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Computing good allocations for combinatorial optimization games

Research output: Working paper

Published

Publication date2005
Place of publicationLancaster University
PublisherThe Department of Management Science
Number of pages0
Original languageEnglish

Publication series

NameManagement Science Working Paper Series

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.

Bibliographic note

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.