A branch-bound algorithm for the capacitated facilities location problem

This paper discusses a mixed integer programming method for solving the Facilities Location Problem with capacities on the facilities. The algorithm uses a Decomposition technique to solve the dual of the associated continuous problem in each branch-bound iteration. The method was designed to produce the global optimum solution for problems with up to 100 facilities and 1,000 customers. Computational experience and a complete example are also presented in the appendix.     

Problems in life cycle support cost estimation

Although industry is expected to design hardware to fit into a general support system and to be capable of arguing life-cycle system costs, adequate information has not been available on the support system in terms of policies and operating decision rules. Policies and operating decisions by users dominate engineering design decisions in determining life-cycle support costs. The relative effect of each of these decision areas on support costs has yet to be resolved empirically. Without an understanding of the sensitivity of support costs to alternative designs, capability is limited in design improvement and support of end items. Life-cycle costing of analysis under cost-effectiveness and the maintainability of integrated logistics support is open to question.     

Bayes sequential strategies for crossing a field containing absorption points

A sequential decision problem is considered in which N particles have to cross a given field. Two alternative crossing paths are available. An unknown number of absorption points J₁ and J₂ are planted at each of the crossing paths. The bivariate prior distribution of (J₁,J₂) is given. If a particle passes close to an absorption point it may survive with probability s, 0 < s < 1. If a particle is absorbed, both the particle and the absorption point are ruined. There is no replacement of ruined absorption points. All absorption points act independently. The particles crciss the field in a consecutive order, and a crossing path can be chosen for each particle. The objective is to maximize the expected number of survivors. The Bayes sequential procedure is characterized. The csmditions under which the Bayes strategy is determined by the maximal posterior survival probabilities are specified.     

Estimating critical path and arc probabilities in stochastic activity networks

This article describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path, and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset ? of the network to produce an upper bound of O[(log K)^N?|?|+1/K] on the absolute error of approximation, where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of 1/K^1/2 that one obtains from the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K. The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of ? = 7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large.     

What you should know about location modeling

Facility location models have been applied to problems in the public and private sectors for years. In this article, the author first presents a taxonomy of location problems based on the underlying space in which the problem is embedded. The article illustrates problems from each part of the taxonomy with an emphasis on discrete location problems. Selected recent research in the area is also discussed. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph—a directed series‐parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series‐parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574–592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031