Fundamentals of Operations Research. Ackoff, R. L. & Sasieni, M. W. 1968.
Many definitions of operations research have been proposed, and many arguments have been advanced as to why the subject cannot be defined at all. In considering the various definitions that have been offered, it should be remembered that none of the older, long-established sciences — nor science as a whole — has ever been defined to the satisfaction of all its practitioners. Nevertheless, the definition below can serve as a useful basis for a general understanding of the nature of operations research, especially in light of the field's history just reviewed.
Operations research is: (1) the application of the scientific method, (2) by interdisciplinary research teams, (3) to problems involving the control of organized (man–machine) systems so as to provide solutions that best serve the purposes of the organization as a whole.
The distinctive features of operations research stated in this definition are: (a) a systems approach, (b) the use of interdisciplinary research teams, and (c) the application of the scientific method to problems of control. Let us now consider each of these features in greater detail.
This approach is based on the premise that, in organizational systems, the behavior of any part ultimately affects every other part. Not all such effects are significant, and some may be altogether undetectable. Therefore, the essence of this approach lies in systematically searching for significant interactions when evaluating the performance or strategy of any part of the organization.
Such an approach to organizational problems differs radically from reducing a problem to a manageable size. Operations researchers almost invariably broaden the initial formulation of the problem presented to them, incorporating interactions that were not included in management's formulation. Addressing these broader, and consequently more complex, problems requires the development of new research methods.
We have become so accustomed to classifying scientific knowledge according to the departmental structure of universities that we sometimes believe this organization reflects the structure of nature itself. Nothing could be further from the truth. There are no such things as physical, biological, psychological, or economic problems per se. There are only problems. Scientific disciplines merely represent different methods of investigating them. Any problem can be viewed from the standpoint of any scientific discipline — though, of course, it is not always expedient to do so. In essence, this is the same idea expressed earlier in a different form: an organization does not have separate production, marketing, or financial problems. Such partitioning merely reflects different approaches to examining the same organizational problems.
Each specialist may achieve certain improvements, but which of these improvements — or which combination of them — is best? With complex problems, we rarely know this in advance. It is therefore advisable to consider and evaluate the widest possible range of approaches to the problem. This is the rationale behind interdisciplinary research teams.
Since there are currently more than a hundred pure and applied scientific disciplines, it is obviously impossible to include a representative of each in every research project. It is, however, desirable to have as many disciplines as possible represented on the team and to subject the team's work to critical review from the broadest possible range of disciplines not represented on it.
Most accounts of the scientific method hold that its distinguishing feature is the experiment. However, when dealing with governmental, military, or industrial organizations, experimentation in the narrow sense — that is, physically altering variable values — is often impossible or impractical. An industrial firm, for example, cannot risk its very existence for the sake of an experiment. Of course, experimentation is sometimes possible, especially at the subsystem level, and it does play an important role in operations research. Nonetheless, as a rule, the system under study as a whole cannot be subjected to experimentation. In most cases, therefore, investigating the system as a whole requires an approach that does not involve experimentation (in the narrow sense of physically altering the object under study).
Operational models take the form of equations that, although mathematically complex, have a very simple structure: the utility or value of a performance criterion characterizing the system's functioning is expressed as a function of controllable variables and of uncontrollable variables (and constants) that nonetheless affect the function.
In addition, one or more equations or inequalities are often required to express the fact that certain controllable variables can vary only within specified limits.
Once a model has been constructed, it can be used to find exact or approximate optimal values of the controllable variables — that is, values that yield the best system performance criterion given the values of the uncontrollable variables. In other words, one can obtain a solution to the problem in the model. How exactly this solution is obtained depends on the model employed.
A solution may be obtained by experimenting on the model (by varying its parameters) or through mathematical analysis. In some cases, the mathematical analysis can be carried out without knowing the specific values of the variables; in other cases, the values must be specified numerically.
Regardless of the method used, the aim is always to find an optimal or near-optimal solution. An optimal solution is one that minimizes or maximizes (depending on the nature of the problem) the performance criterion on the model, subject to the conditions and constraints represented in that model. Optimization thus yields the best solution to the problem as described by the model. However, because a model is never an exact description of the problem, the optimal solution obtained in this way is likewise never the one and only best solution to the real problem. If one assumes that the model provides a "good" representation of the problem, then the optimal or near-optimal solution obtained on the model is a "good" approximation to the optimal solution of the real problem. In any event, it is considerably better than the strategy or procedure it is intended to replace.
Since the optimal values of the variables obtained through solution improve system performance only to the extent that the model accurately describes the system, it is necessary to verify the model's correspondence to reality and to soberly assess the solution. In other words, the predicted outcomes of implementing the solution must be compared with the strategy or procedure it is intended to replace.
Finally, since the purpose of operations research is not the production of scientific reports but the improvement of system performance, the results of the research must be implemented (provided they are acceptable to the decision-maker). It is at this stage that the final test and evaluation of the research results take place. This, then, is the stage at which the greatest opportunity for gaining experience presents itself to the operations researchers.
If the decision for which the research is conducted belongs to the category of recurrent decisions, then — given the nature of the systems studied in operations research — it is quite likely that between successive decisions the values of some uncontrollable variables, and even the structure of the system itself, will change. It is therefore necessary to detect significant changes in the system and in its external environment and to adjust the decision accordingly. In other words, results that take the form of rules for recurrent decisions, or decisions applied over extended periods of time, must be updated and their correct application monitored.