Knowledge that Transforms

The decision problems involved in setting the aggregate production rate of a factory and setting the size of its work force are frequently both complex and difficult. The quality of these decisions can be of great importance to the profitability of an individual company, and when viewed on a national scale these decisions have a significant influence on the efficiency of the economy as a whole. This paper reports some of the findings of a research team that has been developing new methods to enable production executives to make better decisions and to make them more easily than they can with prevailing procedures. With the cooperation of a manufacturing concern, the new methods have been developed in the context of a set of concrete production scheduling problems that were found in a factory operated by the company. The new method which is presented in this paper, involves: (1) formalizing and quantifying the decision problem (using a quadratic approximation to the criterion function) and (2), calculating a generalized optimal solution of the problem in the form of a (linear) decision rule. Like a rule of thumb, an optimal decision rule prescribes a course of action when it is applied to a particular set of circumstances; but, unlike most rules of thumb, an optimal decision rule prescribes courses of action for which the claim can be made that the decisions are “the best possible,” the meaning of “best” being clearly specified. The ultimate test, of course, must be whether the new decision methods do or do not outperform prevailing decision methods when full allowance is made for the cost of obtaining the optimal decisions.

My assignment is to discuss mathematics in the management science of tomorrow. The preceding talks have dealt with potential uses by management of emerging and possible scientific developments. In approaching my assignment I would like to shift the emphasis slightly in order to discuss possible repercussions of a developing science of management on mathematics as well as possible repercussions of mathematical developments for the science of management.

Presidential address about the background leading to TIMS formation. Delivered before the first national meeting of the Institute of Management Sciences, Oct. 21–22, 1954. Parts of the address are omitted.

These remarks are intended to outline a forecast of the future of management and management science, namely that through scientific research management is going to become increasingly automatic. This forecast is based on a survey and projection of some contemporary technological and scientific developments.

In the management science of tomorrow, I predict, there will be a great growth of these and other techniques whereby practitioners and scientists will inform, stimulate and influence each other. One of the most fruitful functions of this new Institute, in my opinion, would be to put some of its intellect and energy into developing such techniques. One of the most important management sciences of tomorrow could well be the science that joins management science and management.

Economists and psychologists are interested in the theory of human decision making behavior. So are neurophysiologists and psychoanalysts. So also are statisticians, game theorists, cyberneticians, information theorists, operations researchers and many others among the management scientists.

My topic in this panel discussion on management science today is the status of research on mathematical solution of programming problems. The word “programming” refers here to optimal allocation, as in machine loading, or to optimal scheduling of one kind or another. “Optimal allocation” may be taken as referring to static problems, while “optimal scheduling” refers to dynamic problems, varying over time. The static and dynamic problems are, at the present stage of management science development, generally speaking, studied by means of the same techniques.

Constitution and by-laws the Institute of Management Sciences adopted at the Founding Meeting of December 1, 1953.

In the course of studying production and inventory control, the author of this paper found it repeatedly necessary to explain his mathematical theory to operating personnel, many of whom have had little or no formal training in mathematics at the college level. This paper, then, is an outgrowth of these presentations and has a twofold purpose: (1) to present a theory of a very small part of the problem of production and inventory control with the objective of acquainting the reader with the nature of the mathematical methodology, (2) to lay emphasis on a didactic presentation to show the principles involved in explaining these mathematical concepts.

Wherever people have gathered to pursue a common and desired end, there has been an inevitable necessity to organize minds, hands, materials, and the use of time for efficient and contributive work. Man has learned that individual and personal rewards derive largely from an harmonious combination of individual work and teamwork in a soundly organized frame of reference, and thus the core of the history of “Scientific Management” is formed from his search for the techniques of joint but voluntary participation while still preserving individual initiative, creative imagination, and increasingly productive output. Any historical survey, to be of more than passing interest, and to be more than a simple chronology of dates and names, needs to seek out the philosophical drives which both stimulated and limited the progress of such a scientific approach to more rational conception and performance of managerial work, that is, of securing results through the organized efforts of others. While it is important to know when things happened, this knowledge only becomes significant and useable when it is understood why things happened. This paper, therefore, is intended to outline the gradual historical development of the search for the basic principles of a “Science of Managing,” and thus of Scientific Management, rather than to be a simple recounting of experiment, methodology, or significant writings in that field.