Incorporating redundancy considerations into stockage models

This article is concerned with evaluating the impact on weapon system availability of component and assembly redundancy. The evaluation must be efficient, and it must be possible to integrate the evaluation into multiechelon stockage models whose objective is to find the least cost mix of stockage consistent with the availability goals for weapon (or other type) systems. The mathematics to be discussed here provides a rigorous solution to the evaluation problem when there is only a single supply echelon; there can be upper-echelon repair, but not supply, unless the supply is from a “perfect” supplier, always in stock. For the more general multiechelon case, approximate approaches are presented.     

Facility location on a grid with a diagonal line

This article extends the traditional median problem on a grid to include a diagonal line (e.g., a street). In contrast to the traditional median problem, this generalized problem is nonconvex and nonseparable, invalidating some of the properties on which well-known median-seeking algorithms are based. This work presents an algorithm for finding the median on this generalized grid and discusses the relationship between it and the traditional median.     

On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

A generalized inspection game

The paper addresses the problem of a patrol trying to stop smugglers who are attempting to ship a cargo of perishable contraband across a strait in one of M time units. The situation was modeled as a two-person zero-sum game of exhaustion by Thomas and Nisgav and this article extends their results. The game has many characteristics in common with the Inspection Game in Owen's book on Game Theory; this Inspection Game is generalized and the relations between the two games are discussed.     

Multiobjective flow-shop scheduling

Previous research on the scheduling of multimachine systems has generally focused on the optimization of individual performance measures. This article considers the sequencing of jobs through a multimachine flow shop, where the quality of the resulting schedule is evaluated according to the associated levels of two scheduling criteria, schedule makespan (C_max) and maximum job tardiness (T_max). We present constructive procedures that quantify the trade-off between C_max and T_max. The significance of this trade-off is that the optimal solution for any preference function involving only C_max and T_max must be contained among the set of efficient schedules that comprise the trade-off curve. For the special case of two-machine flow shops, we present an algorithm that identifies the exact set of efficient schedules. Heruistic procedures for approximating the efficient set are also provided for problems involving many jobs or larger flow shops. Computational results are reported for the procedures which indicate that both the number of efficient schedules and the error incurred by heuristically approximating the efficient set are quite small.     

Estimating component characteristics from system failure‐time data

Suppose that failure times are available from a random sample of N systems of a given, fixed design with components which have i.i.d. lifetimes distributed according to a common distribution F. The inverse problem of estimating F from data on observed system lifetimes is considered. Using the known relationship between the system and component lifetime distributions via signature and domination theory, the nonparametric maximum likelihood estimator _N(t) of the component survival function (t) is identified and shown to be accessible numerically in any application of interest. The asymptotic distribution of _N(t) is also identified, facilitating the construction of approximate confidence intervals for (t) for N sufficiently large. Simulation results for samples of size N = 50 and N = 100 for a collection of five parametric lifetime models demonstrate the utility of the recommended estimator. Possible extensions beyond the i.i.d. framework are discussed in the concluding section. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal search for a moving target with the option to wait

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (Pollock, Operat Res 18 (1970) 883–903). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, J Appl Probab 23 (1986) 708–717). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009