Differential game theoretic analysis of a problem of warfare

The present article considers a problem of missile warfare. It is formulated as a problem of economics and treated as a differential game. Some optimal strategies of targeting and firing of missiles are derived. Conditions under which such a war can be prevented are also developed.     

Optimal inventory policy when stockouts alter demand

An inventory model in which future demand is affected by stockouts has been considered recently by B. L. Schwartz. Some generalizations of Schwartz's model are presented in this paper and properties of the optimal policies are determined. In the case of deterministic demand, a set-up cost is included and a mixture of backlogged and nonbacklogged orders is allowed during stockout. It is proved that the optimal policy entails either no stockout or continual stockout, depending on the values of three parameters. For stochastic demand, the effect of stockouts on demand density is postulated, the resulting optimal inventory policy is discussed, and an example involving an exponential density function is then analyzed in detail.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

The evolution of a selection system

The article is a case study. It describes the initialization and subsequent modifications of the selection process used for the annual Award for Excellence in Teaching at the Naval Postgraduate School (NPS). The method treats highly unbalanced data and utilizes some exploratory data analysis techniques in interesting ways. It leads to a defensible choice for a winner in a very messy setting. The award designates a faculty member as “teacher of the year” and includes a stipend of substantial value. The recipient is chosen by a committee which reviews objective information summarized from ballots submitted by franchised voters. The issues encountered have some general content and the handling of a number of them may have broader interest. ©John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Floor layouts using a multifacility location model

A procedure for obtaining a facilities scatter diagram within a rectangular boundary is developed using a multifacility location model. This method gives favorable computational results and has the advantage over other scatter diagram methods of being able to accommodate fixed facility locations. Examples illustrate how this method can be used by a designer/analyst either as a one-step algorithm or iteratively to build a layout.     

Operations analysis during the underwater search for Scorpions

This paper discusses the operations analysis in the underwater search for the remains of the submarine Scorpion The a priori target location probability distribution for the search was obtained by monte-carlo procedures based upon nine different scenarios concerning the Scorpion loss and associated credibility weights. These scenarios and weights were postulated by others. Scorpion was found within 260 yards of the search grid cell having the largest a priori probability Frequent computations of local effectiveness probabilities (LEPs) were carried out on scene during the search and were used to determine an updated (a posteriori) target location distribution. This distribution formed the basis for recommendation of the current high probability areas for search The sum of LEPs weighted by the a priori target location probabilities is called search effectiveness probability (SEP) and was used as the overall measure of effectiveness for the operation. SEP and LEPs were used previously in the Mediterranean H-bomb search On-scene and stateside operations analysis are discussed and the progress of the search is indicated by values of SEP for various periods during the operation.     

A bivariate normal theory maximum-likelihood technique when certain variances are known

A maximum-likelihood technique is described for estimating the bivariate normal distribution of the estimates of two or more related values when data are obtained from several different sources, each having known variance. The problem is comparable, in the bivariate sense to estimating the mean of a normal population with known variance. The results tend to be dominated by those sources of data associated with the smallest variances.     

On the evaluation of investment proposals having multiple attributes

A framework is developed for analyzing the likelihood of acceptance of an investment project proposal when objectives are uncertain. The foundation is a utility model of top management's choice process, modified if need be through a Bayesian approach which takes into account any apparent inconsistency in the history of past proposal acceptances and rejections.     

Upper and lower bounds for a pattern bombing problem

This paper includes two simple analytic formulas for kill probability that are applicable in circumstances where shots should be fired in a pattern. The two formulas bracket the maximum kill probability achievable with an optimal pattern. The upper bound corresponds to an optimal nonfeasible pattern, and the lower bound to a nonoptimal feasible pattern.