Showing papers in "Management Science in 1961"

A Network Flow Computation for Project Cost Curves

Abstract: A network flow method is outlined for solving the linear programming problem of computing the least cost curve for a project composed of many individual jobs, where it is assumed that certain jobs must be finished before others can be started. Each job has an associated crash completion time and normal completion time, and the cost of doing the job varies linearly between these extreme times. Given that the entire project must be completed in a prescribed time interval, it is desired to find job times that minimize the total project cost. The~method solves this problem for all feasible time intervals.

A Nonlinear Programming Technique for the Optimization of Continuous Processing Systems

Abstract: A description is given of a method for solving some nonlinear programming problems. The mathematics of this method are quite simple and are easy to apply to electronic computation. A numerical example, a model construction example, and a description of a particular existing computer system are included in order to clarify the mode of operation of the method.

Aggregation of Utility Functions

Abstract: We are primarily concerned here with the question of integrability of the total demand in a model in which each consumer acts according to a cardinal utility function and has a fixed monetary income. It is well known that concavity of the various utilities is not sufficient to guarantee integrability, nor even to ensure rationality of the revealed preference. We show that if each personal utility function is homogeneous, in addition to satisfying the usual regularity conditions, then an aggregate utility function can be defined explicitly in terms of the given utilities. Furthermore, under the same assumptions we give a new characterization of equilibrium and show that equilibrium satisfactions are unique.

The Role of Management Games in Education and Research

Abstract: This paper is intended to be a broad survey of both the present and the potential role of management games in education and research. Against a background of the history of business games, we first try to characterize the present development of these games. A few management games are described in some detail, and a number of others are mentioned only briefly. The differences between general and functional business games are discussed. Present uses of management games as a teaching device are surveyed and evaluated. Some hypotheses regarding the relations between the design and administrative characteristics of a business game and its educational properties are also formulated. What might be a major improvement over existing management games, here named the “game case,” is then suggested. In the concluding portion of this paper, the potential use of management games as a laboratory for business and social science research is surveyed. Some methodological problems which would arise from research uses of business games are also discussed.

Inter-Temporal Analysis and Optimization of Bank Portfolios

Abstract: This paper is concerned with formulating, exploring and interpreting the uses and constructs which may be derived from a mathematical model of programming type which expresses more realistically than past efforts the actual conditions of current operations. It is an attempt to provide a means of attaining thereby an objective understanding of the implications of actual Federal Reserve liquidity policy on the actions and opportunities of banking institutions. The model presented corresponds to the problem of determining an optimal portfolio for an individual bank over several time periods in accordance with requirements laid down by bank examiners which are interpreted as defining limits within which the level of risk associated with the return on the portfolio is an acceptable one. The problem is transformed into an equivalent one offering advantages of analysis and of computation. Some methods of effective computation are explored.

Reactions to Intergroup Competition Under Win-Lose Conditions

Abstract: Findings from investigations concerning the dynamics of intergroup competition under win-lose conditions are summarized first. The second step is to demonstrate, by presenting a synopsis of a real case, how these findings can be applied in converting a situation of management-union conflict into one of collaboration. The conclusion is that the industrial ethic which causes groups to interact with one another on a competitive win-lose basis, must and can be replaced by the new ethic which makes it possible for groups to approach their differences in points of view from a problem-solving orientation based on openness and reinforced by mutual respect and trust.

An Inventory Model for Arbitrary Interval and Quantity Distributions of Demand

Abstract: The inventory problem for continuous time is studied under the following assumptions about the demand process (1) an arbitrary distribution of the length of intervals between successive demands; (2) a distribution of the quantity demanded which is independent of the last quantity demanded and any previous events but may depend on the time elapsed since the last demand; (3) unfilled orders are backlogged. The delivery time is fixed. Costs considered are fixed ordering costs and proportional costs of purchase, storage and shortage. The loss function and the equations for reordering point and minimal ordering quantity are derived. Formulae are calculated for the Poisson, stuttering Poisson, geometric, negative binomial, Gamma and compounded distributions.

Queues with Dynamic Priority Discipline

Abstract: A report on the writer's computer simulation studies of queues in which service order is governed by due-date-like priorities. The main results are in the form of conjectures about the upper tails of the waiting-time distributions. Pertinent mathematical research is mentioned.

The Balance Delay Problem

Abstract: Balance delay time is the amount of idle time on production assembly lines caused by the uneven division of work among operators or stations. It is related to the extent and way the total task is subdivided. In this paper the problem of balance delay is treated empirically and analytically. Empirical studies show that high balance delay is associated with a wide range of work-element times and a high degree of line mechanization. The analytical study yields a general algebraic method of minimizing balance delay by the appropriate choice of cycle times. Balance delay functions are drawn and the condition of perfect balance is shown to coincide with the zero points of these functions.

Two Experiments on Bias and Conflict in Organizational Estimation

Abstract: In recent years there has been increased interest in the effects of internal communication on decision processes. A number of hypotheses relating the bias in information to the final decision have been proposed. In this paper we discuss two laboratory experiments which were designed to test two such hypotheses. The first experiment tests the hypothesis that cost and sales estimations are made with the implicit assumption that a biased pay-off structure exists. The second experiment tests explicitly the effects of biased and unbiased pay-off structures on estimation within an organization. An analysis of the data for the two experiments is made and some implications for further research are drawn from the results.

A Family of Inventory Models

Abstract: An inventory control model in which the state of the system is reviewed only at discrete, equally spaced time intervals is studied. A procurement is made if at the review period the inventory position of the system is less than or equal to a number k. The quantity procured is an integral multiple of a number Q. The total expected cost of review, procurement, holding inventory, and stockouts is determined under the assumption that all demands are ultimately met. The cost of a stockout is taken to consist of a fixed cost per unit out of stock plus a variable cost which is proportional to the time out of stock. Specific expressions for all the cost expressions are found for the case of 1 Poisson demands and fixed lead times, and 2 Poisson demands and gamma lead times. It is shown that many of the inventory models discussed in the literature are special cases of the model here described.

On Scheduling Tasks with Associated Linear Loss Functions

Abstract: In a recent paper in Management Science, Robert McNaughton has discussed certain problems encountered in scheduling tasks on one or more processors when penalties are imposed if the tasks are finished after their respective deadlines. In this paper, the general problem of scheduling the tasks on one processor in order to minimize the total loss is solved, and McNaughton's results are generalized.

An Optimal Final Inventory Model

Abstract: A model is developed which allows the determination of the optimal inventory level for an item at any time if no additional procurements are to be made. It is assumed that the item has a known date of obsolescence and that the demand is Poisson distributed with a fixed mean over the useful life of the tem. The model constitutes an extension of other life-of-type models in that both costs which are incurred at a fixed point in time liquidation losses and other costs which are a function of time carrying charges and stock-out costs are included. In many operational situations both of these types of costs are relevant.

Some Team Models of a Sales Organization

Abstract: The models presented in this paper grew out of an attempt to apply the theory of teams of Marschak and Radner to the organization of the sales force in a typical wholesale bakery. As organizations go, the one we have chosen to analyze is an extremely simple one, even when---as is quite obviously not the case in what follows---it is viewed in its full complexity. At the risk of achieving results of quite limited general interest, a “simple,” easily quantified subject was deliberately chosen as the best place to begin to apply a theory that pretends to prescribe optimum decisions of a team in a precise way. We shall not here go much beyond a discussion of some mathematical models which deal only with the day-to-day problem a bakery sales force faces in attempting to “properly” supply its regular customers with a single product. Problems of advertising, of price policy, of product design, and of obtaining new customers are ignored. All the reader needs to know, to begin with, is that the sales force consists of truck-driver salesmen who daily visit each of their given customers i.e. grocery stores leaving, on consignment, an amount of bread to be decided by the salesman. At the end of the day the salesman returns to the plant and submits an order for the next day. For our purposes here the “organization” is characterized by the way in which these orders are jointly formed. In the last section, after the models have pin-pointed the organization problem, we shall return to a more detailed description of procedures found in practice.

A Redistribution Model with Set-Up Charge

Abstract: This paper considers the problem of redistributing stock among several user activities within the period between regular deliveries of new supplies to the system. The cost of redistribution is assumed to be proportional to the number of shipments among the activities. A procedure based on minimizing total redistribution and shortage costs within the period is given for determining the amounts (if any) to be shipped among activities.

On Production Smoothing

Abstract: The production planning model of Modigliani and Hohn and the smoothing model of Hoffman and Jacobs are combined. The most interesting result is that the horizon planning properties of the individual models are retained in the combined model. Methods are also given for the computation of optimal production schedules for certain kinds of requirements schedules.

A Linear Programming Model for Long Range Capacity Planning

Abstract: In comparing long-and short-term commitments to fulfill demand for some kind of capacity, a linear formulation of the problem may prove useful. The general capacity-planning problem treated here is that in which the demand for capacity may be met by ownership, leases of various terms, or spot contracts. Certain kinds of machine capacity, tankers, or trucks might be examples. Variations in demand and prices for the various alternatives give rise to a computational problem of considerable proportions and in addition one must account for the firm's time preference for money. A linear model is presented to aid in developing answers to such questions as the following: 1 What effect will any given demand forecast have on capacity plans, 2 what will be the effect of an expected change in ownership costs, 3 if prices for leased capacity increase by some given amount, how will plans and costs be affected, 4 what is the sensitivity of decisions and costs to forecast error? Computation of an optimal plan under various assumed conditions should provide 1 the best policy for the expected future and 2 those changes in policy which ought to follow from changed conditions.

Characteristics of Optimal Maintenance Policies

Abstract: This paper presents an approach to maintenance planning which utilizes mathematics and economic theory to help select an optimal maintenance condition. The maintenance problem is discussed first with respect to short run (daily) routine operating decisions, and then with respect to long run decisions as they relate to equipment design and to maintenance facilities. The maintenance problem is then stated in mathematical terms. A cost minimizing maintenance model is described which takes account of such factors as deterioration and failure probabilities, manhours for preventive inspection and preventive repair, elapsed time for emergency diagnosis and repair, cost of setting up for periodic maintenance, cost of maintenance men, and cost of system downtime. A numerical example illustrates how the model can be used to determine the least cost combination of time between periodic maintenance, the number of maintenance men, and the number of periodics between inspections of each item for a required level of sys...

The Use of Heuristic Programming in Management Science—A Survey of the Literature

Abstract: Intelligent problem-solving, whether by man or by machine, implies selective rather than just rapid behavior. Humans achieve this selectivity through heuristics—principles that, on the average, contribute to reduction of search in problem-solving. Heuristic programming is the construction of computer problem-solving programs whose behavior is similarly organized. This paper surveys the present and potential use of heuristic programming in management science.

Optimal Inventory Depletion Policies

Abstract: Consider a stockpile of items whose field life is a non-negative function of the age of the item upon being issued. Assume that only one item is in use at a time and that a demand occurs only when the item in use is completely exhausted. Six theorems are given which extend the class of field life functions such that either LIFO or FIFO are optimal issue policies.

FIFO and LIFO Policies in Inventory Management

Abstract: Evaluation of FIFO (=first in first out) versus LIFO (=last in first out) policies in stock depletion problems has hitherto been based on the classification of field life functions as convex and concave, the optimal policy for n > 2 units being determined when the optimal policy for n = 2 units is known. This paper suggests a test for selecting the optimal policy for the n = 2 system, for field life functions with a derivative equal or larger than −1, and by induction the conclusions are extended to n > 2. When the derivative is smaller than −1, LIFO is shown to be an optimal policy.

Notes on Quadratic Programming: The Kuhn-Tucker and Theil-Van De Panne Conditions, Degeneracy, and Equality Constraints

Abstract: The purpose of this note is to prove that the rules on which Theil and van de Panne [Theil, H., C. van de Panne. 1960. Quadratic programming as an extension of conventional quadratic maximization. Management Sci. 7(1) 1–20] based their recent method to follow straightforward from the well-known Kuhn-Tucker conditions and to propose a method for handling degeneracy in quadratic programming.

Three Modes of Conflict

Abstract: It is possible to distinguish three levels of conflict. One level can be exemplified by a “fight,” i.e., a combat motivated only by mutual animosity or mutual fear. In a fight, the opponent is just a noxious stimulus. The actions of the combatants are dominated by an urge to destroy or to drive away this noxious stimulus. The~aggressive acts of each of the opponents stimulate aggressive counter acts of the other. This process, then, is mostly self-perpetuating and automatic. Such are the combats one finds in the sub-human world, combats between enemy species, between rivals for a mate, between competitors for food or living space.

A Pattern for Reporting Operations Research to the Business Executive

Abstract: This paper emphasizes the purpose of an Operations Research report to business executives, discusses some of the problems of language and attitude, defends the need for executive “intuition” and suggests a format for Operations Research reports. Management Technology, ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Management Science.

On an Industrial Programming Problem of Kantorovich

Abstract: This paper is a presentation of a maximization problem treated by L. V. Kantorovich [Kantorovich, L. V. 1957. On methods of analysis of some extremal problems in planning production. Doklady Akademii Nauk SSSR 115 441–444. (Russian) In translation: Rand Corporation T-86 dated 15 April 1958]. The problem concerns a linear model for industrial production, but the objective is to maximize a non-linear function of the output. Specifically, a certain composition or package of final products is ordered, and the size of this output of predetermined composition is to be as large as possible.

Administration of Safety in the Steel Industry

Abstract: Research in a single steel company highlighted the existence of autonomous safety goals and the importance of innovative activity in their realization. A key communications function in the process of innovation is performed by means of an industry-wide organization of staff specialists. Some confirmation of the relevance and effectiveness of this system is given by an analysis of plant injury rates for the steel industry as a whole.

The National Security Dilemma: Challenge to Management Scientists

Abstract: This paper was presented as the banquet address at the 7th International Meeting of TIMS in New York City, October 20, 1960. The following paper, by Anatol Rapoport, was also on the program of this meeting. In view of the interest aroused by the contrasting positions taken, the Editor asked each author to submit his paper for publication in Management Science along with comments on the other's paper. The four resulting papers appear together in this issue of Management Science.

Development of an Efficient Account-Numbering Method

Abstract: The desirability of maintaining customer accounts in both alphabetic and numeric sequence is discussed. An~account-numbering method is described which provides almost exact alphabetic and numeric sequencing even though the original file may grow by several hundred percent. The mathematical basis for the method is developed and an illustrative example shows how the method would be applied to the design of a particular account system.

Computer Management Control Systems Through the Looking Glass

Abstract: A discussion of three aspects of the introduction of real time computer executive control systems into the world of business, using as a frame of reference the experience acquired through the design and operation of a similar military system, SAGE, over the past several years. In particular, consideration is given to the relative effectiveness with which the system communicates with its environment, the necessary compromises in the definition of the rules by which the system will function, and certain difficulties in the concept of executive control systems which are in some sense adaptive.

Management Science and Research in Great Britain

Abstract: This paper is divided into three parts. In the first part, the present stage of development of management science in the United Kingdom is briefly discussed; in the second part are given a few “case histories,” stressing the methodology; the third part discusses a few recent features of management science in the United Kingdom which seem to be interesting.