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200 Blas Pelegrín, Pascual Fernández, Juani L. Redondo, Pilar M. Ortigosa, and I. Garcíathe facilities location (see [6] ), thus the location-price problem becomes a location problemwhen firms charge equilibrium prices. To our knowledge, the resultant location problem onlyhas been studied in discrete space and it will be referred here as the MAXPROFIT problem(see [4]).The aim of this paper is to show that the above mentioned problems can be formulatedin the same framework and solved by using the same type of algorithms. By using integerlinear programming formulations of the problems, standard optimizers can be applied to findoptimal solutions to moderated size problems. By determining its fitness functions, heuristicsalgorithms can be used to get good solutions for large size problems. We propose a newgenetic algorithm with subpopulation support, GASUB , which is related to a previous algorithmgiven in [9]. The new algorithm is compared with the multi-start substitution heuristic,MSH, a procedure widely used for many combinatorial location problems (see [2]).2. The location problems formulationWe will use the following notation when necessary:i, I = 1, 2, ..., n Index and collection of demand pointsj, J = 1, 2, ..., m Index and potential sites for facility locationk, K = 1, 2, ..., q Index and pre-existing facility locationsw iDemand (or buying power) at point id ijDistance between demand point i and point jD i = min{d ik : k ∈ K} Distance from demand point i to the closest pre-existing facilityN < i = {j ∈ J : d ij < D i} Collection of potential locations for servers that are closer to point ithan the closest pre-existing facilityN i = = {j ∈ J : d ij = D i} Collection of potential locations for servers that are at the same distanceto point i than the closest pre-existing facilityI ∗ = {i ∈ I : N < i ∪ N i = ≠ ∅} Collection of demand points that have at least one potential location forserver closer or at the same distance than the pre-existing facilitiestUnit transportation costsNumber of new facilities to be builtIn the p-MEDIAN problem, there is no pre-existing facility in the market (K = ∅) and theobjective is to minimize total transportation cost between demand points and their closestfacilities. The following decision variables are defined:{1 if a new facility is opened in jy j =0 otherwisex ij = proportion of demand at i served from site jThen the problem is formulated as follows:⎧ ∑min tw i d ij x ij⎪⎨(P 1 )⎪⎩s.t.∑ i∈I j∈J∑j∈Jx ij = 1,i ∈ Ix ij ≤ y j , i ∈ I, j ∈ J∑y j = sj∈Jx ij ≥ 0y j ∈ {0, 1}In MAXCAP, there already exist some competing pre-existing facilities. Customer pays fortransportation and buys at its closest facility. If a new facility and a pre-existing facility are