Optimal layered search

This article investigates the problem of planning an optimal layered search for a stationary target. A search is layered if it assigns each point in the search space an integer number of glimpses or looks. General necessary and sufficient conditions and an existence theorem are obtained. The special case in which the initial target distribution is bivariate normal is considered in detail.     

Application of dirichlet integrals for curtailment problems in sampling inspection

The standard problem in sampling inspection is to consider plans with and without curtailment. Curtailment causes difficulty and authors rarely give exact results (i.e., exact OC and ASN functions) for curtailed procedures. In this article we regard curtailment as an inverse sampling procedure and use Dirichlet integrals to obtain exact formulas for the OC, the ASN, and also the variance of the number of observations required under three types of plans: no curtailment, semicurtailment (for rejection only) and two-sided curtailment. Different sections of the article deal with the single sample, the two-stage, and the multiple-stage sampling problems. New tables for carrying out the single-sample procedure are included in the article. The authors feel that this article presents new directions and new ways of dealing with problems associated with quality control.     

A model for critical crack size estimation in fatigue failure of gun barrels

With repeated firing, fatigue cracks are produced in a gun barrel, and the barrel is no longer useful when a crack reaches a critical size. The initial crack size and the critical crack size, as well as the number of firings producing the critical crack size, may be considered as random variables. Assuming a proportional damage model for crack growth, a method for estimating the critical crack size distribution is presented. From these results, an estimate of the barrel life, or the residual barrel life once a crack of a given size is measured, can be obtained.     

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.     

Pareto-optimality in classical inventory problems

In this paper the inventory problem with backorders both deterministic and stochastic is studied using trade-off analysis in the context of vector optimization theory. The set of Pareto-optimal solutions is geometrically characterized in both the constrained and unconstrained cases. Moreover, a new way of utilizing Pareto-optimality concepts to handle classical inventory problems with backorders is derived. A new analysis of these models is done by means of a trade-off analysis. New solutions are shown, and an error bound for total inventory cost is provided. Other models such as multi-item or stochastic lead-time demand inventory problems are addressed and their Pareto-optimal solution sets are obtained. An example is included showing the additional applicability of this kind of analysis to handle parametric problems. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 83–98, 1998     

Solving a selected class of location problems by exploiting problem structure: A decomposition approach

For many combinatorial optimization problems that are NP-hard, a number of special cases exist that can be solved in polynomial time. This paper addresses the issue of solving one such problem, the well-known m-median problem with mutual communication (MMMC), by exploiting polynomially solvable special cases of the problem. For MMMC, a dependency graph is defined that characterizes the structure of the interactions between decision variables. A Lagrangian decomposition scheme is proposed that partitions the problem into two or more subproblems, each having the same structure as the original problem, but with simpler dependency graphs. The dual problems are solved using subgradient or multiplier adjustment methods. An efficient method of adjusting the multiplier values is given. Computational results are reported that show the method to be quite effective. In addition, applications of the approach to other difficult location problems is discussed. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 791–815, 1998     

A class of Bayes-optimal two-stage screens

Items are characterized by a set of attributes (T) and a collection of covariates (X) associated with those attributes. We wish to screen for acceptable items (T ∈ C_T), but T is expensive to measure. We envisage a two-stage screen in which observation of X_ is used as a filter at the first stage to sentence most items. The second stage involves the observation of T for those items for which the first stage is indecisive. We adopt a Bayes decision-theoretic approach to the development of optimal two-stage screens within a general framework for costs and stochastic structure. We also consider the important question of how much screens need to be modified in the light of resource limitations that bound the proportion of items that can be passed to the second stage. © 1996 John Wiley & Sons, Inc.     

Assemble to order and assemble in advance in a single-period stochastic environment

Faced with stochastic demand, a firm may decide to assemble its products in advance or assemble them once actual demand is realized. In general, the production cost for items assembled in advance (AIA) is lower than for items assembled to order (ATO), because there is no need to expedite, and the production process can be planned and executed well in advance. On the other hand, items assembled in advance (AIA) for which there is no demand incur excessive and unnecessary assembly costs. The two policies, AIA and ATO, as well as a composite one, are compared and analyzed in light of these trade-offs. The composite model, which is shown as the dominating policy, is also extended to deal with the following two scenarios. The first assumes a loss of a fraction of the demand when demand cannot be satisfied from the shelf but rather through ATO. The second considers the effects of budget constraints on the total inventory cost. © 1995 John Wiley & Sons, Inc.     

Queueing processes and trade-offs during ship-to-shore transfer of cargo

This article examines the ship-to-shore transfer of cargo from ships that are located offshore. In these situations, cargo is transferred from the ships to smaller craft, which in turn transport the cargo the remaining distance to shore. These craft cycle back and forth from the ship to the shore until the transfer is complete. Queueing of these craft often occurs, as they must wait at either the ship or the shore for a loading or unloading position to become free. Two different methods of modeling this ship-to-shore transfer of cargo are developed and applied. One is an analytic queueing model and the other is a more traditional simulation model. The analytic model is found to produce results quite similar to the simulation model. Examples are shown that use these models to analyze trade-offs between variables affecting the ship-to-shore transfer of cargo and the total time to transfer a given amount of cargo ashore. © 1994 John Wiley & Sons, Inc.