The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.

The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.

: The p-median problem is the problem of locating p facilities (medians) on a network so as to minimize the sum of all the distances from each demand point to its nearest facility. A successful approach to approximately solve this problem is the use of Lagrangean heuristics, based upon Lagrangean relaxation and subgradient optimization. The Lagrangean/surrogate is an alternative relaxation proposed recently to correct the erratic behavior of subgradient like methods employed to solve the Lagrangean dual. We propose in this paper Lagrangean/surrogate heuristics to p-median problems. Lagrangean and surrogate relaxations are combined relaxing in the surrogate way the assignment constraints in the p-median formulation. Then, the Lagrangean relaxation of the surrogate constraint is obtained and approximately optimized (one-dimensional dual). Lagrangean/surrogate relaxations are very stable (low oscillating) and reach the same good results of Lagrangean (alone) heuristics in less computation...

We present a multistart heuristic for the uncapacitated facility location problem, based on a very successful method we originally developed for the p-median problem.

In some industries, a certain part can be needed in a very large number of different configurations. This is the case, e.g., for the electrical wirings in european car factories. Fortunately, a given configuration can be replaced by a more complete, therefore also more expensive, one. The diversity management problem consists in choosing an optimal set of some given number $k$ of configurations that will be produced, any non produced configuration being replaced by the cheapest produced one compatible with it. We model the problem as an integer linear program close to the one commonly used for the $k$-median problem. Our aim is to solve those problems to optimality. The large scale instances we are interested in lead to difficult LP relaxations, which seem to be intractable by the best direct methods currently available. Most of this paper deals with the use of Lagrangean Relaxation to reduce the size of the problem in order to be able subsequently to solve it to optimality via classical integer optimization.

An important challenge for most chemical companies is to simultaneously consider inventory optimization and supply chain network design under demand uncertainty. This leads to a problem that requires integrating a stochastic inventory model with the supply chain network design model. This problem can be formulated as a large scale combinatorial optimization model that includes nonlinear terms. Since these models are very difficult to solve, they require exploiting their properties and developing special solution techniques to reduce the computational effort. In this work, we analyze the properties of the basic model and develop solution techniques for a joint supply chain network design and inventory management model for a given product. The model is formulated as a nonlinear integer programming problem. By reformulating it as a mixed-integer nonlinear programming (MINLP) problem and using an associated convex relaxation model for initialization, we first propose a heuristic method to quickly obtain good quality solutions. Further, a decomposition algorithm based on Lagrangean relaxation is developed for obtaining global or near-global optimal solutions. Extensive computational examples with up to 150 distribution centers and 150 retailers are presented to illustrate the performance of the algorithms and to compare them with the full-space solution. To whom all correspondence should be addressed.

We review the models for telecommunication network design where there is a location problem involved. We classify the models into three classes as uncapacitated, capacitated and dynamic models. For each class, we discuss the core problem, its generalizations and the solution methods in the literature.

The p-median problem, like most location problems, is classified as NP-hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.

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There has been considerable interest in the development of analysis techniques for Geographical Information Systems (GIS). This includes such normative spatial models as vehicle routing models, districting and turfing models for dividing up land into territories for schools, sales/service, and voting, and location models for identifying sites or patterns of sites to provide service accessibility. The GIS system may provide a unique data base for application and analysis. This paper discusses several problems associated with the integration of a normative location model into a GIS. A number of specifics associated with the p-median model are given. These include: demand zone definition, facility site definition, and solution algorithm selection and development. Within the context of selecting a solution process, we show that such a selection is not necessarily an easy one to make. We demonstrate that the best such solution technique may have some potential drawbacks in application. We p...