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On games arising from multi-depot Chinese postman problems

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  • Platz, Trine Tornøe

    ()
    (Department of Business and Economics)

  • Hamers, Herbert

    (Department of Econometrics & OR and CentER)

Abstract

This paper introduces cooperative games arising from multi-depot Chinese postman problems and explores the properties of these games. A multi-depot Chinese postman problem (MDCP) is represented by a connected (di)graph G, a set of k depots that is a subset of the vertices of G, and a non-negative weight function on the edges of G. A solution to the MDCP is a minimum weight tour of the (di)graph that visits all edges (arcs) of the graph and that consists of a collection of subtours such that the subtours originate from different depots, and each subtour starts and ends at the same depot. A cooperative Chinese postman (CP) game is induced by a MDCP by associating every edge of the graph with a different player. This paper characterizes globally and locally k-CP balanced and submodular (di)graphs. A (di)graph G is called globally (locally) k-CP balanced (respectively submodular), if the induced CP game of the corresponding MDCP problem on G is balanced (respectively submodular) for any (some) choice of the locations of the k depots and every non-negative weight function.

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Bibliographic Info

Paper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 24/2012.

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Length: 20 pages
Date of creation: 02 Dec 2012
Date of revision:
Handle: RePEc:hhs:sdueko:2012_024

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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Phone: 65 50 32 33
Fax: 65 50 32 37
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Web page: http://www.sdu.dk/ivoe
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Keywords: Chinese postman problem; cooperative game; submodularity; balancedness;

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  1. Hamers, H.J.M. & Miquel, S. & Norde, H.W., 2011. "Monotonic Stable Solutions for Minimum Coloring Games," Discussion Paper 2011-016, Tilburg University, Center for Economic Research.
  2. Yoshio Okamoto, 2003. "Submodularity of some classes of the combinatorial optimization games," Computational Statistics, Springer, vol. 58(1), pages 131-139, 09.
  3. Hamers, Herbert & Borm, Peter & van de Leensel, Robert & Tijs, Stef, 1999. "Cost allocation in the Chinese postman problem," European Journal of Operational Research, Elsevier, vol. 118(1), pages 153-163, October.
  4. Hamers, Herbert, 1997. "On the concavity of delivery games," European Journal of Operational Research, Elsevier, vol. 99(2), pages 445-458, June.
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