Geodesic
Waiting Time Costs in a Bilevel Location-Allocation Problem
Contributions to game theory and management, Tome 5 (2012), pp. 178-188.

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We present a two-stage optimization model to solve a location-allocation problem: finding the optimal location of new facilitites and the optimal partition of the consumers. The social planner minimizes the social costs, i.e. the fixed costs plus the waiting time costs, taking into account that the citizens are partitioned in the region according to minimizing the capacity costs plus the distribution costs in the service regions. Theoretical and computational aspects of the location-allocation problem are discussed for the linear city and illustrated with examples.
Keywords: bilevel optimization, continuous facility location. 
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Lina Mallozzi; Egidio D'Amato; Elia Daniele; Giovanni Petrone. Waiting Time Costs in a Bilevel Location-Allocation Problem. Contributions to game theory and management, Tome 5 (2012), pp. 178-188. http://geodesic.mathdoc.fr/item/CGTM_2012_5_a17/

[1] Aumann R. J., Hart S., Handbook of Game Theory with Economic Applications, Handbooks in Economics, 11, North-Holland Publishing Co., Amsterdam, 1992 | MR

[2] Başar T., Olsder G. J., Dynamic noncooperative game theory, Classics in Applied Mathematics, 23, Reprint of the second (1995) edition, SIAM, Philadelphia, PA, 1999 | MR | Zbl

[3] Border K. C., Fixed point theorems with applications to economics and game theory, Cambridge University Press, New York, 1989 | MR | Zbl

[4] Buttazzo G., Santambrogio F., “A model for the optimal planning of an urban area”, SIAM J. Math. Anal., 37:2 (2005), 514–530 | DOI | MR | Zbl

[5] Crippa G., Chloè C., Pratelli A., “Optimum and equilibrium in a transport problem with queue penalization effect”, Adv. Calc. Var., 2:3 (2009), 207–246 | DOI | MR | Zbl

[6] D'Amato E., Daniele E., Mallozzi L., Petrone G., “Equilibrium strategies via GA to Stackelberg games under multiple follower's best reply”, International Journal of Intelligent Systems, 27:2 (2012), 74–85 | DOI | MR

[7] D'Amato E., Daniele E., Mallozzi L., Petrone G., Tancredi S., “A hierarchical multi-modal hybrid Stackelberg–Nash GA for a leader with multiple followers game”, Dynamics of Information Systems: Mathematical Foundations, Springer Proceedings in Mathematics, eds. A. Sorokin, P. Pardalos, Springer, 2011

[8] Drezner Z., Facility Location: a Survey of Applications and Methods, Springer-Verlag, New York, 1995 | MR

[9] Hotelling H., “Stability in Competition”, Economic Journal, 39 (1929), 41–57 | DOI

[10] Love R. F., Morris J. G., Wesolowsky G. O., Facility Location: Models and Methods, North Holland, New York, 1988 | MR | Zbl

[11] Mazalov V., Sakaguchi M., “Location game on the plane”, International Game Theory Review, 5:1 (2003), 13–25 | DOI | MR | Zbl

[12] Murat A., Verter V., Laporte G., “A continuous analysis framework for the solution of location-allocation problems with dense demand”, Computer Operations Research, 37:1 (2009), 123–136 | DOI | MR

[13] Nickel S., Puerto J., Location Theory — a unified approach, Springer, Berlin, 2005