A polynomial expression for the Owen value in the maintenance cost game. (2nd April 2016)

• Record Type: Journal Article
• Authors: Costa, Julián
• Is Part Of: Optimization. Volume 65:Number 4(2016)
• Page Start: 797
• Page End: 809
• Publication Date: 2016-04-02
• Subjects: cooperative game -- cost allocation -- maintenance cost game -- Owen value; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1064123
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The class of maintenance cost games was introduced in 2000 to deal with a cost allocation problem arising in the reorganization of the railway system in Europe. The main application of maintenance cost games regards the allocation of the maintenance costs of a facility among the agents using it. To that aim it was first proposed to utilize the Shapley value, whose computation for maintenance cost games can be made in polynomial time. In this paper, we propose to model this cost allocation problem as a maintenance cost game with a priori unions and to use the Owen value as a cost allocation rule. Although the computation of the Owen value has exponential complexity in general, we provide an expression for the Owen value of a maintenance cost game with cubic polynomial complexity. We finish the paper with an illustrative example using data taken from the literature of railways management.