New techniques for cost sharing in combinatorial optimization games

• 成果类型: Article
• 署名作者: Caprara, Alberto; Letchford, Adam N.
• 署名单位: University of Bologna; Lancaster University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0357-7
• 发表日期: 2010
• 页码: 93-118
• 关键词: allocation; projection; polytope; sets

摘要

Combinatorial optimization games form an important subclass of cooperative games. In recent years, increased attention has been given to the issue of finding good cost shares for such games. In this paper, we define a very general class of games, called integer minimization games, which includes the combinatorial optimization games in the literature as special cases. We then present new techniques, based on row and column generation, for computing good cost shares for these games. To illustrate the power of these techniques, we apply them to traveling salesman and vehicle routing games. Our results generalize and unify several results in the literature. The main underlying idea is that suitable valid inequalities for the associated combinatorial optimization problems can be used to derive improved cost shares.