Properties of a source location estimator in the plane

The statistical properties of an estimator of a source location were established by simulation for the case in which the source location is estimated—using transformation of lines to points—from the angles in which different observers see the source, and both the assumed locations of the observer points and the observed angles are subject to error. It was found that for normal error distributions the estimator is unbiased, and the resulting estimates are approximately normally distributed with a small standard deviation. An easy-to-use and reliable forecasting formula was suggested to forecast the parameters of the distributions of the estimates for different observer-source relationships. © 1993 John Wiley & Sons, Inc.     

Production-location problems

The joint problems of determining the optimal plant location and optimal input mix and plant size are addressed. The interrelationship between input substitutability and plant location is stressed. Conditions under which the location problem can be separated from the determination of the optimal input mix are developed for a number of problem variations. The stability of the optimal location in the face of changes in problem parameters is also discussed. It is demonstrated that consideration of input substitutability often makes the resulting problem no more difficult to solve than problem formulations in which the inherent input substitutability is ignored.     

Machine maintenance with workload considerations

Machine maintenance is modeled in the setting of a single‐server queue. Machine deterioration corresponds to slower service rates and failure. This leads to higher congestion and an increase in customer holding costs. The decision‐maker decides when to perform maintenance, which may be done pre‐emptively; before catastrophic failures. Similar to classic maintenance control models, the information available to the decision‐maker includes the state of the server. Unlike classic models, the information also includes the number of customers in queue. Considered are both a repair model and a replacement model. In the repair model, with random replacement times, fixed costs are assumed to be constant in the server state. In the replacement model, both constant and variable fixed costs are considered. It is shown in general that the optimal maintenance policies have switching curve structure that is monotone in the server state. However, the switching curve policies for the repair model are not always monotone in the number of customers in the queue. Numerical examples and two heuristics are also presented. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition

We address the problem of optimal decision‐making in conflicts based on Lanchester square law attrition model where a defending force needs to be partitioned optimally, and allocated to two different attacking forces of differing strengths and capabilities. We consider a resource allocation scheme called the Time Zero Allocation with Redistribution (TZAR) strategy, where allocation is followed by redistribution of defending forces, on the occurrence of certain decisive events. Unlike previous work on Lanchester attrition model based tactical decision‐making, which propose time sequential tactics through an optimal control approach, the present article focuses on obtaining simpler resource allocation tactics based on a static optimization framework, and demonstrates that the results obtained are similar to those obtained by the more complex dynamic optimal control solution. Complete solution for this strategy is obtained for optimal partitioning of resources of the defending forces. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

On a Markov‐modulated shock and wear process

We present transient and asymptotic reliability indices for a single‐unit system that is subject to Markov‐modulated shocks and wear. The transient results are derived from the (transform) solution of an integro‐differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time‐scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space‐scaled version of the systes lifetime distribution. Two numerical examples illustrate the quality of the normal approximation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009