Stock control in a many depot system

The chief problems considered are: (1) In a parallel set of warehouses, how should stocks be allocated? (2) In a system consisting of a central warehouse and several subsidiary warehouses, how much stock should be carried in each? The demands may have known, or unknown, distribution functions. For problem (1), the i-th stock n_i should usually be allocated in proportion to the i-th demand m_i; in special cases, a significant improvement is embodied in the formula (N = total allocable stock)

     

Simulations to explore alternative sequencing rules

A flexible simulation system has been designed to permit investigation of sequencing rules in a large job shop, with continual input of new work. The objective is to understand what happens rather than to find optimum rules, with many conflicting measures of effectiveness: work in process, finished goods investment, delays, machine and labor utilization, and effort to implement. A few problem areas have been explored.     

An application of servomechanisms to inventory

In recent years, some attention has been devoted to the application of techniques of control theory to inventory management. In particular, H. Vassian (1955) developed a model for a periodic review inventory system utilizing techniques of discrete variable servomechanisms to analyze the system in a cost-free structure. The resulting model is inherently deterministic, however, and emphasizes the control of inventory fluctuation about a safety level by selecting an appropriate order policy. Such an order policy is defined only up to an arbitrary method of forecasting customer demands. The present paper is a continuation of the model developed by Vassian in which exponential smoothing is used as a specific forecasting technique. Full recognition of the probabilistic nature of demand is taken into account and the requirement of minimizing expected inventory level is imposed. In addition, explicit formulas for the variance in inventory are derived as functions of the smoothing constant and the tradeoff between small variance and rapid system response is noted. Finally, in an attempt to remove the bias inherent in exponential smoothing, a modification of that technique is defined and discussed as an alternate forecasting method.     

Suboptimal algorithms for the quadratic assignment problem

The idea of combining relatively simple continuous methods with discrete procedures is used for the construction of suboptimal algorithms for quadratic assignment problems. Depending on the nature of the special problem these steps may vary in complexity. The simplest procedures require minimum storage space and result in tolerable computation times. Different choices of parameters and random variations may be used in order to obtain statistical distributions of suboptimal solutions. Computational results for sample problems indicate improvements on results of Steinberg, Gilmore, and Hillier and Connors.     

Impact of an all volunteer force upon the navy in the 1972-1973 timeframe

This paper develops estimates of true volunteer levels for 1972 and 1973, based on experience gained through 1970 draft lottery data. The paper also formulates estimates of the qualitative characteristics of a 1972-1973 Navy volunteer force, and establishes a relationship between rate of volunteerism and military pay. Utilizing estimates generated in the paper, Navy military personnel budget requirements for FY '72 and '73 are presented.     

A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

A finiteness proof for modified dantzig cuts in integer programming

Let be a basic solution to the linear programming problem subject to: where R is the index set associated with the nonbasic variables. If all of the variables are constrained to be nonnegative integers and x_u is not an integer in the basic solution, the linear constraint is implied. We prove that including these “cuts” in a specified way yields a finite dual simplex algorithm for the pure integer programming problem. The relation of these modified Dantzig cuts to Gomory cuts is discussed.     

Stochastic duels with round-dependent hit probabilities

The effect of round dependent hit probabilities in the fundamental stochastic duel are examined. The general solution and several specific examples are derived where one side's hit probabilities are improved from round to round. For these specific cases the advantages of round to round improvement are explicitly displayed.     

The search for an intelligent evader concealed in one of an arbitrary number of regions

This paper considers the search for an evader concealed in one of an arbitrary number of regions, each of which is characterized by its detection probability. We shall be concerned here with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move; his aim is to maximize the expected time to detection, while the searcher attempts to minimize it. The situation where two regions are involved has been studied previously and reported on recently. This paper represents a continuation of this analysis. It is normally true that as the number of regions increases, optimal strategies for both searcher and evader are progressively more difficult to determine precisely. However it will be shown that, generally, satisfactory approximations to each are almost as easily derived as in the two region problem, and that the accuracy of such approximations is essentially independent of the number of regions. This means that so far as the evader is concerned, characteristics of the two-region problem may be used to assess the accuracy of such approximate strategies for problems of more than two regions.