Competitive Multifacility Location on Networks : The (R|Xp)-Medianoid Problem

We investigate the (r|Xp)-medianoid problem for networks. This is a competitive location problem that consists of determining the locations of facilities belonging to a firm in order to maximize its market share in a space where a competitor is already operating with facilities. We consider six scenarios resulting from the combination of three customer choice rules (binary, partially binary, and proportional) with two types of services (essential and unessential). Known discretization results about the existence of a solution for the set of nodes are extended. Some examples and computational experience using heuristic algorithms are presented