On the Asymmetric Connected Facility Location Polytope

  • Markus Leitner
  • Ivana Ljubić
  • Juan-José Salazar-González
  • Markus Sinnl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8596)

Abstract

This paper is concerned with the connected facility location problem, which has been intensively studied in the literature. The underlying polytopes, however, have not been investigated. This work is devoted to the polytope associated with the asymmetric version of the problem. We first lift known facets of the related Steiner arborescence and of the facility location polytope. Then we describe other new families of facet-inducing inequalities. Finally, computational results are reported.

References

  1. 1.
    Gollowitzer, S., Ljubić, I.: MIP models for connected facility location: a theoretical and computational study. Comput. Oper. Res. 38(2), 435–449 (2011)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Leitner, M., Raidl, G.R.: Branch-and-cut-and-price for capacitated connected facility location. J. Math. Model. Algorithms 10(3), 245–267 (2011)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Leitner, M., Ljubić, I., Salazar-González, J.J., Sinnl, M.: The connected facility location polytope: valid inequalities, facets and a computational study. Submitted (2014)Google Scholar
  4. 4.
    Fischetti, M.: Facets of two Steiner arborescence polyhedra. Math. Program. 51, 401–419 (1991)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Cornuejols, G., Thizy, J.M.: Some facets of the simple plant location polytope. Math. Program. 23(1), 50–74 (1982)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1999)MATHGoogle Scholar
  7. 7.
    Guignard, M.: Fractional vertices, cuts and facets of the simple plant location problem. In: Padberg, M. (ed.) Combinatorial Optimization. Mathematical Programming Studies, vol. 12, pp. 150–162. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  8. 8.
    Bardossy, M.G., Raghavan, S.: Dual-based local search for the connected facility location and related problems. INFORMS J. Comput. 22(4), 584–602 (2010)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Cirasella, J., Johnson, D.S., McGeoch, L.A., Zhang, W.: The asymmetric traveling salesman problem: algorithms, instance generators, and tests. In: Buchsbaum, A.L., Snoeyink, J. (eds.) ALENEX 2001. LNCS, vol. 2153, pp. 32–59. Springer, Heidelberg (2001) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Markus Leitner
    • 1
  • Ivana Ljubić
    • 1
  • Juan-José Salazar-González
    • 2
  • Markus Sinnl
    • 1
  1. 1.ISORUniversity of ViennaViennaAustria
  2. 2.DEIOCUniversidad de La LagunaLa LagunaSpain

Personalised recommendations