Skip to main content
Top

2017 | OriginalPaper | Chapter

Sharing Costs in Some Distinguished Location Problems

Author : Justo Puerto

Published in: Spatial Interaction Models

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
2.
go back to reference Blanco, V., Puerto, J., El-Haj Ben-Ali, S.: Continuous multifacility ordered median location problems. Eur. J. Oper. Res. 250 (1), 56–64 (2016)MathSciNetCrossRefMATH Blanco, V., Puerto, J., El-Haj Ben-Ali, S.: Continuous multifacility ordered median location problems. Eur. J. Oper. Res. 250 (1), 56–64 (2016)MathSciNetCrossRefMATH
4.
go back to reference Caprara, A., Letchford, A.N.: New techniques for cost sharing in combinatorial optimization games. Math. Program. 124 (1–2), 93–118 (2010)MathSciNetCrossRefMATH Caprara, A., Letchford, A.N.: New techniques for cost sharing in combinatorial optimization games. Math. Program. 124 (1–2), 93–118 (2010)MathSciNetCrossRefMATH
5.
6.
go back to reference Daskin, M.S.: Network and Discrete Location: Models, Algorithms, and Applications, 2nd edn. Wiley, Hoboken (2013)MATH Daskin, M.S.: Network and Discrete Location: Models, Algorithms, and Applications, 2nd edn. Wiley, Hoboken (2013)MATH
7.
go back to reference Drezner, Z.: Facility Location: A Survey of Applications and Method. Springer, New York (1995)CrossRef Drezner, Z.: Facility Location: A Survey of Applications and Method. Springer, New York (1995)CrossRef
8.
go back to reference Drezner, Z., Hamacher, H.: Facility Location: A Survey of Applications and Theory. Springer, New York (2002)CrossRefMATH Drezner, Z., Hamacher, H.: Facility Location: A Survey of Applications and Theory. Springer, New York (2002)CrossRefMATH
9.
go back to reference Eiselt H.A., Laporte, G., Thisse, J.-F.: Competitive location models: a framework and bibliography. Transp. Sci. 27 (1), 44–54 (1993)CrossRefMATH Eiselt H.A., Laporte, G., Thisse, J.-F.: Competitive location models: a framework and bibliography. Transp. Sci. 27 (1), 44–54 (1993)CrossRefMATH
10.
go back to reference Elzinga, J., Hearn, D.W.: Geometrical solutions for some minimax location problems. Transp. Sci. 6, 379–394 (1972)MathSciNetCrossRef Elzinga, J., Hearn, D.W.: Geometrical solutions for some minimax location problems. Transp. Sci. 6, 379–394 (1972)MathSciNetCrossRef
11.
go back to reference Fragnelli, V., Gagliardo, S.: Open problems in cooperative location games. Int. Game Theory Rev. 15 (3), 1–13 (2013)MathSciNetMATH Fragnelli, V., Gagliardo, S.: Open problems in cooperative location games. Int. Game Theory Rev. 15 (3), 1–13 (2013)MathSciNetMATH
12.
go back to reference 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) 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)
13.
go back to reference Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)MATH Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)MATH
16.
go back to reference Hakimi, S.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12 (3), 450–459 (1964)CrossRefMATH Hakimi, S.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12 (3), 450–459 (1964)CrossRefMATH
17.
go back to reference Hakimi, S.: Optimum distribution of switching centers in a communications network and some related graph theoretic problems. Oper. Res. 13 (3), 462–475 (1965)MathSciNetCrossRefMATH Hakimi, S.: Optimum distribution of switching centers in a communications network and some related graph theoretic problems. Oper. Res. 13 (3), 462–475 (1965)MathSciNetCrossRefMATH
18.
20.
go back to reference Hotelling, H.: Stability in competition. Econ. J. 39, 41–57 (1929) Hotelling, H.: Stability in competition. Econ. J. 39, 41–57 (1929)
22.
go back to reference Larson, R., Odoni, A.: Urban Operations Research. Prentice-Hall, New York (1981) Larson, R., Odoni, A.: Urban Operations Research. Prentice-Hall, New York (1981)
23.
go back to reference Love, R.F., Morris, J.G., Wesolowsky, G.O.: Facilities Location: Models and Methods. North-Holland, Amsterdam (1988)MATH Love, R.F., Morris, J.G., Wesolowsky, G.O.: Facilities Location: Models and Methods. North-Holland, Amsterdam (1988)MATH
24.
26.
go back to reference Megiddo, N., Zemel, E.: An O(nlogn) randomizing algorithm for the weighted Euclidean 1-center problem. J. Algorithms 3, 358–368 (1986)CrossRefMATH Megiddo, N., Zemel, E.: An O(nlogn) randomizing algorithm for the weighted Euclidean 1-center problem. J. Algorithms 3, 358–368 (1986)CrossRefMATH
27.
go back to reference Mirchandani, P., Francis, R.: Discrete Location Theory. Wiley, New York (1990)MATH Mirchandani, P., Francis, R.: Discrete Location Theory. Wiley, New York (1990)MATH
28.
go back to reference Nickel, S., Puerto, J.: Location Theory: A Unified Approach. Springer, Berlin (2005)MATH Nickel, S., Puerto, J.: Location Theory: A Unified Approach. Springer, Berlin (2005)MATH
29.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
30.
go back to reference Nissan, N., Roughgargen, Tardos, E., Vazirzni, V.V. (eds.): Algorithmic Game Theory. Cambridge University Press, Cambridge (2007) Nissan, N., Roughgargen, Tardos, E., Vazirzni, V.V. (eds.): Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
31.
32.
go back to reference Owen, S.H., Daskin, M.S.: Strategic facility location: a review. Eur. J. Oper. Res. 111 (3), 423–447 (1998)CrossRefMATH Owen, S.H., Daskin, M.S.: Strategic facility location: a review. Eur. J. Oper. Res. 111 (3), 423–447 (1998)CrossRefMATH
33.
go back to reference Papadopoulos, A.: Metric Spaces, Convexity and Nonpositive Curvature. European Mathematical Society, Zürich (2005)MATH Papadopoulos, A.: Metric Spaces, Convexity and Nonpositive Curvature. European Mathematical Society, Zürich (2005)MATH
34.
go back to reference 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) 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)
35.
go back to reference Puerto, J.: Lecturas en teoría de localización. Technical Report, Universidad de Sevilla. Secretariado de Publicaciones (1996) Puerto, J.: Lecturas en teoría de localización. Technical Report, Universidad de Sevilla. Secretariado de Publicaciones (1996)
36.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
37.
go back to reference 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) 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)
38.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
39.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
40.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
43.
go back to reference Tamir, A.: On the core of cost allocation games defined on locational problems. Transp. Sci. 27, 81–86 (1992)CrossRefMATH Tamir, A.: On the core of cost allocation games defined on locational problems. Transp. Sci. 27, 81–86 (1992)CrossRefMATH
44.
45.
go back to reference Zurcher, S.: Smallest enclosing ball for a point set with strictly convex level sets. Masters thesis, Institute of Theoretical Computer Science, ETH Zurich (2007) Zurcher, S.: Smallest enclosing ball for a point set with strictly convex level sets. Masters thesis, Institute of Theoretical Computer Science, ETH Zurich (2007)
Metadata
Title
Sharing Costs in Some Distinguished Location Problems
Author
Justo Puerto
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-52654-6_14