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.
The following paper is reproduced from a Russian journal of the character of our own Proceedings of the National Academy of Sciences, Comptes Rendus (Doklady) de I'Académie des Sciences de I'URSS, 1942, Volume XXXVII, No. 7–8. The author is one of the most distinguished of Russian mathematicians. He has made very important contributions in pure mathematics in the theory of functional analysis, and has made equally important contributions to applied mathematics in numerical analysis and the theory and practice of computation. Although his exposition in this paper is quite terse and couched in mathematical language which may be difficult for some readers of Management Science to follow, it is thought that this presentation will: (1) make available to American readers generally an important work in the field of linear programming, (2) provide an indication of the type of analytic work which has been done and is being done in connection with rational planning in Russia, (3) through the specific examples mentioned indicate the types of interpretation which the Russians have made of the abstract mathematics (for example, the potential and field interpretations adduced in this country recently by W. Prager were anticipated in this paper). It is to be noted, however, that the problem of determining an effective method of actually acquiring the solution to a specific problem is not solved in this paper. In the category of development of such methods we seem to be, currently, ahead of the Russians.—A. Charnes, Northwestern Technological Institute and The Transportation Center.
The quantitative aspects of business management were left almost entirely in the hands of accountants prior to the advent of “scientific management” some seventy-five years ago. Although this term has fallen into disuse, the emphasis upon quantitative bases for decision-making and control has increased as the management problem has become more complex. Needs for additional data and for more comprehensive analysis have brought changes in accounting to provide more frequent and more detailed information. New systems for processing data have been developed; in some cases these appear to have replaced or to have amended the traditional notions about accounting. Actually, none of the new methods really alters the basic situation: no one approach to managerial measurements is completely effective in all circumstances. What is really needed is a combination of techniques; traditional and novel methods, census and sampling techniques, general- and special-purpose analyses all contribute to the measurement objective. We should strive to combine all available quantitative techniques in such ways as will provide optimum service to meet the needs of management.