Knowledge that Transforms

The occasion of this meeting marks one more incident in peaceful international existence. The very spirit of the meeting itself, in which intellectuals and managers of different nations meet to discuss their mutual problems, is a sign of our times. We of Canada and the USA have learned to develop sound international relationships just as we are learning to establish sound relationships between science and management. Management science and the profession of operations research are both based on the general supposition that sound relationships between different parties in a decision making situation do exist and can be found by diligent search and research. We follow the pathway of a great historical precedent, which generally goes under the name of rationalism. The precedent says that sound relationships between different parties in a decision making situation can be established by means of reason. It goes on to say that reason is something that all men share, and that when men come to understand clearly, they inevitably will decide in the same ways. Management Technology, ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Management Science.

The July, I960, issue of Management Science contains an English translation of an important original article by L. V. Kantorovich [Kantorovich, L. V. Mathematical Methods of Organizing and Planning Production. Leningrad University, 1939, with a Foreword by A. R. Marchenko (Russian). An English translation, prepared by R. W. Campbell and W. H. Marlow, appears under this same title in Management Science Vol. 6, No. 4, (July, 1960), pp. 366–422.] and an introductory note by T. C. Koopmans [Koopmans, T. C. 1960. A note about Kantorovich's paper, ‘Mathematical Methods of Organizing and Planning Production'. Management Sci. 6 (4, July) 363–365.] which is both evaluative and explanatory. In his penultimate paragraph, Professor Koopmans accords a tribute to this writing of Kantorovich which is at least partly deserved, although it is also paid for, we think, at too high a price in modesty for Professor Koopman's own work as well as the work of others. There is a certain lack of precision at critical points in the Kantorovich article which may tend to compound this price if allowed to stand through time. Professor Koopmans does not take adequate account of this lack of precision—e.g., in his discussion of the computing methods—perhaps because he restricted himself to a very short preface. Also, he runs together various major ideas (resolving multipliers, duality and efficiency prices) which need to be separated for more careful examination. Finally, the discussion is so cryptic as to raise some questions as to what Koopmans had in mind in his closing references wherein he compares Kantorovich's accomplishments (in the instant article) to those of von Neumann, Dantzig, et al. In this paper we shall examine some of these ideas at greater length than Koopmans permitted himself but without necessarily confining ourselves to the instant article by Kantorovich or to its preface by Koopmans.

In this paper a proof of Herbert Scarf's on the optimality of (S, s) policies in inventory theory is extended to cases where differentiability of cost functions may not be available. In addition to an ordering cost composed of a unit cost plus a reorder cost all that is needed in the proof is that the expected holding and shortage cost function be convex.

There have been several publications dealing with the theory of semi-Markov processes, [1–6]. Most of these have been purely theoretical analyses, although it is realized that the theory has many potential applications, [4, 6], particularly to so-called “repairman” problems and to problems in reliability. Other work along these lines has recently appeared in the literature, [8–11]. These papers are concerned with the reliability of multi-state mechanisms [8], with surveillance plans, [9, 10] and with inventory problems. In particular, the work of Barlow and Proschan considers a model almost identical to our own, using renewal theory methods. Since the semi-Markov process can be considered to be a generalization of renewal theory, it is not surprising that such applications are the first to suggest themselves. It is the purpose of this paper to present an application of the theory of semi-Markov processes to a problem in maintenance theory and obtain results which we believe to be new. The body of this paper will consist of material relevant to the actual problem; a development of the theory as needed in our presentation will be found in the Appendix.

Production smoothing (or production planning) methods are used to decide on aggregate production levels for a factory, without specifying what individual products should be produced, or when, or how much. Inventory control of finished goods inventory makes these latter decisions, but does so for each product, independently, without regard for the aggregate effect on the factory. This paper discusses several (unsatisfactory) attempts to make these two sets of decisions consistent, and then presents several ways of making trigger and lot-size inventory decisions (production decisions for individual products) that aim at minimizing total inventory costs while yielding a desired level of aggregate factory production.

When a system is described in terms of a linear programming problem max c T x with Ax ≦ b, x ≧ 0, study of its properties, e.g., sensitivity analyses, etc., focuses on effects of alterations in the triple (A, b, c) on the properties of the system. These effects are non-linear and generally lead one away from a model with convenient special structure to much more complex systems. In this paper, methods (“repricing-reprocessing” theorems) are developed which (under certain assumptions about real world behavior) permit one to assess these effects exactly by means of a model of the same structure which can be prescribed in advance. The proofs of these theorems are accomplished by the “chained construction” methods of Charnes and Cooper. Approximation techniques and exact characterization of the non-linearities are also presented.

The stochastic scheduling problem discussed in this paper is similar to the classical inventory model. It is concerned with the demand for a single commodity expressed as a set of independent stochastic variables with known distributions and an objective functional composed of production and inventory cost variables. The model, however, incorporates a uniquely determined planning horizon, and in the usual application requires only a finite number of time periods. The horizon period is based upon the minimum expected loss in the operation and therefore is subject to the stochastic variables of demand.

n samples are drawn from a known distribution, ordered and placed in groups inside file drawers with a previously decided number of samples going in each drawer; the initial (ordered) sample in a drawer defines the “beginning” of a drawer, and the initial (ordered) sample of the next drawer defines the “end” of the drawer under consideration. If N new samples are drawn from the same distribution, what is the probability that x of them fall “inside” a given filing drawer? Is it shown that this probability depends only on the number of original samples “inside” a drawer, and is independent of the original sampling distributions and of the original sample which defines the beginning of the drawer. Hence, if the design objective is to equalize the overflow probability of each drawer, the best a priori policy is to divide the original ordered samples equally among the file drawers.

A systematic computation procedure is given for determining redistribution of stock among several user activities when set-up charges are involved. The procedure is divided into two phases, the first of which determines whether any redistributions should be made at all. Then the second phase determines the total amount to be shipped or received at each activity.

A goal of good management should be to design a reward system for those who take risks in making decisions in such a manner that the rewards to the individual correlate positively with the worth of the decision to the organization (taking into account the attitude of the top management to variance as well as to expected gain). In many organizations cost accounting supplies much of the information used for control at several levels. In this paper we examine some of the control problems that arise if joint costs are assigned by various cost accounting and some internal pricing conventions.