Operations Research

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The roots of “operations research” (commonly referred to as OR) go back at least to the industrial revolution, which brought with it the mechanization of production, power generation, transportation, and communication. Machines replaced man as a source of power and made possible the development of the large industrial, military, and governmental complexes that we know today. These developments were accompanied by the continuous subdivision of industrial, commercial, military, and governmental management into more and more specialized functions and eventually resulted in the kind of multilevel structure that today characterizes most organizations in our culture.

As each new type of specialized manager appeared, a new specialized branch of applied science or engineering developed to provide him with assistance. For example, in industry this progression began with the emergence of mechanical and chemical engineering to serve production management and has continued into more recent times with the development of such specialties as industrial engineering, value analysis, statistical quality control, industrial psychology, and human engineering. Today, no matter how specialized the manager, at least one relevant type of applied science or engineering is available to him.

Whenever a new layer of management is created, a new managerial function, that of the executive, is also created at the next higher level. The executive function consists of coordinating and integrating the activities of diverse organizational units so that they serve the interests of the organization as a whole, or at least the interests of the unit that contains them. The importance of the executive function has grown steadily with the increase in the size and complexity of industrial, military, and governmental organizations.

The executive function in business and industry has developed gradually. The executive was not subjected to violent stimuli from new technology as was, for example, the manager of production. Consequently the executive “grew” into his problems, and these appeared to him to require for their solution nothing but good judgment based on relevant past experience. The executive, therefore, felt no need for a more rigorous scientific way of looking at his problems. However, the demands on his time grew, and he sought aid from those who had more time for, and more experience with, the problems that he faced. It was this need that gave rise to management consulting in the 1920s. Management consulting, however, was based on experience and qualitative judgment rather than on experimentation and quantitative analysis. The executive function was left without a scientific arm until World War II .

The major difference between the development of military executives and of their industrial counterparts is to be found in the twenty-year gap between the close of World War I and the opening of World War II. Because there was little opportunity to use military technology under combat conditions during this period, this technology developed too rapidly for effective absorption into military tactics and strategy. Thus, it is not surprising that British military executives turned to scientists for aid when the German air attack on Britain began. Initially they sought aid in incorporating the then new radar into the tactics and strategy of air defense. Small teams of scientists, drawn from any disciplines from which they could be obtained, worked on such problems with considerable success in 1939 and 1940. Their success bred further demand for such services, and their use spread to Britain’s allies—the United States, Canada, and France. These teams of scientists were usually assigned to the executive in charge of operations, and their work came to be known in the United Kingdom as “operational research” and in the United States by a variety of names: operations research, operations analysis, operations evaluation, systems analysis, systems evaluation, and management science. The name operations research was and is the most widely used in the United States.

At the end of the war very different things happened to OR in the United Kingdom and in the United States. In the United Kingdom expenditures on defense research were reduced. This led to the release of many OR workers from the military at a time when industrial managers were confronted with the need to reconstruct much of Britain’s manufacturing facilities that had been damaged during the war and to update obsolete equipment. In addition the British Labour party, which had come into power, began to nationalize several major and basic industries. Executives in these industries in particular sought and received assistance from the OR men coming out of the military. Coal, iron and steel, transport, and many other industries began to create industrial OR.

In contrast to the situation in Great Britain, defense research in the United States was increased at the end of the war. As a result military OR was expanded, and most of the war-experienced OR workers remained in the service of the military. Industrial executives did not ask for help because they were slipping back into a familiar peacetime pattern that did not involve either major reconstruction of plant or nationalization of industry.

During the late 1940s, however, the electronic computer became available and confronted the industrial manager with the possibility of automation —the replacement of man by machines as a source of control. The computer also made it possible for a man to control more effectively widely spread and large-scale activities because of its ability to process large amounts of data accurately and quickly. It provided the spark that set off what has sometimes been called the second industrial revolution. In order to exploit the new technology of control, industrial executives began to turn to scientists for aid as the military leaders had done before them. They absorbed the OR workers who trickled out of the military and encouraged academic institutions to educate additional men for work in this field.

Within a decade there were at least as many OR workers in academic, governmental, and industrial organizations as there were in the military. More than half of the largest companies in the United States have used or are using OR, and there are now about 4,000 OR workers in the country. A national society, the Operations Research Society of America, was formed in 1953. Other nations followed, and in 1957 the International Federation of Operational Research Societies was formed. Books and journals on the subject began to appear in a wide variety of languages. Graduate courses and curricula in OR began to proliferate in the United States and elsewhere.

In short, after vigorous growth in the military, OR entered its second decade with continued growth in the military and an even more rapid growth in industrial, academic, and governmental organizations.

Essential characteristics of OR . The essential characteristics of OR are its systems (or executive) orientation, its use of interdisciplinary teams, and its methodology.

Systems approach to problems. The systems approach to problems is based on the observation that in organized systems the behavior of any part ultimately has some effect on the performance of every other part. Not all these effects are significant or even capable of being detected. Therefore the essence of this orientation lies in the systematic search for significant interactions when evaluating actions or policies in any part of the organization. Use of such knowledge permits evaluation of actions and policies in terms of the organization as a whole, that is, in terms of their over-all effect.

This way of approaching organizational problems is diametrically opposed to one based on “cutting a problem down to size.” OR workers almost always enlarge the scope of a problem that is given to them by taking into account interactions that were not incorporated in the initial formulation of the problem. New research methods had to be developed to deal with these enlarged and more complicated problems. These are discussed below.

As an illustration of the systems approach to organizational problems, consider the case of a company which has 5 plants that convert a natural material into a raw material and 15 finishing plants that use this raw material to manufacture the products sold by the company. The finishing plants are widely dispersed and have different capacities for manufacturing a wide range of finished products. No single finishing plant can manufacture all the products in the line, but any one product may be produced in more than one plant.

Many millions of dollars are spent each year in shipping the output of the first group of plants to the second group. The problem that management presented to an OR group, therefore, was how to allocate the output of the raw-material plants to the finishing plants so as to minimize total betweenplant transportation costs. So stated, this is a welldefined, self-contained problem for which a straightforward solution can be obtained by use of one of the techniques of OR, linear programming [seeProgramming].

In the initial phases of their work, the OR workers observed that whereas all the raw-material plants were operating at capacity, none of the finishing plants were. They inquired whether the unit-production costs at the finishing plants varied with the percentage of capacity in use. They found that this was the case and also that the costs varied in a different way in each plant. As a result of this inquiry the original problem was reformulated to include not only transportation costs, but also the increased costs of production resulting from shipping to a finishing plant less material than it required for capacity operation. In solving this enlarged problem it was found that increased costs of production outweighed transportation costs and that a solution to the original problem (as formulated by management) would have resulted in an increase in production costs that would have more than offset the saving in transportation costs.

The OR workers then asked whether the increased costs of production that resulted from unused capacity depended on how production was planned, and they discovered that it did. Consequently, another related study was initiated in an effort to determine how to plan production at each finishing plant so as to minimize the increase in unit-production costs that resulted from unused capacity. In the course of this study of production planning it also became apparent that production costs were dependent on what was held where in semifinished inventory. Therefore, another study was begun to determine at what processing stage semifinished inventories should be held and what they should contain. Eventually the cost of shipping finished products to customers also had to be considered.

In the sequence of studies briefly described, it was not necessary to wait until all were completed before the results of the first could be applied. Solutions to each part of the total problem were applied immediately because precautions had been taken not to harm other operations. With each successive finding previous solutions were suitably adjusted. Eventually some change was made in every aspect of the organization’s activities, but each with an eye on its over-all effect. This is the essence of the systems approach to organizational problems.

The interdisciplinary team. Although division of the domain of scientific knowledge into specific disciplines is a relatively recent phenomenon, we are now so accustomed to classifying scientific knowledge in a way that corresponds either to the departmental structure of universities or to the professional organization of scientists that we often act as though nature were structured in the same way. Yet we seldom find such things as pure physical problems, pure psychological problems, pure economic problems, and so on. There are only problems; the disciplines of science simply represent different ways of looking at them. Nearly every problem may be looked at through the eyes of every discipline, but, of course, it is not always fruitful to do so.

If we want to explain an automobile’s being struck by a locomotive at a grade crossing, for example, we could do so either in terms of the laws of motion, or the engineering failure of warning devices, or the state of physical or mental health of the driver, or the social use of automobiles as an instrument of suicide, and so on. The way in which we look at the event depends on our purposes in doing so. A highway engineer and a driving instructor would look at it quite differently.

Though experience indicates a fruitful way of looking at most familiar problems, we tend to deal with unfamiliar and complicated situations in the way that is most familiar to us. It is not surprising, therefore, that given the problem, for example, of increasing the productivity of a manufacturing facility, a personnel psychologist will try to select better workers or improve the training that workers are given. A mechanical engineer will try to improve the machines. An industrial engineer will try to improve the plant layout, simplify the operations performed by the workers, or offer them more attractive incentives. The systems and procedures analyst will try to improve the flow of information into and through the plant, and so on. All may produce improvements, but which is best? For complicated problems we seldom can know in advance. Hence it is desirable to consider and evaluate as wide a range of approaches to the problem as possible. OR has greatly enlarged our capacity to deal with all the complexities of and the approaches to a given problem and has therefore expanded our opportunities to benefit from the use of interdisciplinary teams in solving problems.

Since more than a hundred scientific disciplines, pure and applied, have been identified, it is clearly not possible to incorporate each in most research projects. But in OR as many diverse disciplines are used on a team as possible, and the team’s work is subjected to critical review by as many of the disciplines not represented on the team as possible.

Methodology. Experimentation lies at the heart of scientific method, but it is obvious that the kind of organized man-machine system with which industrial, military, and governmental managers are concerned can never be brought into the laboratory, and only infrequently can such systems be manipulated enough in their natural environment to experiment on them there. Consequently, the OR worker finds himself in much the same position as the astronomer, and he takes a way out of his difficulty much like that taken by the astronomer. If he cannot manipulate the system itself, he builds a representation of the system, a model of it, that he can manipulate. In OR such models are abstract(symbolic) representations that may be very complicated from a mathematical point of view. From a logical point of view, however, they are quite simple. In general they take the form of an equation in which the performance of the system, P, is expressed as a function, f, of a set of controlled variables, C, and a set of uncontrolled variables, U:

p=f(C,U)

The controlled variables represent the aspects of the system that management can manipulate, for example, production quantities, prices, range of product line, and so on. Such variables are often called decision variables since managerial decision making may be thought of as assigning values to these variables. The uncontrolled variables represent aspects of the system and its environment that significantly affect the system’s performance but are not under the control of management, for example, product demand, competitors’ prices, cost of raw material, and location of customers.

The measure of performance of the system may be very difficult to construct since it must reflect the relative importance of each relevant objective of the organization. This measure is sometimes called the criterion or objective function since it provides the basis for selecting the “best” or “better “courses of action.

Limitations or restrictions may be imposed on the possible values of the controlled variables. For example, in preparing a budget a limitation is normally placed on the total amount that may be allocated to different departments, or there may be legal constraints on the decision-making activities of managers. Such restrictions can usually be expressed mathematically as equations or inequalities and can be incorporated in the model.

Once the decision maker’s choices and the system involved have been represented by a mathematical model, the researcher must find a set of values of the controlled variables that yields the best (or as close as possible to the best) performance of the system. These “optimizing” values may be found either by experimenting on the model(i.e., by simulation) or by mathematical analysis. In either case the result is a set of equations, one for each controlled variable, giving the value of that controlled variable relative to a particular set of values of the uncontrolled variables and other controlled variables that yields the best performance of the system as a whole [seeSimulation].

If the problem is a recurrent one, then the values of the uncontrolled variables (for example, demand) may change from one decision-making period to another. In such cases a procedure must also be provided for determining when values of the uncontrolled variables have undergone significant change and for adjusting the solution appropriately. Such a procedure is called a solution-control system.

The output of an OR study, then, is usually a set of rules for determining the optimal values of the controlled variables together with a procedure for continuously checking the values of the uncontrolled variables. It must be borne in mind, however, that a single, unified, and comprehensive OR study is seldom possible in an organization of any appreciable size. Rather, what usually occurs is a sequence of interrelated studies, each of which is designed to be adjustable to the results of the others.

Ten years of constructing and working with models of managerial problems in industry have shown that, despite the fact that no two problems are ever exactly alike in content, most problems fall into one, or a combination, of a small number of basic types. These problem-types have now been studied extensively so that today we have considerable knowledge about how to construct and solve models that are relevant to them. Adequate definitions of these problem-types require more space than is available here, but the following brief characterizations indicate their nature.

Inventory problem—to determine the amount of a resource to be acquired or the frequency of acquisition when there is a penalty for having either too much or too little available.

Allocation problem—to determine the allocation of resources to a number of jobs where available resources do not permit each job to be done in the best possible way, so as to do all (or as many as possible) of the jobs in such a way as to achieve the best over-all performance, given criteria for measuring performance.

Queuing problem—to determine the amount of service facilities required or how to schedule arrival of tasks at service facilities so that losses associated with idle facilities, waiting, and turned-away tasks are minimized.

Sequencing problem—to determine the order in which a set of tasks should be performed in a multistage facility so as to minimize costs associated with the performance of the tasks and delays in completing them.

Routing problem—to determine which path or route through a network of points or locations is shortest (or longest), has maximum (or minimum) capacity, or is least (or most) costly to traverse subject to certain limitations on the paths or routes that are permissible.

Replacement problem—to determine when to replace instruments, tools, or facilities so that acquisition, maintenance, and operating and failure costs are minimized.

Competition problem—to determine the rule to be followed by a decision maker that yields the best results when the outcome of his decision depends in part on decisions made by others.

Search problem—to determine the amount of resources to employ and how to allocate them in seeking information to be used for a particular purpose so as to minimize the costs associated with the search and with the errors that can result from use of incorrect information.

The future of OR. OR has been primarily concerned with the executive’s decision-making or control process. There are, of course, other approaches to improving the performance of organizations, for example, selecting better personnel, providing better personnel training, better motivating personnel, accelerating their operations through work study, changing equipment and materials, modifying communications, changing organizational structure. This multiplicity of available approaches presents the executive with the additional problem of selecting which approaches to pursue. He seldom has an objective basis for doing so. Clearly it would be desirable to develop an integrated and comprehensive approach to organizations, one that rationally selects from or combines different points of view. OR and other systems-oriented interdisciplinary research are taking steps to develop such an overall approach to organizational problems. This is leading to mathematical descriptions of organizational structures and communications systems, thus providing the ultimate possibility of integrating studies of organizational structure, communication, and control.

Precise solutions of some limited problems of organizational structure have already been found. For example, given an organization’s over-all objective and a description of its task and environment, it is possible to determine the number and types of units into which the organization should be divided and the objectives to be assigned to these units so as to minimize inefficiency arising from the organization’s structure. This is a problem in structural design. Or, given an organization that has an inefficient structure, it is possible to determine the types of decentralized control to be applied to decentralized decision making so as to minimize inefficiency. This is a problem in structural control.

Such developments are leading to an integrated theory of, and generalized methodology for, research on organized systems. Since all of these systems are, in some sense, social systems, the participation of the social scientist in these interdisciplinary efforts is essential.

Russell L. Ackoff

[See alsoSystems Analysis.]

bibliography

Ackoff, Russell L.; and Rivett, Patrick 1963 A Manager’s Guide to Operations Research. New York: Wiley.

Churchman, Charles W.; Ackoff, Russell L.; and Arnoff, E. Leonard 1957 Introduction to Operations Research. New York: Wiley.

Duckworth, Walter E. 1962 A Guide to Operational Research. London: Methuen.

Eddison, R. T.; Pennycuick, K.; and RIVETT, B. H. P.1962 Operational Research in Management. New York: Wiley.

Miller, David W.; and Starr, Martin K. 1960 Executive Decisions and Operations Research. Englewood Cliffs, N.J.: Prentice-Hall.

Progress in Operations Research. Volume 1. Edited by Russell L. Ackoff. Operations Research Society of America, Publications in Operations Research, No. 5. 1961 New York: Wiley.

Sasieni, Maurice; Yaspan, Arthur; and Friedman, Lawrence 1959 Operations Research: Methods and Problems. New York: Wiley.