Methods of operations research

Front matter

DECLASSIFIED By authority Secretary of

Defense memo 2 August 1960 LIBRARY OF CONGRESS

DECLASSIFIED Dy authority Secretary of

Foreword

T his report, constituting Volume 2A of the Division 6 Summary Technical Report, describes the methods developed and employed during the period 1942-1945 by members of the Operations Evaluation Group [OEG] in the Headquarters of the Commander-in-Chief, U.S. Navy. This group, composed of civilian scientists, mathematicians, and statisticians, and initially designated the Anti-Submarine Warfare Operations Research Group [ASWORG] was established early in 1942 under the supervision of the Atlantic Fleet antisubmarine warfare officer, Captain (later Rear Admiral) W. D. Baker.

When Captain Baker requested the formation of this group, he stated that the antisubmarine warfare unit, as then constituted, was not in a position to evaluate properly (1) the probable effectiveness of suggested new weapons and (2) developments and procedures based upon mathematical studies and other available records.

Captain Baker defined what was desired and intended by quoting from a RAF Coastal Command memorandum on the subject, as follows:

“Experience over many parts of our war effort has shown that such analysis can be of the utmost value, and the lack of such analysis can be disastrous. Probably the main reason why this is so, is that very many war operations involve considerations with which scientists are specially trained to compete and in which serving officers are in general not trained. This is especially the case with all those aspects of operations into which probability considerations and the theory of errors enter. Serving officers of the highest caliber are necessarily employed in important executive posts, and are therefore, not available for detailed analytic work.”

As to the type of personnel required to staff these operations, Captain Baker quoted from the same memorandum :

“A considerable fraction of the staff of an operational research section should be of the very highest standing in science, and many of them should be drawn from those who have had experience at the Service Technical Establishments. Others should be chosen for analytic ability, e.g., gifted mathematicians, lawyers, chess players, etc. An ORS which contents itself with the routine production of statistical reports and narratives will be of very limited value. The atmosphere required is that of a first class pure scientific research institution, and the caliber of the personnel should match this. All members of an ORS should spend part of their time at operational stations in close touch with the flying personnel, and where possible, should occasionally go on operational or training flights.”

That the project should be undertaken and the proposed group established in the Navy was never questioned. The experience of the British and of large American industries in carrying on very similar operational analyses made certain that a suitably staffed group could be very effective. The project was assigned to Section C-4, NDRC, and under its contract with Columbia University, a staff was recruited.

Professor P. M. Morse, of the Massachusetts Institute of Technology, became project supervisor, and Dr. William Shackley was granted a leave of absence from the Bell Telephone Laboratories to act as director of research.

The operations performed by the ASWORG closely followed Captain Baker’s conception of how the group could assist the Navy. Also, Professor Morse was able to recruit personnel with qualifications very similar to those specified by Captain Baker. Although organizational changes occurred, the objectives of the group itself were not altered. With the creation of the Tenth Fleet as a means of coordinating antisubmarine warfare, the group, now under the sponsorship of the Office of Field Service [OFS], was made an integral part of the Fleet staff. As the activities of the group expanded to cover other fields, the name was shortened to Operations Research Group [ORG]. At the end of the war, the group was reorganized as the Operations Evaluation Group and assigned to the staff of the Chief of Naval Operations under a direct Navy contract with the Massachusetts Institute of Technology. It is by this latest organization that the present report has been prepared.

The material presented in this volume has been compiled from reports and memoranda issued by the group and from the first hand knowledge and experience which the authors gained during the war with the techniques and problems discussed. Specific examples of these general methods in their application to problems of submarine warfare may be found in Search and Screening , Volume 2B. These methods also underly the more historical treatment given in Volvii

FOREWORD viii ume 3, ASW Operations in World W ar II, as well as a wide category of similar investigations. Although the procedures employed were designed for applications involving the instruments, weapons and conditions prevailing during the last war, the methods and systematic processes of analysis developed have wide application to many military and civilian problems.

The Division wishes to thank the authors, Professor Morse and Dr. Kimball, for their work in preparing the volume. It is impossible to name the long list of Navy officers and some Army officers who gave support to the work of the Operations Research Group and who share credit for its performance. The full list would include many officers at operational bases and stations. However, special acknowledgement should be made of the cooperation and assistance received from Admiral W. D. Baker, from Admiral F. S. Low, Chief of Staff, Tenth Fleet, of the U. S. Navy, and from the British operations research groups.

John T. Tate Chief, Division 6

Preface

I n a sense, ‘this book should have no authors’ names, or else several pages full of names. Parts of the book were written by various persons during the past five years. What the undersigned have done is to collect the material, rewrite some in the light of later knowledge, expand some to make it intelligible for the lay reader, and cement the mosaic into what is fondly hoped to be a logical structure. Operations research during the war had to be anonymous, and much of the work must remain so.

Since the undersigned were members of the Operations Research Group, U. S. Navy, it is perhaps not surprising that the examples given are drawn chiefly from the work of this group, though an effort has been made to include examples from the work of other groups. Many persons have helped by discussions and editorial criticism, including members of other operations research groups in this country and in England. To mention a few would slight many others, so none will be named.

During the war the scope, methods, and triumphs of operations research were not appreciated by most scientists or by most military men because no information was freely available. If we are not to lose this valuable experience and background, some of it must be made available to the scientists and engineers as well as to the armed services. This is particularly important if the methods of operations research have important peacetime applications — as it is believed they do.

Philip M. Morse George E. Kimball

IX

Contents

CHAPTER PAGE

1 Introduction 1

Bibliography 161

Contract Numbers 162

Service Project Numbers 163

Index 165

CONFIDENTIAL xi

Chapter 1

I n world war ii, the phrase “operations research” has come to describe the scientific, quantitative study of operations of war. Perhaps a more descriptive term would be “polemology,” from the Greek word “polemos” meaning warfare, but the more familiar “operations research” will be retained in the present treatise because it suggests that the methods can be used to study other operations than those of war.

The phrase, operations research, is of recent origin, and represents one phase of the expansion of science to study more and more complex phenomena. Previous aid which science had given warfare was chiefly in the direction of providing new weapons and instruments. Perhaps the most celebrated classical example was the work of Archimedes in defending the city of Syracuse from the Romans. In the Renaissance, Leonardo da Vinci spent much of his engineering abilities in military applications, and, in the seventeenth century, the famous Vauban utilized his considerable geometrical abilities in designing fortifications, and his inventive genius in devising the bayonet and the method of ricochet fire. Fourier, Monge, and Bertholet were retained by Napoleon as his scientific advisers. Of these, only Vauban made any real contributions in applying science to suggest better ways of using weapons, rather than adding new “gadgets.”

In more recent times, warfare has become so complex that most scientists have confined their contributions to the devising of new weapons, and have left the tactical use of these weapons to the professional soldier, and their strategic use to the professional politician. The utility, however, of the coordinated scientific attack on a wide variety of nonmilitary problems has been amply demonstrated in the past three decades. It is not surprising, therefore, that World War II has demonstrated the effectiveness of assigning a group of scientists to study warfare itself.

The present volume is a first attempt to describe some of the methods which have proved most valuable in the study of warfare, and to indicate possible fruitful lines for further development, military and nonmilitary. This first chapter outlines the scope and methods of the subject. The second chapter discusses the relevant portions of the theory of probability, which is the field of mathematics most useful for this work. The rest of the chapters discuss techniques which have been particularly useful, with illustrations picked from work done in the recent war. One aspect of this work, the theory of search for an enemy craft, has grown to such considerable proportion that it deserves more space than can be given it here. Another volume of this series will be devoted to the theory of search and screening (see Division 6, Volume 2B).

11 SCOPE OF OPERATIONS RESEARCH

The scope of operations research has been succinctly illustrated in a letter (dated August 17, 1945) from Fleet Admiral E. J. King to Secretary of the Navy James V. Forrestal, concerning the work of the U. S. Navy Operations Research Group:

Since April 1942 the Operations Research Group has been of service to the Navy as a scientific advisory group to the forces afloat and to the Commander in Chief, United States Fleet, and Chief of Naval Operations, dealing with naval scientific evaluation from the point of view of the operational user of naval equipment. This group has been of active assistance in:

(a) The evaluation of new equipment to meet military requirements.

(b) The evaluation of specific phases of operations (e.g., gun support, AA fire) from studies of action reports.

(c) The evaluation and analysis of tactical problems to measure the operational behavior of new material.

(d) The development of new tactical doctrine a to meet specific requirements (e.g., anti-submarine screens, screens for slow moving damaged ships, etc.)

(e) The technical aspects of strategic planning.

(f) The liaison for the fleet with the development and research laboratories, naval and extra-naval.

This description again emphasizes the important point that operations research is not a study of equipment, but of operations which involve equipment and men.

“Doctrine may be defined as a cumulation of principles, applicable to a subject, that have been developed through experience, and theory, that represent the best thought of the units concerned, and that indicate and guide but do not bind in practice. 1

1.1.1 Reasons for Increase in Importance

of Science in Warfare

There are a number of reasons why the scientific study of warfare paid more practical dividends in World War II than in previous ones. In the first place, recent wars have tended more and more to be made up of a series of similar operations rather than a set of disconnected battles. The operation of strategic bombing is very much the same from mission to mission; the target and the weather change, but the enemy antiaircraft and fighter defense are roughly similar. The operations of submarines in attacking enemy shipping are also, in a general sense, repeated experiments in tactics. Even landing operations occurred often enough in World War II, under roughly similar conditions, so that one could begin to look for similarities as well as differences between these actions. With data available on the results of such large sequences of roughly similar operations, it became possible to study the operations in a quantitative manner. As soon as numbers can be obtained, scientific methods can be applied.

In contrast to World War II, earlier wars consisted chiefly in engagements which were strongly conditioned by the terrain, by the winds, or by other nonrepetitive agents. Not enough similar engagements were fought so that these highly variable aspects could be averaged out. Consequently few quantitative measures could have been obtained, and tactics and strategy remained an art, to be learned only by long experience in action.

1.1.2 Increase in Mechanization

Another reason for the growing usefulness of the application of scientific methods to tactics and strategy lies in the increased mechanization of warfare. It has often been said, with disparaging intent, that the combination of a man and a machine behaves more like a machine than it does like a man. This statement is in a sense true, although the full implications have not yet been appreciated by most military and governmental administrators. For it means that a men-plus-machines operation can be studied statistically, experimented with, analyzed, and predicted by the use of known scientific techniques just as a machine operation can be. The significance of these possibilities in the running of wars, of governments, and of economic organizations cannot be overemphasized.

1.1.3 Speed of Technical Advance

A third reason for the increasing importance of operations research in warfare is the increasing tempo of obsolescence in military equipment. In World War II a number of potentially useful weapons became obsolete before the forces at the front had had time to learn how to operate them efficiently. When this condition holds, it becomes extremely important to be able to plan the best employment of each weapon ahead of time. When we can no longer have the time to learn by lengthy trial and error on the battlefield, the advantages of quantitative appraisal and planning become more apparent.

This aspect of the situation is pointed out in the following excerpt from the Final Report by Admiral E. J. King to the Secretary of the Navy, issued December 8, 1945:

The complexity of modern warfare in both methods and means demands exacting analysis of the measures and countermeasures 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.

During the war we succeeded in enlisting the services of a group of competent scientists to carryout operations research. This group was set up as a flexible organization able to reassign personnel quickly when new critical problems arose. Fiscal and administrative control of the group was originally vested in the Office of Scientific Research and Development. The group as a whole was assigned to the Navy for functional control, and in the course of time was attached to my Headquarters.

The initial impulse toward the formation of such a group arose in April 1942, during the early days of the anti-submarine war. With the cooperation of the Anti-submarine Division of the National Defense Research Committee, seven scientists were recruited by Columbia University and assigned to the Anti-submarine Warfare Unit, Atlantic Fleet.

During the year 1942 the group was considerably increased in size, and in July 1943, at a strength of approximately forty members, it was incorporated into the staff of the Tenth Fleet as the Anti-Submarine Warfare Operations Research Group. Subsequently the administrative responsibility for the group was transferred from Columbia University to the Office of Field Service, without alteration in relationships with the Navy. In October 1944, with the decline of the submarine menace, the group was transferred to the Readiness Division of my Headquarters and renamed the Operations Research Group. At the close of the war it consisted of seventy-three scientists, drawn

SCOPE OF OPERATIONS RESEARCH from a wide variety of backgrounds. Many of the members were attached, as the need arose, to the staffs of fleet and type commanders overseas, and at operating bases in war theaters. So far as possible they were afforded the opportunity of observing combat operations at first hand.

Operations research, as it developed, fell into two main categories: theoretical analysis of tactics, strategy and the equipment of war on the one hand; and statistical analysis of operations on the other. Each type of naval operation had to be analyzed theoretically to determine the maximum potentialities of the equipment involved, the probable reactions of the personnel, and the nature of the tactics which would combine equipment and personnel in an optimum manner. Action reports, giving the actual results obtained in this type of operation, were studied in a quantitative manner in order to amplify, correct, and correlate closely the theoretical analysis with what was actually happening on the field of battle. The knowledge resulting from this continued cross-check of theory with practice made it possible to work out improvements in tactics which sometimes increased the effectiveness of weapons by factors of three or five, to detect changes in the enemy’s tactics in time to counter them before they became dangerous, and to calculate force requirements for future operations.

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 anti-submarine 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.

In the normal course of military expediency, strenuous efforts are put forth to develop and manufacture new technical equipment and weapons. These must be distributed to the operating commands, with but limited time in which to develop the best methods for their tactical use. As the weapons get into use, there begins to flow back an increasing mass of data in the form of action reports, performance sheets, and intelligence summaries, which are accumulated in local commands or at theater headquarters. The significance of the experience embodied in these data can only be evaluated through the determined efforts of properly trained men with scientific backgrounds, clothed with sufficient authority, facilitated by proper administrative organization, and freed from other responsibilities to concentrate their efforts to this end. Such evaluation will indicate the relative merits or deficiencies of the new equipment and ordnance, and of the tactics incident to their use. In addition to indicating means of technical improvements, the analyses should also serve as bases for promoting improved training methods, to make more efficient the performance of operating personnel.

1 * 1.4 Scope of Work

The nature of research work is admittedly not subject to exact definition. Without attempting to set a limit to the point where operations research merges into developmental work, there are certain bounds within which the work of an operations research group is defined.

The main function of an operations research group is to analyze actual operations, using the data to be found in action reports, track charts, dispatches, intelligence summaries from actual interviews of operating personnel, etc. The operations research man studies weapons and equipment from the “user” point of view, both in trials and in field use. He is not a statistical clerk; statistical analysis is merely one of the tools which he uses in his analytical task. In order to extract the best operational use of new weapons and gear coming into service, it is necessary not only to evaluate the prospective performance from a priori approaches, but also to analyze observational data from experimental and testing establishments as well as from actual military operations, no matter how complicated. The tactical possibilities and limitations of any such equipment must be studied in relation to the actual facts of military operations. Such a performance analysis is essential to a decision concerning the requirements for a new weapon or device, and to the discovery of the most profitable channel in which to devote developmental efforts.

It must be emphasized again that the operations research worker is not a “gadgeteer,” spending most of his time devising new equipment or modifying old equipment. Such activity is important, and also requires technically trained men to help the services; but it is an activity which should be carried on primarily by scientists attached to the service commands or bureaus, rather than by men attached to the operational commands, as are the operations research men. The operations research worker must often resist the urge to turn from the refractory problems of strategy and tactics, which are primarily his job, to the more congenial task of “playing” with a piece of new equipment. True, there are times when the operations research man is the only technical man with an operational command, and equipment modifications must be done by him or it does not get done. In this case, of course, the necessary “gadgeteering” is carried through. However, the operations research man must keep in mind, in these cases, that he is stepping out of his own field, and that such activity should not be allowed to keep him long from his proper studies of operations. It is possible to call in technical men from the service commands to do the gadgeteering, but there is no one else to do the operations research if he does not do it.

An important difference between operations research and other scientific work is the sense of urgency involved. In this field a preliminary analysis based on incomplete data may often be much more valuable than a more thorough study using adequate data, simply because the crucial decisions cannot wait on the slower study but must be based on the preliminary analysis. The worker cannot afford to scorn superficial work, for wars do not wait for exhaustive study (although the exhaustive study should also be made, to back up the preliminary work) . This is an additional reason for divesting the operations research worker from extraneous responsibilities and duties, so that he can have as much leisure time as possible to make as thorough a study as can be made before the crucial decision must be made.

12 METHODS OF OPERATIONS RESEARCH

The methodology of this new application of science is, of course, related to the type of data which can be obtained for study; in the present case, it usually turns out that a limited amount of numerical data is ascertainable about phenomena of great complexity. The problems are therefore somewhat nearer, in general, to many problems of biology or of economics rather than to most problems of physics, where usually a great deal of numerical data is ascertainable about relatively simple phenomena. However, operations research, like every science, must not copy in detail the technical methods of other sciences, but must work out methods of its own, suited to its own special material and problems. The object here is to assist in the finding of means to improve the efficiency of operations in progress or planned for the future. To do this, past operations are studied to determine the facts, theories are elaborated to explain the facts, and finally the facts and theories are used to make predictions about future operations. This procedure insures that the maximum possible use is made of all past experience.

1.2.1 Statistical Methods

The most important single mathematical tool of operations research is probability and statistical theory. The data upon which the research is based will come, for the most part, from statistical studies of operations. These operations are uncontrolled in the scientific sense, and therefore cannot be considered as the equivalent of experiments. The data are observational, therefore, rather than experimental; as is usual in such cases, ingenuous statistical techniques may lead to serious errors in the results obtained.

Statistical analysis is not fruitful unless there are available for study a large number of reports on operations which are roughly similar in nature. For this reason, operations research is at first most successful in those fields of warfare where the individual operations are numerous, simple, and roughly similar. Bombing operations on a target of a given type satisfy these requirements, for a great number of such operations are carried out under similar weather conditions and under somewhat similar conditions of enemy opposition. Other examples have been mentioned earlier in this chapter.

When we come to the larger actions of warfare, however, the occasions are few, the complexities of the action are great, and the dependence of the outcome on the exigencies of the moment are obvious. In studying such actions in a statistical manner, the progress of operations research will naturally be slow. Certain aspects of these larger operations can be studied in detail, and the whole picture perhaps can eventually be put together. From what has been said, however, it can be appreciated that the classical naval engagement between surface vessels, or the classical land battle, is, in general, difficult for operational research to attack early in its development. Only after the simpler cases mentioned above have been thoroughly understood, can an attempt be made to analyze these more complex operations. Strategy and tactics in the large will always be an art, though operations research may help its practice by providing tools of increasing power, just as the study of physiology has improved the art of medicine.

1.2.2 Field Assignments, Collection of Data

The rapid collection of operational data in wartime is immeasurably improved by the assignment of a scientifically trained observer as close to the opera-

METHODS OF OPERATIONS RESEARCH tions as is feasible. In earlier centuries this was quite possible because of the small scope of most operations. In the World War I however, it became exceedingly difficult, primarily because the scope of the operations was so large that, if the scientist got close enough to see the details of operations, he inevitably became a participant rather than an observer. The problem has become somewhat more simplified in World War II, due primarily to the introduction of the airplane. In all combat involving aircraft, the technical observer can be placed at a forward air base and get his reports at first hand from the participants immediately after they have returned from the operations. It has been found by experience that important facts concerning the operations can often only be determined by having a technically trained observer question the operational personnel at first hand.

Another important function of the men in the field is to see that the usual action reports contain as much useful data as possible. Because these men know the kind of data that are most amenable to analysis, they can try to see that the reports are as complete as possible and are as “painless” as possible for the person making them out, and that the reports get sent as quickly as possible to the headquarters group for analysis. They can also detect at first hand what kinds of intelligence material are likely to be unreliable, due to local factors which are not always appreciated at headquarters.

The observers’ reports, together with the usual operational reports, must then be sent in to a central group which analyzes the results from all theaters and compares them for differences and similarities. The importance of the close interrelation between the field observers and the central group is obvious. In practice it has been arranged that members of the central group spend a certain part of their time in the field, to return later to the central group with increased insight into the operations they are studying.

1-2.3 Limitations of Operational Data

Statistical analysis is part of the observational aspect of operational research. The operations are not controlled in the scientific sense, and insight into the reasons for their success or failure can only be obtained by studying large numbers of similar operations, so as to find out by statistical methods the effects of the variation of one or more components of the operation. This imposes certain limitations on the usefulness of the results of the statistical analysis, for the range of variation of the various components in the operation will, by the nature of things, be rather limited. Once successful tactics have been devised, it becomes less and less likely that the opponents in the individual operation will deviate widely from the accustomed mean. Consequently the operational data can only be utilized (by calculus of variations methods) to find whether small changes in components will improve or diminish the results.

The results of such variational studies are quite useful, and the applications sometimes quite striking, since often the enemy’s reaction to a quantitative change in our operation is a qualitative change in his counteraction. However, a study of small variations is not usually sufficient. In many cases what is interesting is not a small change in the tactics used but a completely different combination of actions, a “mutation” of the operation, as it were. These new tactics may not be predictable from the old operations by variational calculation, for the extrapolations may be too large for first order terms. Here a purely mathematical analysis of the whole operation, or of parts of it, may supply the necessary knowledge; or it may be possible that a series of discussions with the operating personnel may bring the necessary insight.