We consider the (r|X_p)-medianoid problem in networks. Goods are assumed to be essential and the only decision criterion is the travel distance. The portion of demand captured by the competitors is modelled by a general capture function which includes the binary, partially binary and proportional customer choice rules as specific cases. We prove that, under certain conditions of the capture function, a finite dominating set exists, extending some known results given for maximal covering location problems.
Competitive location in networks with threshold-sensitive customer behaviour/Version 2-February 2012 Dpto de Métodos Cuantitativos en Economía y Gestión-Universidad de Las Palmas de Gran Canaria