Environment and Planning tl Planning and Design \ 1 ) 1 ) 1 ), volume 26, pages 741 750 Market capture models under various customer-choice rules D Sernt Department of Heonomies and Business, Univcrsilat Pompeu Fnbra, Balmes 132, Barcelona 08022. Spain; e-mail: dnnicl.serra(fi'ceon.upf.es II A Riselt Faculty of Administration, University of New Brunswick, PC) Box 4400, Fredericton, New Brunswick, Canada F3B 5A3: e-mail: HAF:isdt(</>UNB.eA G I.aportc Centre de recherche stir les transports, University de Montreal, Case postale 6128, succursale Centre-viile, Montreal, Canada H3C 3.17; e-mail: gilbertcnC'RT.UMontreal.CA C S RcVcIlc Department of Geography and Hnvironmcntul Fngineering, The Johns Hopkins University, Baltimore, MI) 21218-2686, USA; e-mail: revelief^jhu.edu Received 18 November 1998; in revised form 5 April 1999 Abstract. 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|/V r )-mcdianoid 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. 1 Introduction Multifacility location models hold a central place in regional science. Such models require a rule that allocates customers to facilities. In general, we distinguish between two different types of model: one in which the facility planners decide which customer is served from a facility, and a second in which customers decide themselves which facility they want to patronize. The first type is typically applicable when customers receive goods from warehouses. In this case, provided the goods from the different warehouses are homogeneous, they are indifferent as to which warehouse they are served from and they do not in fact control that choice. On the other hand, customers in the retail context have full control over which facility they choose to patronize. This class of customer-choice models is the subject of this paper. Though there exist many models dealing with different aspects of multifacility customer-choice problems, most assume total homogeneity of the products. Coupled with equal prices charged at the facilities, this choice rule results in customers patroniz- ing the nearest facility and satisfying their entire demand there. Two issues need to be addressed at this point. First, most geographers attempt to capture the fact that in many instances facilities and products are not completely homogeneous. They do so by associating an attractiveness factor with each facility. This does of course require a function that specifies a trade-off between attractiveness and customer - facility distance. Typical examples of such functions are gravity models dating back to Reilly (1929)