Knowledge that Transforms

The common loop overhead conveyor linking two manufacturing process areas is studied as a mechanism for transforming the output flow of one area into the input flow of the other. The variables relevant to a smooth transformation of flows and their inter-relationships are explored. Findings are formulated into three principles. On the conveyor operation problem, distinguished from the design problem, two methods of simulation are developed and practical suggestions advanced for use in feasibility and optimality considerations. A fundamental observation is that a conveyor is part of a dynamic system, hence information on the connected areas is essential to its smooth operation.

Most commodities move from points of production through successive stages of processing or manufacture and further stages of intermediate distribution before reaching points of final purchase. The final value of a commodity, in fact, is often analyzed by observing the amounts of labor and capital services that are added to it at each of these stages by the firm which owns it at each stage. The setting of the problem is this. Successive stages of dealing in a commodity are in general required on account of any of the following considerations: a) an activity may need to be undertaken at a different scale—i.e., plant size—than that at which a preceding or a succeeding activity needs to be conducted; b) changes in the combinations of commodities may be required from one stage to another; or c) information and contacts need to be mobilized in order to connect disparate groups of actors in the complex of activities.

In their paper (Derman, C., M. Klein. Inventory depletion management. Technical Report No. 2, Oct. 1957, Statistical Engineering Group, Columbia University.), Derman and Klein present sufficient conditions on the field life of an item function under which a LIFO policy is optimal. This paper presents an alternate set of sufficient conditions under which a LIFO policy is optimal.

A simplex computation for an arc-chain formulation of the maximal multi-commodity network flow problem is proposed. Since the number of variables in this formulation is too large to be dealt with explicitly, the computation treats non-basic variables implicitly by replacing the usual method of determining a vector to enter the basis with several applications of a combinatorial algorithm for finding a shortest chain joining a pair of points in a network.

The Institute of Management Sciences joined with the Operations Research Society of America, and with The Operational Research Society of the United Kingdom, to co-sponsor an International Conference on Operations Research. This is a report about this conference.

In a paper which appeared in the 1957 edition of this journal (Weinwurm, Ernest H. 1957. Limitations of the scientific method in management science. Management Sci. (April) 225–233.), Professor Weinwurm suggests that the use of mathematics in management science may so dominate a given model as to cause the disregard of vital human values. He cites Professor Bodenhorn who warns that the trend toward mathematical frameworks in economics may be associated with an application of good mathematical assumptions but poor economics (Bodenhorn, Diran. 1956. The problem of economic assumptions in mathematical economics. J. Political Econom. (February) 25–32.). In some dispute with Professor Flood's philosophy (Flood, Merrill M. 1956. The objective of TIMS. Management Sci. (January) 178–183.), he feels that we cannot ignore the nonquantitative factors in human relations.

This paper presents the derivation of decision rules for determining the amount of each item to produce and hold in inventory in a multi-product factory. Under certain conditions the rules are good approximations to optimal minimum cost solutions. The model assumes that production is determined for all the items at the beginning of the production period. It uses as a framework a decision rule for the determination of aggregate inventory; this aggregate rule is based upon the approximation of factory cost by a quadratic cost function. A total inventory cost function, based upon the aggregation of the individual item rules, is derived.

This paper reports the results of six experiments and analyses performed to explore the applicability of the non-constant-sum case of the theories of von Neumann-Morgenstern, and others, to the actual behavior of people playing games or involved in bargaining situations. The paper suggests directions in which the theory of games might be modified and extended to improve its applicability and usefulness. A “split-the-difference principle” is suggested to augment the usual theory, so as to specify the exact amount of payments to be made in an ordinary two-person bargaining situation such as the sale of a used car. The application of this principle seems satisfactory in the experiments. One experiment suggests that, in a sequence of trials in the same game situation, people tend to start near an equilibrium point and then try to find a better equilibrium, if there is one. The experiments show examples of non-optimal behavior of the bargainers when the judgment necessary to estimate the relevant payoff is obscure. A fair division of five parcels of objects among five players when each player attaches different values to the parcels is outlined and computed, and the effect of coalitions is discussed.

Comments based on material originally prepared for the Seminar on Theory and Research in Modern Management. Cooperative Center for Educational Administration, Columbia University.

The following type of problem has arisen in various contexts in applications of management science: to determine a program of future levels of activity (e.g., production or employment) subject to known future requirements, which will minimize the total cost of the projected program over the entire planning interval of time. Mathematical methods have been developed for treating variants of this problem, and the purpose of this paper is to present an outline of methods appropriate to problems which share a certain common mathematical form.