Knowledge that Transforms

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.

This paper is about the use of simple statistical techniques by middle management in the solution of day-to-day problems. It is based almost entirely on term papers prepared by students in the statistics course of the Executive Program at the School of Business of the University of Chicago in 1952, 1953, and 1954.

Report of the First National Meeting, Institute of Management Sciences, October 21–22, 1954, Pittsburgh, Pennsylvania.

In a previous paper (The Use of Mathematics in Production and Inventory Control—I, (Theory of Parts Listing). Paper published in Management Science, vol. 1, no. 1, October 1954. We refer to this report as (I).), the problem of parts requirements was analyzed with the aid of matrix equations. In the present paper, this analysis is extended to include the time dependence of parts requirements. A system of equations is developed which relates to a given shipping schedule the schedule of requirements for each assembly, or subassembly.

Linear graphs have been utilized by several authors to provide a geometric depiction of the structure of a group. Graphs will be defined in the next section where it will also be shown that they are in a one-to-one correspondence with certain square matrices whose only elements are 0 and 1. These corresponding matrices have been used as a mathematical model by others. Both viewpoints are combined here to provide a systematic procedure for identifying the liaison persons in an organization.

In the literature of economics the notion of utility differences has been much discussed in connection with the theory of measurement of utility. However, to the best of our knowledge, no adequate axiomatization for this difference notion has yet been given at a level of generality and precision comparable to the von Neumann and Morgenstern construction of a probabilistic scheme for measuring utility. (The early study of Wiener is not axiomatically oriented.) The purpose of this paper is to present an axiomatization of this notion and to establish the expected representation theorem guaranteeing measurement unique up to a linear transformation.

Bavelas, Smith and Leavitt (Bavelas, A. 1950. Communication patterns in task-oriented groups. J. Acoustical Soc. Amer. 22 725–730.) have posed the problem: what effect do communication patterns have upon the operation of groups? To study this problem they designed a laboratory situation that is a prototype of those occurring in “natural” organizations existing in government and business. Each member of the group is given certain information. Their task is to assemble this information, use it to make a decision, and then issue orders based on the decision. This design provides a situation stripped of the complexities of large-scale social groups but retaining some essential characteristics of the organizational communication problem. In it we can examine how the communication net affects simultaneously (a) the development of the organization's internal structure, and (b) the group's performance of its operating task.

The essential character of the general models under consideration is that activities are divided into two or more stages. The quantities of activities in the first stage are the only ones that are required to be determined; those in the second (or later) stages can not be determined in advance since they depend on the earlier stages and the random or uncertain demands which occur on or before the latter stage. It is important to note that the set of activities are assumed to be complete in the sense that, whatever be the choice of activities in the earlier stages (consistent with the restrictions applicable to their stage), there is a possible choice of activities in the latter stages. In other words it is not possible to get in a position where the programming problem admits of no solution.

The success of any industrial enterprise is obviously dependent upon the effectiveness of its managerial organization and its supervisory personnel. There are differences in management in different industries and even within the same industry in a single country. And these managerial differences may be the single most important competitive difference. But, the differences may be even greater and more significant when comparisons are made on a cross-national basis. In Europe, for example, the concept of the function of management is quite different from that in the United States, as are the variances in the avenues of access to managerial positions.