A major impetus behind operations research was the recognition that complex, goal-oriented processes must be studied and solved as integrated wholes, since solutions to individual parts of the overall problem turned out to be isolated, while practice demanded unity among all partial solutions.
Initially, "operations research" was confined to developing methods for analyzing a problem as a single whole, without isolating its constituent parts. Another distinctive feature of these studies in the early period was the use of the interdisciplinary team approach. Its essence lay not in assembling all relevant specialists in one place, but in creating a group that commanded quantitative methods and was free from the narrow perspective inherent in any single discipline. This approach reflected two realities: first, the need to bring quantitative methods into management science, and second, the shortage of methods (and specialists) in the area that came to be called "operations research."
Subsequently, "operations research" evolved from the joint activity of specialists of various profiles into an independent branch of science and organizational practice, splitting in the process into two main directions.
The first of these is associated with the construction of mathematical models for the most frequently encountered sub-problems of management, in which it is possible to some degree to dispense with the need to account for the behavior of individual people participating in the operation. Here, the principal problems of the mathematical theory of "operations research" were identified, along with the associated further specialization of scientists working in this area.
A large number of problems solved by managers can be attributed to such tasks, for example:
- inventory management, concerned with determining the necessary size of "stored" resources (human, material, financial, raw material, etc.), given that storage entails certain costs;
- allocation of limited resources among various consumers, each of whom uses them with varying degrees of efficiency;
- queuing problems, which involve distributing tasks in a strict sequence, forming one process or another, and establishing priority rules;
- route selection and scheduling of work over time;
- problems related to the replacement of obsolete equipment;
- finding solutions through rational (rather than exhaustive) enumeration of possibilities;
- competitive problems, or game theory problems, which investigate rational strategies of behavior in situations where the outcome of an operation depends not only on the behavior of the subject but also on the behavior of an opponent whose goals contradict those of the subject.
Thus, the method of "operations research" came to be applied to different types of operations and processes, using various approaches and diverse mathematical tools depending on the object of analysis (methods of mathematical programming, combinatorial and statistical modeling). Along with mathematical tools, heuristic methods were also employed in "operations research."
In developing methods for the analysis of goal-directed actions (operations) and comparative evaluation of solutions, predominantly in quantitative terms, "operations research" is grounded in systems methodology, according to which the phenomena under study are regarded as systems representing interacting aggregates of elements designed to achieve specific objectives.
Analysis of specific operations or phenomena from the standpoint of "operations research" involves constructing a mathematical model of the phenomenon, analyzing the model and searching for a solution, verifying the adequacy of the model and the solution to the phenomenon, making the necessary adjustments ("tuning") to the model and the solution, and finally applying the chosen solution in practice.
Closely related to the mathematical problems of this method (though not formally part of them) is the large area of so-called network methods of planning and management. The development of network methods and network systems is closely linked to the branch of "operations research" that studies scheduling models. These methods made it possible to find a new and highly convenient language for describing, modeling, and analyzing complex multi-stage operations. Such are, in particular, the network methods of modeling and operational control: CPM — the "Critical Path Method" and PERT — "Program Evaluation and Review Technique."
The emergence of various formalized management systems, methods of long-range planning, programming, and forecasting was driven by the need to create conditions for correct decision-making in an environment where management was confronted with enormous volumes of information, thousands of factors whose accounting, evaluation, and integration proved impossible under the conventional organization of management.
Studies by a number of American psychologists have shown that a person experiences difficulty in making decisions when it requires taking into account more than 10 variables or mutually contradictory factors, or more than 20 factors of the same order. However, since an optimal solution can only result from accounting for and analyzing all factors, regardless of whether a person at a given level of management is able to cope with this task, there objectively arises a need to divide problems into sub-problems and sub-tasks. The main principle underlying most existing programming systems consists of the logical decomposition of tasks. The premise was the need to reduce the number of factors or the volume of information to levels that allow a person to evaluate them.
The second direction of "operations research" developed along somewhat different lines, emphasizing not so much the mathematization of management problems and the introduction of exact science methods, but rather the application of principles of studying an operation as a unified whole, using "fresh," "unbiased" research teams. The emergence of systems engineering is associated with this direction. It should be noted that many scientists who studied management processes using the "operations research" method subsequently went beyond the boundaries of this type of inquiry. In this connection, they proposed increasingly broad definitions of the scientific discipline whose foundation is this method, which not infrequently led to terminological confusion.
Many American specialists recognize that, although "operations research" on the whole represented a very important step toward creating a new science of management, it nonetheless covered a comparatively narrow range of problems. Furthermore, as mathematical specialization developed, a tendency emerged to regard "operations research" as special branches of applied mathematics — that is, not to consider them as forming an independent scientific discipline with a distinct subject of study.
Therefore, as early as the beginning of the 1950s, an active search began for a more precise definition of the specificity of those management problems whose solution presupposes the application of mathematical methods, even though the problems themselves should be attributed to the subject matter of organization and management theory. The result was the identification of decision theory as an independent scientific discipline (within management science), conceived as a further development of "operations research," which was correspondingly interpreted as specific methods of decision-making. However, in decision theory (and this distinguishes it from "operations research"), the main attention was paid to the decision-making process itself, to the formation of selection principles, to the development of quality criteria, and to determining methods for finding solutions that correspond to these principles. Proponents of this theory assert that decision-making constitutes the core of managerial activity and defines its specific features.
Work in this area proceeds mainly along two directions. The first is concerned primarily with mathematical modeling of decision-making processes as they are actually carried out in real teams. The second concentrates its efforts on developing algorithms that make it possible to obtain optimal solutions. The first direction includes various "behavioral" studies, for example, those of E. Fogel and R. Luce, while the second encompasses numerous investigations in the theory of statistical decisions, game theory, and the like. The work of representatives of both directions makes extensive use of the tools of mathematical logic, mathematical statistics, as well as linear, nonlinear, dynamic, and systems programming. The need to evaluate the consequences of one decision or another under conditions of uncertainty led to the widespread use of statistical testing methods, or "Monte Carlo methods."
At the same time, within the "new" school, another point of view took shape, according to which the specific features of management are associated with the economic aspect of the activity of various systems, and therefore the central focus of management science should be the task of quantification and mathematical modeling of economic phenomena. This point of view gave rise to the so-called econometric approach to the analysis and programming of management processes.
Of great importance for the development of the econometric approach was the discovery in 1939 by the Soviet mathematician and Nobel laureate L. V. Kantorovich of the linear programming method, on which research in this area is largely based. Only 10 years later was this method independently rediscovered by the American mathematician G. Dantzig.
At the foundation of the econometric approach lies the construction of models that reflect particular economic phenomena or processes in schematic form through scientific abstraction of the most characteristic features of these phenomena and processes. Unlike an economic model, an econometric model is expressed in mathematical form. According to this approach, every developed economic-mathematical model has four distinct aspects:
- It reflects certain economic phenomena of qualitative content, expressed in particular units of measurement. These quantities are, in a sense, the parameters of the model.
- The model includes certain quantitative relationships and dependencies among the parameters. These may be balance equations that define the structure of the modeled process, or more complex dependencies that link the outcomes of processes to their causes.
- The model defines the domain of permissible changes in the model's parameters over time, space, and volume. These are the so-called constraints imposed on the quantitative dependencies.
- The model must represent a system of interrelated parameters, dependencies, and constraints with defined inputs and outputs. Managing such a system — that is, obtaining specific results at the output — must occur through one form of action on the inputs or another, without interfering with its internal structure.
The construction of econometric models is divided into four main stages.
- The first stage is specification, when the principal economic variables are formalized, and mathematical equations are sought on the basis of initial assumptions and propositions.
- The second stage is identification, which consists of finding the values of the parameters of the equations obtained in the first stage as a result of specification.
- The third stage is verification, which consists of defining and selecting criteria for evaluating the quality of the results of specification and identification — that is, the degree of adequacy of the models to real economic processes. If the models obtained through specification and identification are inadequate, then the validity of the initial premises and the choice and formalization of economic variables are examined.
- The fourth stage is prediction, which is the procedure of determining the future values of the variables included in the econometric model.