Knowledge that Transforms

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.

In Hoffman, A. J., Walter Jacobs. 1954. Smooth patterns of production. Management Sci. 1 86–91, the problem of smooth patterns of production—with which we presume the reader is familiar—a formula was found for the solution of the problem in the special case that the requirements are increasing. In this note, we point out that a similar formula holds if the requirements increase up to a certain value, then decrease.

Recent scientific research has made available a variety of tools which can be brought to bear on managerial problems. One of these tools, which has already proved its worth in practical applications, is linear programming. It is not the purpose of this article to explore the full ramifications of these research developments or even to explore the general field of linear programming. Only transportation-type problems and models will be discussed in any detail.

The equations used in the examples were formulated with the aid of a spiral diagram which represents the result of preliminary scheduling in so far as it assigns each bus to a definite route and indicates how the various branches are geared together. In complicated networks the construction of a suitable spiral diagram may itself become a difficult problem, particularly when the buses flowing into a main branch have to be geared with the buses flowing out of this branch. The following procedure has been found useful in this case. Of the possible arrangements of the buses flowing into and out of the main branch, select the two which present the most symmetric appearance; perform the minimizing calculation on the various ways of fitting these patterns together. The optimum schedule is likely to be one of these combinations.

In past decades there have been occasional upsurges of intensive interest in inventory control problems, sometimes in the aftermath of forced inventory liquidation. For the most part, the literature consisted of a few articles in business journals that had but little impact on the current business behavior of the time. In the last few years we have witnessed another upsurge of interest which far surpasses any of its predecessors, with respect to the quantity and quality of the work accomplished as well as its overall impact on the business community. This vigorous research and the interest it has aroused have been made possible by parallel development in research and in business. Statisticians and economists have become interested in industrial problems concomitantly with the increased attention in business to techniques of advanced management. The appearance of this journal is an example of this harmony of interests that has come into being. The fact that modern statistical methods have been applied successfully in several instances has had much influence on the interest level of both research workers and industrialists.

A number of authors have considered mathematical models for scheduling rates of production to meet a projected series of requirements. In particular, linear models have been used in several studies. This paper considers a simple model of that type, which explicitly allows for inventory costs.