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Computing good allocations for combinatorial optimization games

Caprara, A and Letchford, A N (2005) Computing good allocations for combinatorial optimization games. Working Paper. The Department of Management Science, Lancaster University.

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Abstract

Much of the literature on cooperative games associated with combinatorial optimization problems is concerned with finding necessary or sufficient conditions under which the core is non-empty. In this paper however we are concerned with a rather different question, which may be of more use in practice: how to find partial cost allocations with high value. This question is addressed from both theoretical and algorithmic viewpoints. We begin by defining a very general class of games, called Integer Minimization (IM) games, and show that it includes many well-known combinatorial optimization games as special cases. We then show that finding the optimal allocation is strongly NP-hard for many IM games of interest. This gives the motivation for seeking general techniques for computing `good' (though not necessarily optimal) allocations. We give three such techniques, based on column generation, row generation, or both. To illustrate the power of these techniques, we apply them to various travelling salesman and vehicle routing games.

Item Type: Monograph (Working Paper)
Additional Information: This was eventually published as: A. Caprara & A.N. Letchford (2010) New techniques for cost sharing in combinatorial optimization games. Math. Program., 124(1-2), 93-118.
Uncontrolled Keywords: combinatorial optimization games ; travelling salesman problem ; vehicle routing
Subjects:
Departments: Lancaster University Management School > Management Science
ID Code: 48795
Deposited By: ep_importer_pure
Deposited On: 11 Jul 2011 22:13
Refereed?: No
Published?: Published
Last Modified: 09 Apr 2014 20:50
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/48795

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