[en] We consider a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities, opening new facilities and/or closing existing ones with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at prespecified candidate sites. We employ Huff's gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find a feasible solution of this model, we develop a hybrid tabu search heuristic which makes use of two exact methods as subroutines: a gradient ascent method and a branch-and-bound algorithm with nonlinear programming relaxation.
Adjiman, C.S., Androulakis, I.P., Floudas, C.A., Global optimization of MINLP problems in process synthesis and design (1997) Computers and Chemical Engineering, 21, pp. 445-450
Adjiman, C.S., Androulakis, I.P., Floudas, C.A., Global optimization of mixed-integer nonlinear problems (2000) AIChE, 46, pp. 176-248
Bhadury, J., Eiselt, H.A., Jaramillo, J.H., An alternating heuristic for medianoid and centroid problems in the plane (2003) Computers and Operations Research, 30, pp. 553-565
Bertsekas, D.P., (1995) Nonlinear Programming, , Athena Scientific, Boston
Drezner, Z., Competitive location strategies for two facilities (1982) Regional Science and Urban Economics, 12, pp. 485-493
Drezner, T., Drezner, Z., Facility location in anticipation of future competition (1998) Location Science, 6, pp. 155-173
Fischer, K., Sequential discrete p-facility models for competitive location planning (2002) Annals of Operations Research, 111 (1-4), pp. 253-270
Hotelling, H., Stability in competition (1929) Economic Journal, 39, pp. 41-57
Huff, D.L., Defining and estimating a trade area (1964) Journal of Marketing, 28, pp. 34-38
Huff, D.L., A programmed solution for approximating an optimum retail location (1966) Land Economics, 42, pp. 293-303
Küçükaydin, H., Aras, N., Altinel, I.K., (2009) A Discrete Competitive Facility Location Model with Variable Attractiveness, , Boǧaziçi University Research Paper, FBE-IE-01/2009-01
Küçükaydin, H., Aras, N., Altinel, I.K., (2010) A Bilevel Competitive Facility Location Model with Competitor's Response, , Boǧaziçi University Research Paper, FBE-IE-01/2010-01
Moore, J.T., Bard, J.F., The mixed-integer linear bilevel programming problem (1990) Operations Research, 38, pp. 911-921
Pérez, M.D.G., Pelegrín, B., All stackelberg location equilibria in the hotelling's duopoly model on a tree with parametric prices (2003) Annals of Operations Research, 122 (1-4), pp. 177-192
Plastria, F., Vanhaverbeke, L., Discrete models for competitive location with foresight (2008) Computers and Operations Research, 35 (3), pp. 683-700
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., (1986) Numerical Recipes: The Art of Scientific Computing, , Cambridge University Press, New York
Sáiz, M.E., Hendrix, E.M.T., Fernández, J., Pelegrín, B., On a branch-and-bound approach for a huff-like stackelberg location problem (2009) OR Spectrum, 31 (3), pp. 679-705
Serra, D., ReVelle, C., Market capture by two competitors: The pre-emptive location problem (1993) Economics Working Paper Series, 39
