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Algorithms for multiplayer multicommodity flow problems

Author

Listed:
  • Attila Bernáth
  • Tamás Király
  • Erika Kovács
  • Gergely Mádi-Nagy
  • Gyula Pap
  • Júlia Pap
  • Jácint Szabó
  • László Végh

Abstract

We investigate the multiplayer multicommodity flow problem: several players have different networks and commodities over a common node set. Pairs of players have contracts where one of them agrees to route the flow of the other player (up to a given capacity) between two specified nodes. In return, the second player pays an amount proportional to the flow value. We show that the social optimum can be computed by linear programming, and we propose algorithms based on column generation and Lagrangian relaxation. In contrast, we prove that it is hard to decide if an equilibrium solution exists, although some natural conditions guarantee its existence. Copyright Springer-Verlag 2013

Suggested Citation

  • Attila Bernáth & Tamás Király & Erika Kovács & Gergely Mádi-Nagy & Gyula Pap & Júlia Pap & Jácint Szabó & László Végh, 2013. "Algorithms for multiplayer multicommodity flow problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 699-712, December.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:4:p:699-712
    DOI: 10.1007/s10100-012-0255-6
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    References listed on IDEAS

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    1. L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    2. F. Babonneau & O. du Merle & J.-P. Vial, 2006. "Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM," Operations Research, INFORMS, vol. 54(1), pages 184-197, February.
    3. Derks, J.J.M. & Tijs, S.H., 1985. "Stable outcomes for multi-commodity flow games," Other publications TiSEM f643e6a4-cf4e-4892-8f00-c, Tilburg University, School of Economics and Management.
    4. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
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    Cited by:

    1. Tibor Csendes & Tibor Jordán & Tamás Szántai, 2013. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 663-664, December.

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