We consider a continuous location problem in which a firm wants to set up two or more new facilities in a competitive environment. Both the locations and the qualities of the new facilities are to be found so as to maximize the profit obtained by the firm. This hard-to-solve global optimization problem has been addressed in [38] using several heuristic approaches. Through a comprehensive comput...

As introduced earlier, the Euclidean Multifacility Location Problem (EMFLP) seeks to locate n new facilities at some points (xi, yi), i = 1, .., n in R 2 , in the presence of some m existing facilities located at specified points (aj, bj), j = 1, .., m, given certain interaction weights wij > 0 between designated pairs (i, j) of new and existing facilities in some indexpair set A NE , as well a...

In this paper, we address the ordered p-median problem, which includes as special cases most of the classical multifacility location problems discussed in the literature. Finite dominating sets (FDS) are known for particular instances of this problem: p-median, p-center, and p-centdian. We find an FDS for the ordered p-median problem. This set allows us to gain a better insight into the general...

In the minimum 0-extension problem (a version of the multifacility location problem), one is given a metric m on a subset X of a finite set V and a non-negative function c on the unordered pairs of elements of V . The objective is to find a semimetric m on V that minimizes the inner product c ·m, provided that m coincides with m within X and each element of V is at zero distance from X . For m ...

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function f : X×Y → R is called biconvex, if f(x, y) is convex in y for fixed x ∈ X, and f(x, y) is convex in x for fixed y ∈ Y . This paper presents a ...

• Branch-and-price algorithm for the Continuous Multifacility Monotone Ordered Median Problem. Three matheuristic algorithms same problem. Complete computational experience a large battery of instances. In this paper, we address The goal problem is to locate p facilities in R d minimizing monotone ordered weighted median function distances between given demand points and its closest facility. W...

In continuous location problems we are given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing ones. In this paper, we consider a pointwise deened objective function where the weights are assigned to the existin...