directly from them the results of their studies, which are to form a basis for his decisions.

The concept of staff function is perhaps more clearly understood in military organizations than in industrial or other governmental ones. Clearly operations research is a staff function. For this reason the group should be as small as possible, and all contact should be as personal as possible. Research activity need not be all short-range, however. There is need for long-range research in any operational problem. Yet, as with any applied science, the work must be directed towards the main goal. As with much scientific research, it is often the operations research group that can best decide whether a certain research is pertinent to the problem at hand or not.

1.1.3 Early Development

It should be apparent by now that there is no fundamental reason why operations research, as a distinct activity, should be less useful in nonmilitary operations than it has been in military operations, nor even that its major application should continue in the military field. The reasons for its start in World War II are not hard to find, however. During that struggle lives and national freedom were at stake, whereas with most industrial problems only money is at stake. The urges for scientists to enter the field were thus much greater, and the benefits, to begin with, were perhaps more obvious. In addition, more men of higher ability were available to turn to this field than there are usually in peacetime. The creation of a new field of applied science involves nearly as much ability and scientific initiative as does the creation of a field of pure science. In the present case it appeared necessary for research scientists of high caliber to take part in the initial effort. Naturally these same scientists would be of similar great utility later in the development of the field, but during peacetime they are usually engaged in more important research (more important to them) in pure science and so are unavailable to start a new field of applied science. Perhaps it required a great war to provide the proper combination of needs and willing intellects. The requirements for scientific experience and research ability are still quite high, in operations research, however.

1.1.4 Value of Operations Research

During the war operations research proved its worth in military applications, and today the Services, both in the United States and England, are provided with groups attached to the planning and operational parts of the higher staffs. An interesting appraisal of this work was given by Admiral E. J. King in his Final Report, issued December 8, 1945:

The complexity of modern warfare in both methods and means demands exacting analysis of the measures and counter-measures introduced at every stage by ourselves and the enemy. Scientific research can not only speed the invention and production of weapons, but also assist in insuring their correct use. The application, by qualified scientists, of the scientific method to the improvement of naval operating techniques and material, has come to be called operations research. Scientists engaged in operations research are experts who advise that part of the Navy which is using the weapons and craft—the fleets themselves. To function effectively they must work under the direction of, and have close personal contact with, the officers who plan and carry on the operations of war.

* * *

The late war, more than any other, involved the interplay of new technical measures and opposing countermeasures. For example, the German U-boats had to revise their tactics and equipment when we began to use radar on our antisubmarine aircraft; and we, in turn, had to modify our tactics and radar equipment to counter their changes. In this see-saw of techniques the side which countered quickly, before the opponent had time to perfect the new tactics and weapons, had a decided advantage. Operations research, bringing scientists in to analyze the technical import of the fluctuations between measure and countermeasure, made it possible to speed up our reaction rate in several critical cases.

Since the war operations research has been applied in a variety of industrial and governmental activities, with fairly universal success. If the subject is to develop in a healthy manner, its basis of support requires widening, and courses of training for work in the field are needed. It is the purpose of this book to indicate the techniques utilized by operations research, to indicate to students in science the existence of a career in this subject, and to illustrate by examples the possible range of usefulness of the techniques. Most of the examples chosen are from military applications, because these applications were first to be worked upon and the implications have had a longer time to be digested. The implications of these examples with regard to other, nonmilitary applications, should be obvious to the reader, however. It is expected that another five years of experience in this field will provide an equal number of industrial and nonmilitary governmental examples.


Before we attempt even a preliminary discussion of the techniques, personnel, and organization of operations research it will be well to quote a few examples of its working. These examples will be chosen, not for their importance or for the value of the results, but primarily to illustrate one or more of the points already made or to be made in this chapter. Many other examples illustrating these and other points will be given later in this volume.

1.2.1 Rearrangement of Use of Equipment

The first example, simple to the point of triviality, involves the line-up of soldiers washing their mess kits after eating at a field mess station. An operations research worker during his first day of assignment to a new field command noticed that there was considerable delay caused by the soldiers having to wait in line to wash and rinse their mess kits after eating. There were four tubs, two for washing and two for rinsing. The operations research worker noticed that on the average it took three times as long for the soldier to wash his kit as it did for him to rinse it. He suggested that, instead of there being two tubs for washing and two for rinsing, there should be three tubs for washing and one for rinsing. This change was made, and the line of waiting soldiers did not merely diminish in size; on most days no waiting line ever formed.

This example, trivial as it is, illustrates a number of the points already discussed in the first section and to be amplified later. In the first place the solution, when seen, was absurdly simple; anyone could have seen it, and it seems surprising that it required a trained scientist to point it out. Perhaps the scientist's preoccupation with problems involving flow had given him a predisposition to see the possibility of a solution and to ask the right questions. Here the right question concerned the relative time spent at each tub.

The next point to note is that the improvement was obtained with no added requirement in equipment. The tubs were merely rearranged as far as use goes. No "gadgetry" was needed.

The third point of interest is that the observation concerning the waiting line and the suggestion for improvement were made to someone who could do something about it and did. No doubt many of the soldiers waiting in line could, and perhaps did, make the observations made by the operations research worker. If so, the results of their observations and their possible suggestions for improvement never got to the person who could make the necessary operational decision, and so no improvement occurred.

One more point of interest here, to be expanded later in this volume, concerns the result of the suggested change. In theory, a change from two wash tubs plus two rinse tubes to three wash tubs plus one rinse tub should increase the flow through the line by 50 per cent. The result, however, was that the waiting line reduced practically to zero; in other words the dividends obtained were even greater than those predicted. It is an operational property of waiting lines that, the longer they get, the longer they tend to get. Many operations have this same self-aggravating property. A high-speed arterial highway, for instance, may carry Sunday traffic easily as long as no accident or other perturbation occurs to cause a momentary slowing down; as soon as a slowdown does occur, a traffic jam results. Some of the most rewarding applications of operations research turn up in the study of such self-aggravating operations. Although they are primarily nonlinear effects, they can usually be handled by known mathematical techniques and by the probability theory outlined in Chapter 2.

1.2.2 Changes in Setting, Rearrangement of Unit Size

In this first example the solution could have been given in a short time by any qualified efficiency expert; indeed a solution should have been arrived at by any intelligent person who took the trouble to look at the problem. In many cases, however, considerably greater amount of technical background is needed before the nature of the problem is seen and its solution is obtained. In the example quoted in section 3.4.8, where a simple change in the depth-setting of the aircraft antisubmarine depth charges was recommended to improve U-boat sinkings, a detailed probability study and some knowledge of the physical properties of depth charge fuzes was needed in order to arrive at the solution. Here again, however, an improvement in results by a factor of 2 was obtained with no substantial change in the equipment involved, simply a change in the depth-setting of the fuze. To have attempted to obtain an equivalent improvement by increasing the explosive charge, or by improvement of fire control, would have required years of development time and millions of dollars in production and installation cost.

The decision to increase the size of convoys and the result, that of reducing average ship loss, outlined in section 3.2.2, is another example of large effects being obtained with no change in equipment used, only change in the way it was used. Here again it was necessary to have a certain amount of knowledge concerning the behavior of ships in port and in convoy in order to see that an increase in size of a convoy would not bring concomitant deleterious effects. The operations research worker need not be an expert in the operation involved (indeed, too great familiarity with its details may handicap him), but he must have enough technical background to understand the fundamentals of the operation, enough mathematical ability to carry out the analysis involved, and, above all, the sort of impersonal curiosity that is the prime requisite of any scientific research worker.


Excerpted from Methods of Operations Research by Philip M. Morse, George E. Kimball. Copyright © 2003 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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