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OPERATIONS RESEARCH AND INDUSTRIAL ENGINEERING: THE APPLIED SCIENCE AND ITS ENGINEERING Norman N. Barish New York University (Received May 4, 1962) Programs of education in industrial engineering, operations research, and management science should be based upon definitions of the respective fields; upon a concept of the present and future scopes and limitations of professional activity in these fields; as well as upon an evaluation of what academic disciplines provide the most suitable preparation for the respec- tive professional activities. This paper examines these subjects and con- cludes that educational programs for these professions should have much in common and that, although a wide variety of quite different types of edu- cational experience can provide the basis for professional work in industrial engineering and in operations research, these educational programs should emphasize the system and the decision-making approaches to the science, engineering, and practice of management. DEFINITIONS of the fields of operations research,management science, and industrial engineering are prerequisite to the development of programs of education for these professions. Definition of Operations Research MORSE AND KIMBALL, 1] in one of the first books on operations research published in the United States, state that operations research is a scientific method of providing executive departments with the quantitative basis for decisions regarding the operations under their control. JOHNSONM2' defines operations research as the prediction and comparison of the values, effectiveness, and costs of a set of proposed specific courses of action involving man-machine systems. It is based on a model of the action that has been analytically described by a logical, and, when feasible, a mathematical methodology and that has had the values of the basic action parameters determined either from a historical analysis of past actions, from designed operations, experiments, or by calculations. Be- cause all human and machine factors are meant to be included, an estimate of the uncertainty in the predicted outcome, and in the values, effectiveness, and costs of the proposed action, is provided. CHURCHMAN, ACKOFF, AND ARNOFF[3' describe operations research as 387

Transcript of OPERATIONS RESEARCH AND INDUSTRIAL ENGINEERING… Research and Industrial... · OPERATIONS RESEARCH...

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OPERATIONS RESEARCH AND INDUSTRIAL ENGINEERING: THE APPLIED SCIENCE AND

ITS ENGINEERING

Norman N. Barish

New York University

(Received May 4, 1962)

Programs of education in industrial engineering, operations research, and management science should be based upon definitions of the respective fields; upon a concept of the present and future scopes and limitations of professional activity in these fields; as well as upon an evaluation of what academic disciplines provide the most suitable preparation for the respec- tive professional activities. This paper examines these subjects and con- cludes that educational programs for these professions should have much in common and that, although a wide variety of quite different types of edu- cational experience can provide the basis for professional work in industrial engineering and in operations research, these educational programs should emphasize the system and the decision-making approaches to the science, engineering, and practice of management.

DEFINITIONS of the fields of operations research, management science, and industrial engineering are prerequisite to the development of

programs of education for these professions.

Definition of Operations Research

MORSE AND KIMBALL, 1] in one of the first books on operations research published in the United States, state that operations research is a scientific method of providing executive departments with the quantitative basis for decisions regarding the operations under their control.

JOHNSONM2' defines operations research as the prediction and comparison of the values, effectiveness, and costs of a set of proposed specific courses of action involving man-machine systems. It is based on a model of the action that has been analytically described by a logical, and, when feasible, a mathematical methodology and that has had the values of the basic action parameters determined either from a historical analysis of past actions, from designed operations, experiments, or by calculations. Be- cause all human and machine factors are meant to be included, an estimate of the uncertainty in the predicted outcome, and in the values, effectiveness, and costs of the proposed action, is provided.

CHURCHMAN, ACKOFF, AND ARNOFF[3' describe operations research as 387

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the application of scientific methods, techniques, and tools to problems involving the operations of a system so as to provide those in control of the system with optimum solutions to the problems.

Definition of Management Science

THE INSTITUTE OF MANAGEMENT SCIENCES[41 identifies its objects as the identification, extension, and unification of scientific knowledge that con- tributes to the understanding and practice of management.

SYMONDSW51 defines management science as the science of the conduct of group enterprises directed in purpose. Management science, in its present state of development, has little in the way of general laws and general truths. But, says Symonds, from the great body of general management knowledge and experience and from specific operations-re- search applications, will come the fundamental relations of predictive theory that will distinguish management science as a true science.

Operations Research and Management Science

The definitions of management science can apply equally well to oper- ations research. Differences between operations research and management science are difficult to establish.

LATHROP,P] discussing the question of a merger of the Institute of Management Sciences and the Operations Research Society of America, writes that there have been some efforts to distinguish between manage- ment science and operations research, but it is difficult to see where any differences have been well established. TIMS speaks of the science of managing rather than the science of operating, but this seems to be a distinction without a difference. Lathrop cites MERRILL FLOOD as implying that operations research is more engineering application to practical prob- lems than it is research, that operations research is problem oriented, whereas management science is knowledge oriented. It has been suggested that management science embraces a much wider field theories of organi- zation, of communications within groups, of decisioning, of utility and that operations research is a smaller part of management science. These possible distinctions, though worthy, are not yet reflected in the activities of the two societies, nor are they generally recognized or accepted. Lathrop concludes that a case has been made to support the conclusion that the two organizations have virtually identical objectives, fields of research, meetings, publications, and membership cross-sections.

Operations research, in this writer's opinion, is almost, but not com- pletely, synonymous with management science. It emphasizes the study of those areas of management science which have more immediate usefulness for practical application. Arguments can be made for some additional

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distinctions between operations research and management science. But these distinctions do not serve any useful purpose in connection with the issues that are discussed in this paper. Operations research and manage- ment science will therefore be treated as the same from here on in this paper.

Definition of Industrial Engineering

The official definition of the American Institute of Industrial Engineers reads as follows: industrial engineering is concerned with the design, im- provement, and installation of integrated systems of men, materials, and equipment; drawing upon specialized knowledge and skill in the mathe- matical, physical, and social sciences together with the principles and methods of engineering analysis and design, to specify, predict, and evaluate the results to be obtained from such systems.

In a section of the Industrial Engineering Handbook, URWICK [71 states that industrial engineering activities, while not directly concerned with the installation and maintenance of mechanical appliances, are directly con- cerned with their effective use and, hence, with their adaptation to the human element in the business complex on scientific lines. The common distinguishing feature of these activities, according to Urwick, is that they are primarily concerned with the most effective use of mechanical equip- ment and hence postulate a basic knowledge of the principles on which such equipment works, regardless of the function to which it is applied. They range from plant and office layout through work methods and planning, the reduction of material and labor costs, simplification and standardization, to base-rate analysis and quality control.

Operations Research and Industrial Engineering

Science is accumulated knowledge systematized and formulated with reference to the discovery of general truths or the operation of general laws.P8] COHEN AND NAGEL[9] say that if we look at all the sciences not only as they differ among each other but also as each changes and grows in the course of time, we find that the constant and universal feature of science is its general method, which consists in the persistent search for truth by the application of logic. Science is thus characterized by the orderly accumulation of knowledge about phenomena and their relations as well as the methods of acquiring this knowledge.

Engineering includes the arts and sciences by which the properties of matter and the sources of power in nature are made useful to man in systems, structures, equipments, machines, and manufactured products.

We may distinguish between unapplied and applied science. When the purpose of the search for knowledge is to provide systems, structures, etc.,

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which are useful to man, the science is an applied one. When the purpose is to extend the boundaries of knowledge of a class of phenomena regardless of its practical utility, the science is unapplied. Obviously, there is much overlap between unapplied and applied science because most knowledge has potential, if not immediate, usefulness.

The distinguishing characteristic of scientific activity is research. Thus, a scientist may engage in unapplied research or applied research. (Engineering research is applied research.) The distinguishing character- istic of engineering activity is design. Thus, an engineer may engage in the design of systems, structures, products, etc.

TABLE I

CONCEPTUAL RELATIONS BETWEEN SCIENCE, APPLIED SCIENCE, AND ENGINEERING

Applied research Dsg n Activity Unapplied research (including engi- Design and

neering research) application

Field Science Applied science Engineering

Physics, chemistry, mathematics, etc. Aeronautical Aeronautical science engineering

Examples Physiology, biochemistry, psychol- Medical science Medicine ogy, etc.

Statistics and mathematics, psychol- Operations re- Industrial engi- ogy, economics, etc. search neering

Some engineers will engage in applied research. A few engineers will even engage in unapplied research. These engineers are then functioning as applied and pure scientists, respectively. Also, some scientists will engage in engineering design. However, by and large, scientists will per- form unapplied and applied research and engineers will perform engineering design and some applied research.

The conceptual relations between science, applied science, and engi- neering, with examples drawn from several fields including operations research and industrial engineering, are illustrated diagrammatically in Table I.

Engineering disciplines are not always based upon previous scientific developments. Much engineering therefore partakes of the properties of an art. When there is a real need for a product, process, or system, engineering will frequently develop the practical technology before the scientific background has been fully discovered. Rules-of-thumb based

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upon past experience and modified by the intuitive judgment that is de- veloped by working with problems are therefore important parts of much engineering practice.

The field of knowledge covered by operations research, management science, and industrial engineering is managerial systems. The body of scientific knowledge in this field is not as large as many would like. How- ever, as CHURCHMAN, ACKOFF, AND ARNOFF[101 have pointed out, no science has ever been born on a specific day. Each science emerges out of a con- vergence of an increased interest in some class of problems and the develop- ment of scientific methods, techniques, and tools that are adequate to solve these problems. Operations research is no exception. Its roots are as old as science and the management function.

Operations research is the applied science of managerial systems. In- dustrial engineering is the engineering of managerial systems. Manage- ment is the practice of directing and controlling managerial systems. The relation between industrial engineering and operations research is the same as that of any field of engineering and its applied science.* It is analogous to the relation between medicine and medical science or aeronautical engineering and aeronautical science.

Thus, among other things, industrial engineering practitioners are called upon to locate new plants and design their physical layouts; to analyze and plan production schedules and inventories; to diagnose and correct causes of poor quality in production; to devise ways to improve the pro- ductivity and morale of people at work; to study the feasibility of equip- ment replacement; to evaluate opportunities for increased automation; to measure the effectiveness of marketing, advertising, and other distribution policies; to design organization structures to meet the requirements of modern industry.

While the industrial engineer should be primarily concerned with the application and modification of existing techniques to these problems as they occur, the operations researcher should be endeavoring to discover fundamental relations and to develop new approaches, models, and tech- niques. Obviously, the two fields overlap in many areas.

The progress of operations research, the applied science, is important to the development of industrial engineering, the professional application. The progress of industrial engineering is also important to operations re- search because industrial engineering provides the payoff for the scientific research and development.

* The term 'industrial' in industrial engineering is used very broadly to include service, distributive, governmental, medical, agricultural, military, and many other types of activities. Industrial engineering and operations research are thus not confined to the factory.

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LEHRERn[t1 an industrial engineer, states that the operations-research scientist should remain a scientist in his orientation and the industrial engineer should remain an engineer and be preoccupied with solving practical problems.

JOHNSON,[12] an operations researcher, takes much the same point of view as Lehrer and this writer. He states his belief that unless operations research remains primarily research it will wither and die and retain no desirable professional content of its own. It must be concerned continu- ously with research in the broadest operational sense, rather than merely with the repetitive operational engineering application of previously suc- cessful research.

Operations-Research and Industrial-Engineering Practice

This distinction between operations research and industrial engineering is not clear-cut in practice. A large proportion of persons calling them- selves operations researchers are engaged in activities that Johnson and this writer would classify as engineering.

Many persons who call themseves operations researchers are really performing the work of industrial engineers. This is not unusual: scientists frequently perform the work of engineers when a field is developing rapidly. It is usually an indication that, in one or more areas, the engineering discipline has not yet developed educational patterns that will enable its practitioners to perform in the most effective manner. Electrical and nuclear engineering versus electronic and nuclear science provide parallels to the industrial-engineering versus operations-research relation.

A large percentage of the persons practicing electronic engineering years ago were applied scientists, with training in physics. This situation occurred because electrical engineers were not, in general, trained to perform this function. These persons practicing electrical engineering considered themselves physicists because their academic training was in physics. Today, a substantial percentage of the persons performing nuclear engi- neering were trained as physicists or chemists because engineering training is only now being developed to provide the necessary background for this engineering work. A similar situation exists in many aspects of industrial engineering in which operations researchers with scientific education are performing engineering tasks. These persons consider themselves oper- ations researchers (scientists) because their training was as scientists. But they are doing engineering work, analogous to a physicist doing electrical or nuclear engineering work. Of course, a good deal of this intermixture of scientists and engineers is due to the impossibility of placing people into neat occupational compartments and keeping them there.

It is the responsibility of industrial engineering to adjust its training

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programs to provide the necessary backgrounds that will enable its prac- titioners to perform effectively in all its phases.

Surveys of Industry Practice

Various surveys designed to indicate the activities performed by persons who are called industrial engineers or operations researchers confirm the view that many persons with the title industrial engineer or operations researcher are performing functions in the same areas.

On the basis of information from over one hundred industrial plants, OVERCASTM]3' notes the following percentages of companies in which the industrial engineering department was responsible for the indicated func- tions: time study, 94 per cent; work simplification, 91 per cent; methods, 88 per cent; wage incentives, 85 per cent; materials handling, 72 per cent; cost reduction, 68 per cent; machine utilization, 60 per cent; plant layout, 54 per cent; job evaluation, 50 per cent; cost analysis, 48 per cent; oper- ations research, 45 per cent; customer estimating, 34 per cent; equipment selection, 28 per cent; administrative procedures, 27 per cent; planning and scheduling, 17 per cent; production control, 11 per cent; product design, 8 per cent; and safety, 4 per cent.

HOVEY AND WAGNER[141 report the following percentages of positive responses (from the 90 firms who replied to the questionnaire) indicating actual operations research applications in the areas noted: forecasting, 57 per cent; production scheduling, 47 per cent; inventory control, 45 per cent; quality control, 33 per cent; transportation, 26 per cent; advertising and sales research, 20 per cent; maintenance and repair, 16 per cent; accounting procedures, 16 per cent; plant location, 15 per cent; equipment replacement, 15 per cent; packaging, 13 per cent; and capital budgeting, 11 per cent. Several companies also added to the operations-research application areas: weapon system analysis, tax assessment analysis, opti- mum capacity studies, product development, personnel selection and ad- vancement, and paperwork scheduling.

Comparing these survey results, it is apparent that industrial engineers and operations researchers are working in many of the same areas. The survey results do not, of course, reveal whether the persons are engaged in scientific research or in engineering design and application. However, one may surmise that a larger percentage of operations researchers than in- dustrial engineers are engaged in scientific research and a larger percentage of industrial engineers than operations researchers are engaged in engineer- ing practice.

Educational Backgrounds of Practitioners

We are also concerned with the question: what are the best educational backgrounds for work in these respective fields? A first approach to this

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question is to examine the educational backgrounds of currently active practitioners.

OVERCAST[151 reports the following distribution of degrees in various areas by 1015 practitioners in the industrial engineering departments in- cluded in his survey: industrial engineering, 24.6 per cent; business adminis- tration, 17.7 per cent; mechanical engineering, 10.7 per cent; other degrees, 8.9 per cent; no degree, 38.1 per cent.

HOVEY AND WAGNER[161 report the following distribution of degrees in various areas by 451 practitioners on operations-research staffs; mathe- matics, 22.6 per cent; mechanical engineering, 12.1 per cent; aeronautical engineering, 10.3 per cent; chemistry, 8.4 per cent; business administration, 6.8 per cent; industrial engineering, 6.6 per cent; electrical engineering, 6.6 per cent; economics, 3.9 per cent; statistics, 3.4 per cent; chemical engineering, 2.8 per cent; physics, 2.0 per cent; others, 14.5 per cent.* Of these operations-research practitioners, 61 per cent held bachelor's degrees only, 28.2 per cent master's degrees, and 10.6 per cent doctorates. (The percentage of advanced degrees reported for industrial engineers by Over- cast was negligible.)

Thus, 35.3 per cent of the persons titled industrial engineer and 38.4 per cent of the persons titled operations researcher are reported to have degrees in a branch of engineering. Of the industrial engineers, 17.7 per cent had business administration degrees as compared to 6.8 per cent of the operations researchers. Mathematics and statistics degrees were held by 26.0 per cent of the operations researchers, but by relatively few in- dustrial engineers. All operations researchers had at least a bachelor's degree, whereas 38.1 per cent of the industrial engineers had no college degree. A substantial portion of industrial engineers appear to have ob- tained their engineering competence on the job and through in-plant training programs.

A large proportion of operations researchers have undertaken graduate studies. This is what should be expected because they are engaged in the more scientific-research aspects of the field. It is interesting to note the distribution of areas of specialization of the doctorates reported by Hovey and Wagner: mathematics, 35 per cent; chemistry, 10 per cent; statistics, 10 per cent; physics, 8 per cent; mechanical engineering, 6 per cent; elec- trical engineering, 6 per cent; economics, 4 per cent; business, 2 per cent;

* HERTZ, independently, using a somewhat larger sample of 729 individuals, reported quite comparable percentage figures if we consider mathematics and sta- tistics as one group: engineering, 42.3 per cent; science, 18.4 per cent; mathematics, 15.6 per cent; statistics, 11.4 per cent; miscellaneous, 4.8 per cent; accounting and business, 4.7 per cent; economics, 2.4 per cent. (D. B. Hertz, "Progress of Indus- trial Operations Research in the United States," in Proceedings of the First Inter- national Conference on Operational Research, OPERATIONS RESEARCH SOCIETY OF AMERICA, 1957, p. 462.)

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aeronautical engineering, 2 per cent; others, 17 per cent. The persons with doctorates, who are probably engaged in the most scientific aspects of operations research, have educational backgrounds more concentrated in mathematics, statistics, and physics than do operations researchers who do not have doctorates.

These statistics provide a general description of the educational back- grounds that current industrial-engineering and operations-research prac- titioners possess. The statistics therefore provide clues to some of the disciplines that may be usefully emphasized in our educational programs. However, they also indicate that a wide variety of quite different types of educational experience can provide the basis for professional work in industrial engineering and operations research.

Opinions of Operations-Research Practitioners

We thus see that the educational background of operations researchers who are engaged in the scientific rather than the engineering aspects of the industrial-engineering-operations-research field has tended to be concen- trated in mathematics, statistics, and physical science. This is to be ex- pected because, lacking specialized educational programs that train persons for operations research, the persons who will most naturally enter this field will be those trained in the methods of mathematics and science. They can adapt these methods in their research to develop approaches that will solve the complex problems faced by management in modern industry.

There is considerable variation of opinion among leading practitioners of operations research regarding the best training and background for this field. Thus, MORSE AND KIMBALL[17I suggest that the particular type of mentality that is a success in operations research appears to be found most frequently in physics and biology and their associated sciences. A tend- ency to look at an operation as a whole, common to theoretical research, is needed. The special outlook seems to be found somewhat less commonly in mathematics, engineering, and economics, although there are some brilliant exceptions, according to Morse and Kimball.

CHURCHMAN, ACKOFF, AND ARNOFF[181 believe that the scientist who is intent upon the pursuit of knowledge for its own sake is a poor risk. So is the scientist who is wedded to the laboratory: the complicated data of the real world are in too great contrast to the controlled conditions of the laboratory. The perfectionist, who is more intent upon the complete- ness of the end result than he is upon meeting a deadline, is also a poor risk. The scientist or engineer who has worked in two or three related fields of specialization, ostensibly because he has not been satisfied with the answers to be found in any one, is a good risk.

GOODE AND MACHOL1191 suggest that the operations researcher is char- acterized by academic training in one of the scientific disciplines, usually

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in one of the natural sciences, and almost always with a solid grounding in mathematics. He has a flare for broad study and the ability to take the large viewpoint. He wishes to study operations and to drop out of the picture as soon as equipment must be designed, but to return later to evaluate the equipment and determine the best way of using it.

DORFMAN[201 feels that economists have contributed to the development of operations research far out of proportion to their numbers. The econo- mist comes to operations research with a number of important ideas already instilled, among them an appreciation of the importance of economic substitution, a sophistication about the objectives of enterprises, an aware- ness of the importance of marginal trade-offs, and, most important, a realization that physical quantities are subsidiary to values in a decision process. According to Dorfman, the economist also inherits from his training a number of disabilities, including ignorance of the technical side of business and industry and a belief in the existence of production func- tions.

Similar arguments are made for other physical, social, and human sciences, including chemistry, psychology, physiology, sociology, etc., as the best educational background for operations research.*

There is merit in all of these and other prescriptions of desirable edu- cational backgrounds for operations research. Many aspects of the various operations-research curricula being developed in universities throughout the country are in accord with these suggestions. Moreover, students should be permitted to follow programs specifically designed to meet their indi- vidual interests and needs.

Flexible Educational Programs

Relatively few schools have as their objective the training of applied scientists exclusively. The more common situation is to have an engineer- ing school with a high orientation towards applied science or to have a science school with a high orientation towards applied science. Applied scientists have usually received their training either in schools of science or in schools of engineering.

The student wishing to enter the operations-research field may study in a school of science that has developed a program oriented towards operations research or he may study in a school of engineering that has an applied science program oriented towards operations research. One might expect that there would be different emphases in the operations-research programs under each alternative: the engineering school program oriented somewhat more towards applied research and design and the science school program oriented somewhat more towards unapplied research. (This is

* It would be interesting to compare the educational backgrounds of the various proponents of different educational backgrounds with their own recommendations.

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frequently, but not always, true.) This paper has concerned itself pri- marily with the relations between operations research and industrial engi- neering and educational backgrounds for work in these fields.

Operations researchers and industrial engineers, in accordance with the basic premise of this paper, are both concerned with the same productive systems and enterprises. Educational programs for both professions should therefore have much in common. However, the operations-research pro- gram should give more emphasis to research and analysis, that is, with contributing to the understanding of how and why the system operates, to building models that embody the laws and principles underlying systems, as well as stating these laws in formulations and equations that enable prediction and decision. The industrial-engineering program should be designed to educate engineers who will be concerned with the design of sue h systems and with methods for their effective operation. It should be addressed more to the application and modification of existing techniques toward the improvement of planning and control, production technology, work methods, product quality, and the reduction of production costs.

Studies for operations research should normally continue beyond the bachelor level, preferably to the doctorate. On the other hand, under- graduate study for industrial engineering is frequently the terminal aca- demic work of the engineer.

Both the operations-research program and the industrial-engineering program should emphasize mathematics, probability, and statistics, engi- neering sciences, behavioral and economic sciences, humanities, as well as the methodologies of operations research, industrial engineering, and man- agement. However, the operations-research program should place con- siderably greater emphasis on science and scientific methodology than the industrial engineering program. The operations-research student should take additional mathematics, statistics, economics, psychology, logic, and philosophy of science, etc., in place of engineering science and engineering design courses.

At the graduate level, a higher level of mathematical, statistical, and scientific competence should be expected of the operations-research student, whereas a higher level of engineering design and applied research compe- tence should be expected of the industrial engineering student. Students in both operations research and industrial engineering should be required to develop a high level of competence in a relevant field such as statistics, mathematics, physical science, chemistry, psychology, economics, etc. (The logic of requiring a minor field is based to some extent on the concept that the methodological discipline of various fields are transferable to a great extent. The ability to apply a systems concept in depth in one field is useful and advantageous to other types of systems. Operations research and industrial engineering have not yet developed an independent body of

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scientific knowledge in sufficient depth to provide this discipline. There is thus an educational need for competence in depth in related fields to provide necessary methodological discipline.)

These educational programs should emphasize the systems and the decision-making approaches to the science, engineering, and practice of management. They should be flexible and experimental so that they can be changed as new developments and criticisms dictate and as experiences with their operation suggest.

REFERENCES

1. P. M. MORSE AND G. E. KIMBALL, Methods of Operations Research, p. 1. Wiley, New York, 1951.

2. E. A. JOHNSON, "Introduction: The Executive, The Organization, and Opera- tions Research," in Operations Research for Management (J. F. MCCLOSKEY AND F. N. TREFETHEN, eds.), pp. XXIII-XXIV, Johns Hopkins Press, Baltimore, 1954.

3. C. W. CHURCHMAN, R. L. ACKOFF, AND E. L. ARNOFF, Introduction to Opera- tions Research, p. 18, Wiley, 1957.

4. THE INSTITUTE OF MANAGEMENT SCIENCES, "Information as to Its Objectives, History, Organizations, Functions, Membership."

5. G. H. SYMONDS, "The Institute of Management Sciences-A Synopsis of the 1956 Presidential Address," Opnal. Res. Quart. 8, 61 (1957).

6. J. B. LATHROP, "A Proposal for Merging ORSA and TIMS," Opns. Res. 5, 124-5 (1957).

7. L. F. URWICK, "Development of Industrial Engineering," Chapter I in In- dustrial Engineering Handbook (H. B. MAYNARD, ed.), pp. 1-7, McGraw- Hill, New York, 1956.

8. Webster's New Collegiate Dictionary, p. 757, G. C. Merriam Co., Springfield, Mass., 1960.

9. M. R. COHEN AND E. NAGEL, An Introduction to Logic and Scientific Method, p. 192, Harcourt, Brace & World, New York, 1934.

10. CHURCHMAN, ACKOFF, AND ARNOFF, op. cit., p. 3. 11. R. N. LEHRER, "The Challenge of Operations Research," J. Indust. Eng.

10, 87, 1959. 12. E. A. JOHNSON, "Long-Range Future of Operational Research," Opns. Res.

8, 2 (1960). 13. P. E. OVERCAST, "This Profession-Industrial Engineering," J. Indust. Eng.

8, 301 (1957). 14. R. W. HOVEY AND H. M. WAGNER, "A Sample Survey of Industrial Operations-

Research Activities," Opns. Res. 6, 880 (1958). 15. OVERCAST, op. cit., pp. 302-3. 16. HOVEY AND WAGNER, op. cit., p. 879. 17. MORSE AND KIMBALL, Op. cit., p. 19. 18. CHURCHMAN, ACKOFF, AND ARNOFF, op. cit., p. 627. 19. H. H. GOODE AND R. E. MACHOL, System Engineering, p. 129, McGraw-Hill,

1957. 20. R. DORFMAN, "Operations Research," Am. Econ. Rev., p. 621 (September

1960).