Search

The article presents abstracts of contributed papers submitted for presentation at the Chicago Meeting. The paper "Computer Simulation in a Missile Operational Cycle," by Robert T. Morrison explains a model of a hypothetical weapon system is analyzed by simulation techniques using a digital computer. All the important parameters affecting the model are identified and values selected. Random numbers selected by the computer are used to determine the occurrence of missile and GSE malfunctions according to the failure rates established and also to determine the repair times for the missiles and GSE if malfunctions occur. Another paper "A Measure of Effectiveness for Weapon-System Evaluation," by Robert T. Morrison explains a concept for a measure of effectiveness is developed for evaluating and judging weapon-system design and operation The proposed measure of effectiveness considers the most important factors in any complex system-maximum performance and reliability with minimum cost and time This paper shows how the measure of effectiveness is valuable for system analysis in judging between alternative proposed systems in preliminary design and measuring and evaluating the selected system progress from prototype design through final system operation and maintenance.

Comments on the paper 'A General Method for Nonlinear Programming,' by Anthony V. Fiacco, Nicholas M. Smith and David Blackwell. Application of the principle of entry into a constrained space to Carroll's technique; Computation of the starting point for the original problem.

The article presents comments on the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. The paper focused on an integer programming formulation of a one-machine job shop problem. The author contends that Maxwell made in error in proving the validity of an optimal algorithm by applying cutting plane constraints to the problem. The author explains that the problem cannot be solved through traditional cutting plane procedures. The author provides a mathematical model in an attempt to correct the proof.

Presents a letter to the editor about the optimal policy in a maintenance cost problem.

Copyright of International Journal of Production Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A central question of many previous monetary studies has been the determination of the effects of various forces upon the actual supply of money in the economy. One of a number of competing monetary supply hypotheses (Brunner and Meltzer) has focused on the relationship between bank reserves and deposit creation. This theoretical structure was first suggested in earlier works by Phillips and Crick. Recent studies of similar nature, including those of Mellon and Orr, Morrison, and Brown and Lloyd, have employed the techniques of inventory theory to examine the factors influencing bank credit expansion. Similar inventory treatments of other cash balance and portfolio adjustment models are presented in the works of Baumol, Eppen and Fama, Lloyd, and Chitre. In the present paper, the effects of various forces on the optimal expansion of credit and the holding of reserves are investigated using the techniques of dynamic programming (see, for example, Bellman and Dreyfus). Discussed in the paper are the effects on bank credit expansion of uncertainty about reserve losses, various types of penalty costs, costs of adjustment, uncertain future interest rates, and of various institutional structures under which the bank must operate. This latter topic is important because of the Federal Reserve policy change of September 1968. Prior to that time, required reserves and actual reserves were computed over the same reserve period. Since that time, however, the required reserves in any period are known with certainty at the beginning of the period and depend upon deposit levels two periods earlier. For purposes of mathematical convenience, this latter structure is treated here as a one-period lag. [ABSTRACT FROM AUTHOR]

This article informs about the Operations Research Society of America's "Thirteenth National Meeting" which was held at Boston, Massachusetts from May 15-17, 1958. From a total 521 registrations, there were 301 were members, 186 were non-members, 34 were students. Seventy-one contributed and twelve invited papers were read. For the purpose twelve sessions were held, nine of which were half-day sessions. All-day sessions were held on Dynamic Programming, on Operational Gaming and Simulation and on Techniques of Simulation Using Digital Computers, the latter was the only session on May 17 and was held at the Computation Center of the Massachusetts Institute of Technology. The subjects of some of the individual sessions, and their chairmen, were: George E. Kimball for Dynamic Programming; Philip M. Morse for Forecasting; William Young for Contributed Papers; John M. Magee for Experimentation; Jay W. Forrester for Operations Research in Data Processing and Leon S. Pocinky for Techniques in Simulations Using Digital Computers.

The article presents an analytical model for the derivation and selection of an optimal profit curve for a given firm by utilizing its internal financial data. The underlying model of the Riesz-Kakutani representation theorem is reviewed and used as a basis to select optimal examples from a firm's various possible profit curves.

This paper examines properties and interrelations of several concepts of generalized concavity. It shows that the class of functions that are both ‘generalized concave’ and ‘generalized convex’ is closely related to the class of monotone functions of a single variable. After excluding a certain small class of exceptions, the paper shows that, for arbitrary (perhaps not differentiable) functions, concave implies pseudoconcave, pseudoconcave implies strictly quasiconcave, and strictly quasiconcave implies quasiconcave. Several results characterizing the extreme values of generalized concave functions are given. [ABSTRACT FROM AUTHOR]

This paper considers the case of a product consisting of several components, each of which is batch manufactured. It assumes that the product demands occur singly, and that the components are manufactured in equal-batch quantities in a reorder level-batch quantity system. The paper is concerned with the optimal phasing of the components in order to minimize the variance of holding cost for the product. It shows that the optimal policy is independent of the order of sequencing of the components and is given when the phase lag between consecutive components in the cycle is equal to [(Ai+Aj)/∑all i Ai. (q/2), where Ai, Aj are the unit values of the components, and q is the batch quantity. A specific example is included to illustrate the three-component case and the discrete practical solution for any number of components is indicated. [ABSTRACT FROM AUTHOR]

The past decade has given rise to a considerable amount of research in the fields of inventory control and production planning. One of the most useful mathematical models originated with the paper of K. D. ARROW, T. E. HARRIS, AND J. MARSCHAK, "Optimal Inventory Policy," Econometrica 19, 250-272 (1951). This model was further improved in RICRARD BELLMAN'S book, Dynamic Programming, pp. 152-182, Princeton University Press, Princeton, New Jersey, 1957. In the present paper, another formulation of the same problem is exhibited. The attentive reader will observe many similarities to the dynamic programming formulation. [ABSTRACT FROM AUTHOR]

Although the earliest discussions of linear programming date back to the 1930's, to the work of German and Austrian mathematicians and economists, the mathematics has been extensively developed only in the past six or eight years. Because of the relative newness of the subject, the literature is widely scattered and it is rather difficult for one just starting to learn about linear programming to know where to begin. Because of human limitations, the bibliography is necessarily incomplete. All papers and books that could be acquired that seemed to deal with the subject were perused and, if applicable, included. No extensive effort was made, however, to include papers dealing more or less exclusively with closely related topics, for example, the problem of determination of value and optimal strategies in a zero-sum, two-person game, the pure inequalities problem with no optimization, the subjects of convex functions and convex polyhedra, unless they also relate these topics directly to linear programming.

This paper introduces an efficient branch and bound algorithm for a special class of mixed integer programming problems called the warehouse location problem. A set of branching decision rules is proposed for selecting warehouses to be constrained open and closed from any node of the branch and bound tree. These rules are tested for their efficiency in reducing computation times and storage requirements to reach optimal solutions. An improved method of solving the linear programming problems at the nodes which substantially reduces the computations is also introduced in this paper. [ABSTRACT FROM AUTHOR]

Many manufacturing firms produce component parts both for assembly into new products and to meet orders for spare parts. An inventory model for this situation would involve two types of demands: probabilistic demand as spares and deterministic (or scheduled) withdrawals as components for assembly. Relevant costs would include a setup cost for replenishment orders, inventory carrying costs, and backorder costs. An analytical model approximating these characteristics is formulated. An optimal dynamic program for the periodic review case is briefly discussed; this policy is extremely costly to implement, however. Two feasible operating policies are considered in the paper: a continuous review (Q, r)-type policy and a simple periodic review scheduling heuristic. The paper concludes with sample economic comparisons of the cost of the (Q, r)-type policy and the heuristic policy for a set of numerical examples. [ABSTRACT FROM AUTHOR]

In an earlier paper [5], we generalized and extended Beckmann's results [1] for a production and inventory problem with proportional smoothing costs and demands being random variables. Our previous results concerned the finite horizon nonstationary case. Here we consider the infinite horizon stationary case. Two curves in the plane determine an optimal policy. They are shown to have slopes between minus one and zero, to be differentiable, and to be bounded by two straight lines with a slope Of minus one. These results are used (a) to accelerate each iteration of a successive approximations algorithm and (b) to formulate a linear programming problem from whose solution an optimal policy can be determined. [ABSTRACT FROM AUTHOR]

The paper presents a method for solving the linear programming problems, which is itself a step towards the generalization of the classical Simlex Method. It replaces two basic variables by two non-basic variables at each iteration. Naturally this will reduce the total number of steps to reach the final solution. The paper also includes the solution of one example to illustrate the applicability of the method. [ABSTRACT FROM AUTHOR]

This paper considers non-linear programming models in which randomized solutions are allowed. That is, we consider the minimization of the expected value of a non-linear function subject to constraints on the expectation of nonlinear functions, where the expectations are taken with respect to randomized decision strategies. Saddle-point and related optimality conditions similar to those given in [10] and [11] for convex functions are obtained with only very mild restrictions on the shape of the optimizing and constraint functions. We also consider when the optimal solution need not be randomized and how the notions of Lagrange multipliers and game theory are related to our results. We offer an economic interpretation of our solution. A few simple examples are given to illustrate the implications of randomized strategies. It is also pointed out how the results of this paper are related to the decomposition methods widely used to solve mathematical programming problems. [ABSTRACT FROM AUTHOR]

This article provides a framework for clarifying and testing a version of the "income-smoothing" hypothesis. In general, each version of the hypothesis is concerned with the extent to which managers may attempt to affect the volatility of a series of reported accounting numbers via selections and applications of accounting procedures. Two classes of stochastic processes will be considered with respect to rates of return. These classes are martingales and mean-reverting processes. A characterization of optimal smoothing action for an N-period horizon was derived via dynamic programming tools. This characterization provided access to several propositions regarding optimal smoothing actions under each kind of stochastic process and at various stages within the N-period horizon. These propositions indicate what one should expect if optimal smoothing is pursued by firms' managements. Moreover, they indicate that nonzero smoothing is no: always optimal. The paper only dealt with the effects of optimal smoothing actions on reported accounting numbers.

Presents a letter to the editor about the optimal design of optimization experiments.

A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz=min[sub i] c[sub i]x[sub i], subject to AX = b, X * (This character cannot be converted in ASCII text) O. Although the c[sub i] can be in the interval (-- ∞, ∞), the paper discusses the more common practical case where all c[sub t] * (This character cannot be converted in ASCII text) 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the 'fixed proportion' type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented. [ABSTRACT FROM AUTHOR]