"Facility location optimization is an optimization problem in operations research, particularly in network design decisions in the supply chain. In it most standard form (the Uncapacited Facility Location Problem), the problem can be stated as follows. Given some facilities, with known capacities (possibly infinite), some candidate sites, and customer demands, the problem consists in locating facilities on sites and assigning customers in such a way to satisfy all demands, without exceeding capacities, and at minimal fixed and variable costs. It is assumed that the decision problem occurs in some deterministic and reliable conditions. The customer demands and different costs are predictable, and facilities are so reliable that customers always get the service. Over the life of a logistic network, some services, transportation links, demands and costs, may experience disruptions or fluctuations. Thus, a network design that looks very good taking into account deterministic evaluation may be quite poor if the situation were to change. Our first purpose is to propose a “new” mathematical model for optimal location subject to disruptions on services. We first analyze the case of unlimited capacities and move to the limited capacities case. As a corollary, we examine the problem of optimally sizing safety capacity to satisfy additional demands. Finally, the failure aspects will be considered jointly with uncertainty on demands and costs. The general aim is to propose, for each problem, models, solution methods and algorithms that may be used by managers in designing logistic network taking into account uncertainties both on facilities availability, and on demands and costs. The theoretical and algorithmic elements that will be developed may be the backgrounds of a network design decision-aid software for network design with uncertainties. A prototype of such type of application will be developed to demonstrate the quality of our approach and to test various algorithms."
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