On Games Arising from Multi-Depot Chinese Postman Problems

CentER Discussion Paper Series No. 2013-005

21 Pages Posted: 24 Jan 2013

See all articles by Trine T. Platz

Trine T. Platz

University of Copenhagen - Department of Economics

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Date Written: January 23, 2013

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.

Keywords: Chinese postman problem, cooperative game, submodularity, balancedness

JEL Classification: C71

Suggested Citation

Platz, Trine T. and Hamers, Herbert, On Games Arising from Multi-Depot Chinese Postman Problems (January 23, 2013). CentER Discussion Paper Series No. 2013-005. Available at SSRN: https://ssrn.com/abstract=2205692 or http://dx.doi.org/10.2139/ssrn.2205692

Trine T. Platz (Contact Author)

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Herbert Hamers

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

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