Knowledge that Transforms

The area of railroad scheduling and associated problems offers a potentially fruitful field for research in management science. The mass of data; the need for considering numerous aspects of the problem simultaneously; and the variety of restrictions (arising from the technology, labor agreements and government regulation) make the control of day to day operations a management problem of great complexity. The problems at this level are further compounded by the need for developing, at the same time, methods for planning and evaluating major changes in facilities. Such methods, if they are to be effective, must be capable of tracing out the implications of these changes on the day to day operation and appraising the results in the light of the long-run objectives of the railroad. This paper is an account of an attempt to apply certain techniques of management science to some of these scheduling problems as they were found to exist on a large terminal switching railroad.

In the present paper, the Caterer Problem is shown to be equivalent to a Hitchcock Distribution Problem [Hitchcock, F. L. 1941. The distribution of a product from several sources to numerous locations. J. Math. Phys. 20 224–230.] with a very special cost matrix. For the case q = p − 1, a simple procedure taking advantage of this fact is developed and shown to yield Jacobs' solution. The possible extension of the procedure to the case p − q > 1 is illustrated by a numerical example.

In recent years increasing need has been felt for a body of systematic theoretical constructs which will discuss the general relationships of the empirical world. This is the quest of General Systems Theory. It does not seek, of course, to establish a single, self-contained “general theory of practically everything” which will replace all the special theories of particular disciplines. Such a theory would be almost without content, for we always pay for generality by sacrificing content, and all we can say about practically everything is almost nothing. Somewhere however between the specific that has no meaning and the general that has no content there must be, for each purpose and at each level of abstraction, an optimum degree of generality. It is the contention of the General Systems Theorists that this optimum degree of generality in theory is not always reached by the particular sciences.

The primary purpose of this report is to point up the interrelations found among selected conflicting company objectives, the criteria by which one may evaluate alternate course of action indicated by each of the stated objectives, and some methods for reducing similar problems to a reasonable size, susceptible of analysis by available mathematical techniques. The problem discussed herein is a real problem, but in order to protect the interests of the company which sponsored this particular study, the entire report is paraphrased, and numbers such as quantities and dollars are deliberately changed.

The business firm is not merely “facts”, modified by logic, engineering, and intuition forming communication networks among rational individuals with perdictable reactions. Nevertheless, it is true that intercommunication of facts is necessary for continuance and that the prosperity of the firm does depend to a significant degree on the efficiency, effectiveness, and application of facts toward operations throughout the enterprise. The form and manner of data transmittal must be prescribed and organized. It is to this portion of the problems of management that the considerations in this paper are directed.

In a recent report, [Charnes, A., W. W. Cooper. Generalizations of the warehousing model. O. N. R. Research Memorandum, No. 34, 1955, Graduate School of Industrial Administration, Carnegie Institute of Technology.], Charnes and Cooper present a solution by means of linear programming techniques of one version of what is called the “warehouse problem”. The purpose of this note is to indicate how problems of this general nature may be approached by means of the functional equation technique of the theory of dynamic programming, and thereby reduced to a very simple and straight-forward computational problem.

A problem in the study of production smoothing leads to the problem of minimizing a linear form [Formula: see text] subject to constraints of the type x i ≧ 0, [Formula: see text]. A computational solution of this problem is given, using the methods of dynamic programming.

This paper attempts the solution of a practical problem. Given an international organisation with branches in n different countries and concerned with publicity for a commodity X—in competition with a substitute X′—how should such an organisation allocate its expenditure among them so as to get the maximum overall return. Though our model is necessarily based to some extent on intelligent guess-work, it has the merit of providing at least a logically consistent solution of the problem.

This paper is concerned with two topics: (1) the development of mathematical models for several simple inventory situations, and (2) an industrial application of a mathematical model of inventory. Because T. M. Whitin has described in detail in this journal the present state of research in inventory control (Whitin, T. M. 1954. Inventory control research. Management Sci. I (November).), no attempt will be made to provide a review here. This paper is not an attempt to solve the “general inventory problem.” On the contrary, the object is to deal with specific situations, and with an illustrative industrial application. The emphasis is on methodology of approach rather than on a general solution.