Rendezvous of three agents on the line

This paper considers a three‐person rendezvous problem on the line which was introduced earlier by the authors. Three agents are placed at three consecutive integer value points on the real line, say 1, 2, and 3. Each agent is randomly faced towards the right or left. Agents are blind and have a maximum speed of 1. Their common aim is to gather at a common location as quickly as possible. The main result is the proof that a strategy given by V. Baston is the unique minimax strategy. Baston's strategy ensures a three way rendezvous in time at most 3.5 for any of the 3!2³ = 48 possible initial configurations corresponding to positions and directions of each agent. A connection is established between the above rendezvous problem and a search problem of L. Thomas in which two parents search separately to find their lost child and then meet again. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 244–255, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10005     

Analysis of down times of jib cranes—A stochastic approach

In this paper a case study dealing with the maintenance problem of jib cranes is presented. A jib crane is viewed as a complex system whose performance is observed as a single realization over period of time. After pointing out limitations of existing stochastic models to analyze the observed realization a new family of bivariate stochastic processes is introduced. The data of jib crane is analyzed using new model and cross‐validated using part of the data set. It is noted that the new family of stochastic processes is useful to analyze bivariate data where one of the variables is finitely valued and the other is nonnegative and continuous. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 231–243, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10006     

Duality in constrained multi‐facility location models

We consider the ??_p‐norm multi‐facility minisum location problem with linear and distance constraints, and develop the Lagrangian dual formulation for this problem. The model that we consider represents the most general location model in which the dual formulation is not found in the literature. We find that, because of its linear objective function and less number of variables, the Lagrangian dual is more useful. Additionally, the dual formulation eliminates the differentiability problem in the primal formulation. We also provide the Lagrangian dual formulation of the multi‐facility minisum location problem with the ??_pb‐norm. Finally, we provide a numerical example for solving the Lagrangian dual formulation and obtaining the optimum facility locations from the solution of the dual formulation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 410–421, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10010     

Rendezvous search on labeled networks

Two players are independently placed on a commonly labelled network X. They cannot see each other but wish to meet in least expected time. We consider continuous and discrete versions, in which they may move at unit speed or between adjacent distinct nodes, respectively. There are two versions of the problem (asymmetric or symmetric), depending on whether or not we allow the players to use different strategies. After obtaining some optimality conditions for general networks, we specialize to the interval and circle networks. In the first setting, we extend the work of J. V. Howard; in the second we prove a conjecture concerning the optimal symmetric strategy. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 256–274, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10011     

Rare‐event component importance for the consecutive‐k system

Various indices of component importance with respect to system reliability have been proposed. The most popular one is the Birnbaum importance. In particular, a special case called uniform Birnbaum importance in which all components have the same reliability p has been widely studied for the consecutive‐k system. Since it is not easy to compare uniform Birnbaum importance, the literature has looked into the case p = ½, p → 1, or p ≥ ½. In this paper, we look into the case p → 0 to complete the spectrum of examining Birnbaum importance over the whole range of p. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 159–166, 2002; DOI 10.1002/nav.10001     

Scheduling with variable time slot costs

In this article, we study a class of new scheduling models where time slot costs have to be taken into consideration. In such models, processing a job will incur certain cost which is determined by the time slots occupied by the job in a schedule. The models apply when operational costs vary over time. The objective of the scheduling models is to minimize the total time slot costs plus a traditional scheduling performance measure. We consider the following performance measures: total completion time, maximum lateness/tardiness, total weighted number of tardy jobs, and total tardiness. We prove the intractability of the models under general parameters and provide polynomial‐time algorithms for special cases with non‐increasing time slot costs.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Adaptive random search for continuous simulation optimization

We present, analyze, and compare three random search methods for solving stochastic optimization problems with uncountable feasible regions. Our adaptive search with resampling (ASR) approach is a framework for designing provably convergent algorithms that are adaptive and may consequently involve local search. The deterministic and stochastic shrinking ball (DSB and SSB) approaches are also convergent, but they are based on pure random search with the only difference being the estimator of the optimal solution [the DSB method was originally proposed and analyzed by Baumert and Smith]. The three methods use different techniques to reduce the effects of noise in the estimated objective function values. Our ASR method achieves this goal through resampling of already sampled points, whereas the DSB and SSB approaches address it by averaging observations in balls that shrink with time. We present conditions under which the three methods are convergent, both in probability and almost surely, and provide a limited computational study aimed at comparing the methods. Although further investigation is needed, our numerical results suggest that the ASR approach is promising, especially for difficult problems where the probability of identifying good solutions using pure random search is small. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy

We consider a two‐level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order‐up‐to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot‐sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state‐of‐the art solver reveal that our formulations are very effective in solving large‐size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Equivalent accelerated life testing plans for log‐location‐scale distributions

Accelerated life testing (ALT) is widely used to determine the failure time distribution of a product and the associated life‐stress relationship in order to predict the product's reliability under normal operating conditions. Many types of stress loadings such as constant‐stress, step‐stress and cyclic‐stress can be utilized when conducting ALT. Extensive research has been conducted on the analysis of ALT data obtained under a specified stress loading. However, the equivalency of ALT experiments involving different stress loadings has not been investigated. In this article, a log‐location‐scale distribution under Type I censoring is considered in planning ALT. An idea is provided for the equivalency of various ALT plans involving different stress loadings. Based on this idea, general equivalent ALT plans and some special types of equivalent ALT plans are explored. For demonstration, a constant‐stress ALT and a ramp‐stress ALT for miniature lamps are presented and their equivalency is investigated. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010