On a branch-and-bound approach for a Huff-like Stackelberg location problem

Modelling the location decision of two competing firms that intend to build a new facility in a planar market can be done by a Huff-like Stackelberg location problem. In a Huff-like model, the market share captured by a firm is given by a gravity model determined by distance calculations to facilities. In a Stackelberg model, the leader is the firm that locates first and takes into account the actions of the competing chain (follower) locating a new facility after the leader. The follower problem is known to be a hard global optimisation problem. The leader problem is even harder, since the leader has to decide on location given the optimal action of the follower. So far, in literature only heuristic approaches have been tested to solve the leader problem. Our research question is to solve the leader problem rigorously in the sense of having a guarantee on the reached accuracy. To answer this question, we develop a branch-and-bound approach. Essentially, the bounding is based on the zero This work has been supported by the Ministry of Education and Science of Spain through grant SEJ2005/06273/ECON. M. Elena Sáz was supported by a junior research grant of Mansholt Graduate School (Wageningen Universiteit). M. Elena Sáiz (B) Radboud Universiteit Nijmegen, Thomas van Aquinostraat 3.01.04, P.O.Box 9108, 6500 HK, Nijmegen, The Netherlands e-mail: [email protected] E. M. T. Hendrix Wageningen Universiteit, Hollandseweg 1, 6706 KN Wageningen, The Netherlands e-mail: [email protected] J. Fernández · B. Pelegrín Universidad de Murcia, Campus Universitario de Espinardo, 30071 Espinardo, Murcia, Spain e-mail: [email protected] B. Pelegrín e-mail: [email protected]