Scheduling stochastic jobs on a single machine subject to breakdowns

A single machine is available to process a collection of stochastic jobs. There may be technological constraints on the job set. The machine sometimes breaks down. Costs are incurred and rewards are earned during processing. We seek strategies for processing the jobs which maximize the total expected reward earned.     

Design of a process control scheme for defects per 100 units based on aoql

A process control scheme is developed in which decisions as to the frequency of sampling are made based upon the choice of an Average Outgoing Quality Limit. The scheme utilizes plotted points on a U-control chart for defects and the theory of runs to determine when to switch among Reduced, Normal, Tightened, and 100 percent inspection. The scheme is formulated as a semi-Markov process to derive steady stale equations for the probabilities of being in Reduced, Normal, Tightened, or 100 percent inspection and for Average Outgoing Quality and Average Fraction Inspected. The resulting system and the computer programs used to derive it are discussed.     

Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

An F approximation for two-parameter weibull and log-normal tolerance bounds based on possibly censored data

An approximation suggested in Mann, Schafer and Singpurwalla [18] for obtaining small-sample tolerance bounds based on possibly censored two-parameter Weibull and lognormal samples is investigated. The tolerance bounds obtained are those that effectively make most efficient use of sample data. Values based on the approximation are compared with some available exact values and shown to be in surprisingly good agreement, even in certain cases in which sample sizes are very small or censoring is extensive. Ranges over which error in the approximation is less than about 1 or 2 percent are determined. The investigation of the precision of the approximation extends results of Lawless [8], who considered large-sample maximum-likelihood estimates of parameters as the basis for approximate 95 percent Weibull tolerance bounds obtained by the general approach described in [18]. For Weibull (or extreme-value) data the approximation is particularly useful when sample sizes are moderately large (more than 25), but not large enough (well over 100 for severely censored data) for asymptotic normality of estimators to apply. For such cases simplified efficient linear estimates or maximum-likelihood estimates may be used to obtain the approximate tolerance bounds. For lognormal censored data, best linear unbiased estimates may be used, or any efficient unbiased estimators for which variances and covariances are known as functions of the square of the distribution variance.     

Sequential tests for hypotheses concerning the product of poisson parameters with applications to problems in reliability and biometry

Sequential tests for the product of Poisson parameters based on the generalized incomplete modified Bessel (g.i.m.B.) distributions are given. Applications to reliability and biometry are indicated.     

A bayesian approach to evaluating military investments in product improvement and testing

Two issues of frequent importance in new product development are product improvement and reliability testing. A question often faced by the developer is: Should the product be distributed in its present state, or should it be improved further and/or tested before distribution? A more useful statement of the question might be: What levels of investment in further improvement and testing are economically permissible? Products for which this question is relevant may vary widely in type and intended use. This paper presents a model for determining these levels for one such product—an equipment modification procedure. The model presented makes use of present value analysis to compare cost streams and of Bayesian statistics to relate the costs to various outcomes under conditions of uncertainty. The model is applied to an actual military problem and a method is described for examining the sensitivity of the results to changes in the prior probabilities and discount rate.     

The impact of inventory information distortion due to customer order cancellations

In this paper we study the impact of cancellations of customer orders on an inventory system. We develop a periodic review (s, S) inventory model with Poisson demands, deterministic demand leadtimes and supply leadtimes. When no set up cost is present for replenishment, the behavior of the system cost can be studied analytically. For the case with a fixed set up cost, we derive the operating characteristics of the model via an embedded Markov chain analysis. Based on this, we formulate the total cost function and suggest a two‐phase approach to optimization. Our model can be used to compute cancellation fees and to evaluate the impacts of various conditions of cancellation. We find that cancellations, as major sources of inventory information distortion, increase total system costs, and the magnitude of the cost impact depends on the probability of cancellation and the expected cancellation time. Other relevant lessons and insights are also discussed. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 213–231, 1999