Market capture models under various customer-choice rules

Given that a firm currently operates p facilities in a (retail) market, a competing firm considers entering this market by locating r facilities so as to maximize its market share. This problem, known as the maximum capture problem or as the (r \X-p)-medianoid problem, assumes, as do most location decision problems, that consumers always patronize the closest facility regardless of ownership or proximity to alternative facilities. In this paper we relax this assumption by allowing different customer-choice rules. Two new models are proposed for the optimal location for the entering firm under different consumer decision rules. The models are solved by using an exact method and a heuristic. Solutions are then compared with those obtained by the classical maximum capture problem with the usual nearest facility allocation rule. Computational experiments suggest that the maximum capture problem provides locational patterns whose objective values, that is, captures, are very similar to those of the other two objectives.