Abstract
A chain (the leader) wants to set up a single new facility in a planar market where similar facilities of a competitor (the follower), and possibly of its own chain, are already present. The follower will react by locating another single facility after the leader locates its own facility. Fixed demand points split their demand probabilistically over all facilities in the market in proportion to their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational model. Both the location and the quality (design) of the new leader’s facility are to be found. The aim is to maximize the profit obtained by the leader following the follower’s entry. Four heuristics are proposed for this hard-to-solve global optimization problem, namely, a grid search procedure, an alternating method and two evolutionary algorithms. Computational experiments show that the evolutionary algorithm called UEGO_cent.SASS provides the best results.
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Benati, S., Laporte, G.: Tabu search algorithms for the (r|{X} p )-medianoid and (r|p)-centroid problems. Location Sci. 2(4), 193–204 (1994)
Bhadury, J., Eiselt, H.A., Jaramillo, J.H.: An alternating heuristic for medianoid and centroid problems in the plane. Comput. Oper. Res. 30(4), 553–565 (2003)
Drezner, T.: Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. J. Retail. 70(1), 49–64 (1994)
Drezner, T.: Location of multiple retail facilities with limited budget constraints in continuous space. J. Retail. Consum. Serv. 5(3), 173–184 (1998)
Drezner, T., Drezner, Z.: Facility location in anticipation of future competition. Location Sci. 6(1), 155–173 (1998)
Drezner, T., Drezner, Z.: Retail facility location under changing market conditions. IMA J. Manag. Math. 13(4), 283–302 (2002)
Drezner, T., Drezner, Z.: Finding the optimal solution to the Huff based competitive location model. Comput. Manag. Sci. 1(2), 193–208 (2004)
Drezner, Z.: Competitive location strategies for two facilities. Reg. Sci. Urban Econ. 12(4), 485–493 (1982)
Drezner, Z.: Facility Location: A Survey of Applications and Methods. Springer, Berlin (1995)
Drezner, Z., Hamacher, H.W.: Facility Location. Applications and Theory. Springer, Berlin (2002)
Eiselt, H.A., Laporte, G.: Sequential location problems. Eur. J. Oper. Res. 96(2), 217–231 (1997)
Eiselt, H.A., Laporte, G., Thisse, J.F.: Competitive location models: a framework and bibliography. Transp. Sci. 27(1), 44–54 (1993)
Fernández, J., Pelegrín, B., Plastria, F., Tóth, B.: Solving a Huff-like competitive location and design model for profit maximization in the plane. Eur. J. Oper. Res. 179(3), 1274–1287 (2007)
Francis, R.L., McGinnis, L.F., White, J.A.: Facility Layout and Location: An Analytical Approach. Prentice Hall, Englewood Cliffs (1992)
González-Linares, J.M., Guil, N., Zapata, E.L., Ortigosa, P.M., García, I.: Deformable shapes detection by stochastic optimization. In: 2000 IEEE International Conference on Image Processing (ICIP’2000). Vancouver, Canada, 2000
Hakimi, S.L.: On locating new facilities in a competitive environment. Eur. J. Oper. Res. 12(1), 29–35 (1983)
Hodgson, M.J.: A location–allocation model maximizing consumers’ welfare. Reg. Stud. 15(6), 493–506 (1981)
Huff, D.L.: Defining and estimating a trading area. J. Mark. 28(3), 34–38 (1964)
Kilkenny, M., Thisse, J.F.: Economics of location: a selective survey. Comput. Oper. Res. 26(14), 1369–1394 (1999)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Love, R.F., Morris, J.G., Wesolowsky, G.O.: Facilities Location. Models and Methods. North-Holland, Amsterdam (1988)
Okabe, A., Suzuki, A.: Stability of spatial competition for a large number of firms on a bounded two-dimensional space. Environ. Plan. A 19(8), 1067–1082 (1987)
Ortigosa, P.M., García, I., Jelasity, M.: Reliability and performance of UEGO, a clustering-based global optimizer. J. Glob. Optim. 19(3), 265–289 (2001)
Plastria, F.: Static competitive facility location: an overview of optimisation approaches. Eur. J. Oper. Res. 129(3), 461–470 (2001)
Plastria, F., Carrizosa, E.: Optimal location and design of a competitive facility. Math. Program. 100(2), 247–265 (2004)
Redondo, J.L., Fernández, J., García, I., Ortigosa, P.M.: A robust and efficient global optimization algorithm for planar competitive location problems. Ann. Oper. Res. (2008, to appear). DOI: 10.1007/s10479-007-0233-x
Redondo, J.L., Ortigosa, P.M., García, I., Fernández, J.J.: Image registration in electron microscopy. A stochastic optimization approach. In: Proceedings of the International Conference on Image Analysis and Recognition, ICIAR 2004. Lecture Notes in Computer Science, vol. 3212(II), pp. 141–149 (2004)
Solis, F.J., Wets, R.J.B.: Minimization by random search techniques. Math. Oper. Res. 6(1), 19–30 (1981)
Weber, A.: Uber den Standort der Industrien 1. Teil: Reine Theorie des Standortes. Tübingen, Niemeyer (1909)
Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. J. 43, 355–386 (1937)
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This paper has been sponsored by the Ministry of Education and Science of Spain under the research projects SEJ2005-06273/ECON and TIN2005-00447, in part financed by the European Regional Development Fund (ERDF).
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Redondo, J.L., Fernández, J., García, I. et al. Heuristics for the facility location and design (1|1)-centroid problem on the plane. Comput Optim Appl 45, 111–141 (2010). https://doi.org/10.1007/s10589-008-9170-0
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DOI: https://doi.org/10.1007/s10589-008-9170-0