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Proceedings of GO 2005, pp. 61 – 65.Locating Competitive Facilities via a VNS Algorithm ∗Emilio Carrizosa, 1 José Gordillo, 1 and Dolores R. Santos-Peñate 21 Universidad de Sevilla, Spain{ecarrizosa,jgordillo}@us.es2 Universidad de Las Palmas de Gran Canaria, Spaindrsantos@dmc.ulpgc.esAbstractKeywords:We consider the problem of locating in the time period [0, T ] q facilities in a market in which competingfirms already operate with p facilities. Locations and the entering times maximizing profitsare sought.Assuming that demands and costs are time-dependent, optimality conditions are obtained, anddifferent demand patterns are analyzed. The problem is posed as a mixed integer nonlinear problem,heuristically solved via a VNS algorithm.Competitive location, Variable Neighborhood Search, Dynamic Demand, Covering Models, MaximalProfit.1. IntroductionThe problem of locating facilities in a competitive environment has been addressed, both at themodelling and computational level, in a number of papers in the field of Operations Researchand Management Science, see e.g. [2, 3, 5–9, 12, 14] and the references therein.The simplest models accommodating competition are those related with covering: a firmis planning to locate a series of facilities to compete against a set of already operating facilities,in order to maximize its profit, usually equivalent to maximizing the market share.Different attraction rules may be (and have been) considered to model consumer behavior,and thus to evaluate market share. For instance, with the binary attraction rule, one assumesthat consumers demand is fully captured by the closest facility, or more generally by the mostattractive facility, where attractiveness is measured by a function decreasing in distance andprice, e.g. [1, 10, 11, 13].Serious attempts have been made to model different metric spaces (a discrete set, a transportationnetwork or the plane), or different attraction rules (e.g. the above-mentioned binaryrule, as well as rules relying upon the assumption that consumer demand is split into the differentfacilities, each capturing a fraction of the demand, this demand being decreasing in distance,. . . ). However, most models assume that consumer demand remains constant throughthe full planning horizon, which may be a rather unrealistic assumption for new goods orhigh seasonality products. See e.g. [4, 15] for facility location models which do accommodatetime-dependent demand.In this talk we introduce a covering model for locating facilities in a competitive environmentin which demand is time-dependent. This implies that, as e.g. in [4], not only the facility∗ Partially supported by projects BFM2002-04525, Ministerio de Ciencia y Tecnología, Spain, and FQM-329, Junta de Andalucía,Spain