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Sharing Costs in Some Distinguished Location Problems

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Spatial Interaction Models

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 118))

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Abstract

A location problem occurs whenever a set of users have to agree on the position of one or several facilities in order to provide some service for them. The goal is to minimize the overall service cost and depending on the framework space, nature of the service and the globalizing cost function many different models appear: median, center, ordered median, coverage, hub-location, etcetera. Any of these problems has produced a large body of literature in order to find optimal or approximate solutions to their corresponding optimization problems. However, even knowing the exact solution of those problems there is another interesting problem that deserves the attention of researchers: How to share the cost of implementing such an optimal solution among the users of that system? This chapter addresses this question for several well-known location problems that appears in location problems in the continuous setting.

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References

  1. Blanco, V., Puerto, J., El-Haj Ben-Ali, S.: Revisiting several problems and algorithms in continuous location with l τ norms. Comput. Optim. Appl. 58 (3), 563–595 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blanco, V., Puerto, J., El-Haj Ben-Ali, S.: Continuous multifacility ordered median location problems. Eur. J. Oper. Res. 250 (1), 56–64 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Borm, P., Hamers, H., Hendrickx, R.: Operations research games: a survey. TOP 9 (2), 139–216 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Caprara, A., Letchford, A.N.: New techniques for cost sharing in combinatorial optimization games. Math. Program. 124 (1–2), 93–118 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Curiel, I.: Cooperative Game Theory and Applications. Kluwer Academic, Dordrecht (1997)

    Book  MATH  Google Scholar 

  6. Daskin, M.S.: Network and Discrete Location: Models, Algorithms, and Applications, 2nd edn. Wiley, Hoboken (2013)

    MATH  Google Scholar 

  7. Drezner, Z.: Facility Location: A Survey of Applications and Method. Springer, New York (1995)

    Book  Google Scholar 

  8. Drezner, Z., Hamacher, H.: Facility Location: A Survey of Applications and Theory. Springer, New York (2002)

    Book  MATH  Google Scholar 

  9. Eiselt H.A., Laporte, G., Thisse, J.-F.: Competitive location models: a framework and bibliography. Transp. Sci. 27 (1), 44–54 (1993)

    Article  MATH  Google Scholar 

  10. Elzinga, J., Hearn, D.W.: Geometrical solutions for some minimax location problems. Transp. Sci. 6, 379–394 (1972)

    Article  MathSciNet  Google Scholar 

  11. Fragnelli, V., Gagliardo, S.: Open problems in cooperative location games. Int. Game Theory Rev. 15 (3), 1–13 (2013)

    MathSciNet  MATH  Google Scholar 

  12. Gabszewicz, J., Thisse, J.: Location. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory with Economic Applications, vol. 1, Chap. 9, pp. 281–304. Elsevier, Amsterdam (1992)

    Google Scholar 

  13. Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  14. Goemans, M., Skutella, M.: Cooperative facility location games. J. Algorithms 50, 194–214 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Granot, D.: The role of cost allocation in locational models. Oper. Res. 35, 234–248 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hakimi, S.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12 (3), 450–459 (1964)

    Article  MATH  Google Scholar 

  17. Hakimi, S.: Optimum distribution of switching centers in a communications network and some related graph theoretic problems. Oper. Res. 13 (3), 462–475 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  18. Handler, G.Y.: Minimax location of a facility in an undirected tree graph. Transp. Sci. 7, 287–293 (1973)

    Article  MathSciNet  Google Scholar 

  19. Hassin, R., Tamir, A.: On the minimum diameter spanning tree problem. Inf. Process. Lett. 53 (2), 109–111 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hotelling, H.: Stability in competition. Econ. J. 39, 41–57 (1929)

    Google Scholar 

  21. Laporte, G., Nickel, S., Saldanha, F.: Location Science. Springer, Cham (2015)

    Book  MATH  Google Scholar 

  22. Larson, R., Odoni, A.: Urban Operations Research. Prentice-Hall, New York (1981)

    Google Scholar 

  23. Love, R.F., Morris, J.G., Wesolowsky, G.O.: Facilities Location: Models and Methods. North-Holland, Amsterdam (1988)

    MATH  Google Scholar 

  24. Mallozzi, L.: Cooperative games in facility location situations with regional fixed costs. Optim. Lett. 5, 171–183 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Megiddo, N.: The weighted Euclidean 1-center problem. Math. Oper. Res. 8, 498–504 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  26. Megiddo, N., Zemel, E.: An O(nlogn) randomizing algorithm for the weighted Euclidean 1-center problem. J. Algorithms 3, 358–368 (1986)

    Article  MATH  Google Scholar 

  27. Mirchandani, P., Francis, R.: Discrete Location Theory. Wiley, New York (1990)

    MATH  Google Scholar 

  28. Nickel, S., Puerto, J.: Location Theory: A Unified Approach. Springer, Berlin (2005)

    MATH  Google Scholar 

  29. Nickel, S., Puerto, J., Rodríguez-Chía, A.M.: An approach to location models involving sets as existing facilities. Math. Oper. Res. 28 (4), 693–715 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  30. Nissan, N., Roughgargen, Tardos, E., Vazirzni, V.V. (eds.): Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  31. Owen, G.: Game Theory. Academic, San Diego (1995)

    MATH  Google Scholar 

  32. Owen, S.H., Daskin, M.S.: Strategic facility location: a review. Eur. J. Oper. Res. 111 (3), 423–447 (1998)

    Article  MATH  Google Scholar 

  33. Papadopoulos, A.: Metric Spaces, Convexity and Nonpositive Curvature. European Mathematical Society, Zürich (2005)

    MATH  Google Scholar 

  34. Plastria, F.: Continuous location problems. In: Drezner, Z. (ed.) Facility Location - A Survey of Applications and Methods. Springer Series in Operations Research, pp. 225–260. Springer, New York (1995)

    Google Scholar 

  35. Puerto, J.: Lecturas en teoría de localización. Technical Report, Universidad de Sevilla. Secretariado de Publicaciones (1996)

    Google Scholar 

  36. Puerto, J., Rodríguez-Chía, A.M.: On the structure of the solution set for the single facility location problem with average distances. Math. Program. 128, 373–401 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  37. Puerto, J., Rodríguez-Chía, A.: Ordered median location problems. In: Laporte, G., Nickel, S., Saldanha da Gama, F. (eds.) Location Science, pp. 249–288. Springer, Heidelberg (2015)

    Google Scholar 

  38. Puerto, J., García-Jurado, I., Fernández, F.: On the core of a class of location games. Math. Meth. Oper. Res. 54 (3), 373–385 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  39. Puerto, J., Tamir, A., Perea, F.: A cooperative location game based on the 1-center location problem. Eur. J. Oper. Res. 214, 317–330 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Puerto, J., Tamir, A., Perea, F.: Cooperative location games based on the minimum diameter spanning Steiner subgraph problem. Discret. Appl. Math. 160, 970–979 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  41. Skorin-Kapov, D.: On cost allocation in hub-like networks. Ann. Oper. Res. 106, 63–78 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  42. Tamir, A.: On the core of network synthesis games. Math. Program. 50, 123–135 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  43. Tamir, A.: On the core of cost allocation games defined on locational problems. Transp. Sci. 27, 81–86 (1992)

    Article  MATH  Google Scholar 

  44. Tamir A., Puerto, J., Pérez-Brito, D.: The centdian subtree of a tree network. Discret. Appl. Math. 118 (3), 263–278 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  45. Zurcher, S.: Smallest enclosing ball for a point set with strictly convex level sets. Masters thesis, Institute of Theoretical Computer Science, ETH Zurich (2007)

    Google Scholar 

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Acknowledgements

The research of the author has been partially supported by the Spanish Ministry of Economy and Competitiveness through grants MTM2013-46962-C02-01 and MTM2016-74983-C02-01 (MINECO/FEDER). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Instituto de Investigación Matemática de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis, Universidad de Sevilla, Sevilla, Spain

    Justo Puerto

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  1. Justo Puerto
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Correspondence to Justo Puerto .

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Editors and Affiliations

  1. Department of Mathematics and Applications, University of Naples Federico II, Napoli, Italy

    Lina Mallozzi

  2. Department of Industrial and Information Engineering, Second University of Naples, Aversa, Italy

    Egidio D'Amato

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Puerto, J. (2017). Sharing Costs in Some Distinguished Location Problems. In: Mallozzi, L., D'Amato, E., Pardalos, P. (eds) Spatial Interaction Models . Springer Optimization and Its Applications, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-52654-6_14

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