Knowledge that Transforms

A simplified description of a new computing procedure for the Hitchcock-Koopmans transportation problem is given, together with a step by step solution of an illustrative example. The procedure is based on Kuhn's combinatorial algorithm for the assignment problem and a simple “labeling process” for solving maximal flow problems in networks. The proposed computation appears to be considerably more efficient than the specialized form of the simplex method which is in common use.

Interest in management science, especially under the name “operations research,” on the part of industry has grown since World War II due partly to the publicity given to military applications and partly to the return to industry of men trained along these lines. The techniques have become more fully developed and it is the purpose of this article to develop some conclusions we have been able to draw from our experience in applying the concepts. These conclusions resulted from an analysis of what was needed to apply operations research techniques to manufacturing. In particular, attention was given to stabilizing procedures, to making decisions in the face of uncertainty and to improving communication. It was found that these and related operating problems could be handled in an engineering fashion so that operations research would be more effective.

The purpose of this paper is to illustrate an application of linear programming to the problem of allocation of aircraft to routes in order to maximize expected profits when there is uncertain customer demand. The approach is intuitive; the theoretical basis of this work is found in an earlier study. The allocations are compared with those obtained under the usual procedure of assuming a fixed demand equal to the expected value. The computational procedure is similar to the fixed demand case, with only slightly more computational effort required. This paper is intended both for readers interested in routing (and analogous resource allocation) problems and for those interested in studying an example of an application of linear programming under uncertainty.

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.