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Bilevel Models on the Competitive Facility Location Problem Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Huff-Like Stackelberg Location Problems on the Plane

Authors : José Fernández, Juana L. Redondo, Pilar M. Ortigosa, Boglárka G.-Tóth

Published in: Spatial Interaction Models

Publisher: Springer International Publishing

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Abstract

The so-called leader-follower (or Stackelberg) problem is researched. A chain, the leader, wants to locate a single new facility in a region of the plane. After that, as a reaction, the competitor chain, the follower, will locate a single new facility too, knowing the decision taken by the leader. Several variants of the problem are analyzed. In the simplest one, the objective of both the leader and the follower is to maximize the market share, the qualities of the facilities to be located are given beforehand, and the demand is fixed (no costs are considered). In the second one, the qualities of the facilities to be located are considered variables of the problem, and costs related both to location and quality are taken into account; the demand is fixed as in the first model. Finally, the last model extends the previous one considering that the demand varies depending on the location and the quality of the facilities. Exact (for the first problem) and heuristic (for the second and third problems) approaches proposed for the aforementioned location models are described and analyzed. High performance computing approaches for the heuristic methods are also reviewed. A new exact branch-and-bound method for the last two problems is also suggested.

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Literature
1.
Arrondo, A.G., Redondo, J.L., Fernández, J., Ortigosa, P.M.: Solving a leader-follower facility problem via parallel evolutionary approaches. J. Supercomput. 70 (2), 600–611 (2014)CrossRef
2.
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)CrossRefMATH
3.
Biesinger, B., Hu, B., Raidl, G.: Models and algorithms for competitive facility location problems with different customer behavior. Ann. Math. Artif. Intell. 76 (1), 93–119 (2016)MathSciNetCrossRefMATH
4.
Daskin, M.S.: Network and Discrete Location: Models, Algorithms and Applications. Wiley, New York (1995)CrossRefMATH
5.
Dempe, S.: Foundations of Bilevel Programming. Springer, New York (2002)MATH
6.
Dorta-González, P., Santos-Peñate, D.R., Suárez-Vega, R.: Spatial competition in networks under delivered pricing. Pap. Reg. Sci. 84, 271–280 (2005)CrossRef
7.
Drezner, Z.: Competitive location strategies for two facilities. Reg. Sci. Urban Econ. 12 (4), 485–493 (1982)CrossRef
8.
Drezner, T.: Locating a single new facility among existing unequally attractive facilities. J. Reg. Sci. 34 (2), 237–252 (1994)CrossRef
9.
Drezner, T.: Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. J. Retail. 70 (1), 49–64 (1994)CrossRef
10.
Drezner, T., Drezner, Z.: Replacing continuous demand with discrete demand in a competitive location model. Nav. Res. Logist. 44, 81–95 (1997)CrossRefMATH
11.
Drezner, T., Drezner, Z.: Facility location in anticipation of future competition. Locat. Sci. 6 (1), 155–173 (1998)CrossRef
12.
13.
Drezner, T., Drezner, Z., Kalczynski, P.: Strategic competitive location: improving existing and establishing new facilities. J. Oper. Res. Soc. 63 (12), 1720–1730 (2012)CrossRef
14.
Drezner, T., Drezner, Z., Kalczynski, P.: A leader–follower model for discrete competitive facility location. Comput. Oper. Res. 64, 51–59 (2015)MathSciNetCrossRefMATH
15.
Eiselt, H.A., Laporte, G.: Sequential location problems. Eur. J. Oper. Res. 96 (2), 217–231 (1996)CrossRefMATH
16.
Eiselt, H.A., Laporte, G.,Thisse, J.F.: Competitive location models: a framework and bibliography. Transp. Sci. 27 (1), 44–54 (1993)CrossRefMATH
17.
Fernández, J., Fernández, P., Pelegrín, B.: Estimating actual distances by norm functions: a comparison between the l k, p, θ -norm and the \(l_{b_{1},b_{2},\theta }\)-norm and a study about the selection of the data set. Comput. Oper. Res. 29 (6), 609–623 (2002)
18.
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)CrossRefMATH
19.
Fernández, J., Salhi, S., Tóth, B.G.: Location equilibria for a continuous competitive facility location problem under delivered pricing. Comput. Oper. Res. 41 (1), 185–195 (2014)MathSciNetCrossRefMATH
20.
21.
Hansen, E., Walster, G.W.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (2004). Second revised and expanded edition
22.
Huff, D.L.: A programmed solution for approximating an optimum retail location. Land Econ. 42 (3), 293–303 (1966)CrossRef
23.
Jelásity, M.: The shape of evolutionary search: discovering and representing search space structure. Ph.D. thesis, Leiden University (2001)
24.
Jelásity, M., Ortigosa, P.M., García, I.: UEGO, an abstract clustering technique for multimodal global optimization. J. Heuristics 7 (3), 215–233 (2001)CrossRefMATH
25.
Küçükaydin, H., Aras, N., Altinel, I.K.: Competitive facility location problem with attractiveness adjustment of the follower: a bilevel programming model and its solution. Eur. J. Oper. Res. 208 (3), 206–220 (2011)MathSciNetCrossRefMATH
26.
Küçükaydin, H., Aras, N., Altinel, I.K.: A leader-follower game in competitive facility location. Comput. Oper. Res. 39 (2), 437–448 (2012)MathSciNetCrossRefMATH
27.
28.
McGarvey, R.G., Cavalier, T.M.: Constrained location of competitive facilities in the plane. Comput. Oper. Res. 32, 359–378 (2005)MathSciNetCrossRefMATH
29.
Miller, T.C., Friez, T.L., Tobin, R.L.: Equilibrium Facility Location on Networks. Springer, New York (1996)CrossRef
30.
Mirchandani, P.B., Francis, R.L. (eds.): Discrete Location Theory. Wiley, New York (1990)MATH
31.
Ortigosa, P.M., García, I., Jelásity, M.: Reliability and performance of UEGO, a clustering-based global optimizer. J. Glob. Optim. 19 (3), 265–289 (2001)MathSciNetCrossRefMATH
32.
Plastria, F.: GBSSS, the generalized big square small square method for planar single facility location. Eur. J. Oper. Res. 62, 163–174 (1992)CrossRefMATH
33.
Plastria, F.: Avoiding cannibalization and/or competitor reaction in planar single facility location. J. Oper. Res. Soc. Jpn. 48, 148–157 (2005)MathSciNetMATH
34.
35.
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. Springer, Berlin/Heidelberg (2004)
36.
Redondo, J.L., Fernández, J., García, I., Ortigosa, P.M.: Parallel algorithms for continuous competitive location problems. Optim. Methods Softw. 23 (5), 779–791 (2008)MathSciNetCrossRefMATH
37.
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. 167 (1), 87–106 (2009)MathSciNetCrossRefMATH
38.
Redondo, J.L., Fernández, J., García, I., Ortigosa, P.M.: Solving the multiple competitive facilities location and design problem on the plane. Evol. Comput. 17 (1), 21–53 (2009)CrossRef
39.
Redondo, J.L., Fernández, J., García, I., Ortigosa, P.M.: Heuristics for the facility location and design (1 | 1)-centroid problem on the plane. Comput. Optim. Appl. 45 (1), 111–141 (2010)
40.
Redondo, J.L., Fernández, J., García, I., Ortigosa, P.M.: Solving the facility location and design (1 | 1)-centroid problem via parallel algorithms. J. Supercomput. 58 (3), 420–428 (2011)
41.
Redondo, J.L., Fernández, J., Arrondo, A.G., García, I., Ortigosa, P.M.: Fixed or variable demand? Does it matter when locating a facility? Omega 40 (1), 9–20 (2012)CrossRef
42.
Redondo, J.L., Fernández, J., Arrondo, A.G., García, I., Ortigosa, P.M.: A two-level evolutionary algorithm for solving the facility location and design (1 | 1)-centroid problem on the plane with variable demand. J. Glob. Optim. 56 (3), 983–1005 (2013)
43.
Saidani, N., Chu, F., Chen, H.: Competitive facility location and design with reactions of competitors already in the market. Eur. J. Oper. Res. 219 (1), 9–17 (2012)MathSciNetCrossRefMATH
44.
Sáiz, M.E., Hendrix, E.M.T., Fernández, J., Pelegrín, B.: On a branch-and-bound approach for a Huff-like Stackelberg location problem. OR Spectrum 31, 679–705 (2009)MathSciNetCrossRefMATH
45.
Serra, D., ReVelle, C.: Competitive location in discrete space. In: Facility Location: A Survey of Applications and Methods, pp. 367–386. Springer, New York (1995)
46.
47.
Tóth, B., Fernández, J.: Interval Methods for Single and Bi-objective Optimization Problems - Applied to Competitive Facility Location Problems. Lambert Academic, Saarbrücken (2010)
48.
49.
Tóth, B., Plastria, F., Fernández, J., Pelegrín, B.: On the impact of spatial pattern, aggregation, and model parameters in planar Huff-like competitive location and design problems. OR Spectrum 31 (1), 601–627 (2009)CrossRefMATH
Metadata
Title
Huff-Like Stackelberg Location Problems on the Plane
Authors
José Fernández
Juana L. Redondo
Pilar M. Ortigosa
Boglárka G.-Tóth
Copyright Year
2017
Book
Spatial Interaction Models

Print ISBN: 978-3-319-52653-9

Electronic ISBN: 978-3-319-52654-6

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52654-6_7

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