An efficient characterization of some cost allocation solutions associated with capacitated network design problems

Abstract

We analyze some game-theoretic solution concepts associated with a cost allocation problem arising from the Capacitated Network Design (CND) problem. The problem is formulated as a cost cooperative game in characteristic function form to be referred to as the CND game. We provide an efficient representation of several game-theoretic solution concepts associated with the CND game. In particular, we efficiently characterize the core, and in some cases the nucleolus, the least weighted?-core and a certain "central" point in the least weighted?-core. Our model properly generalizes several previously studied cooperative games. We also employ our model to analyze cost allocation problems associated with several classes of network design problems, which were not previously studied in the literature. Specifically, we efficiently characterize the above cost allocation solutions for cost allocation problems associated with the Capacitated Concentrator Location problem, the Capacitated Minimum Spanning Tree problem, the Capacitated Fixed Cost Spanning Forest problem, and the Capacitated Steiner Tree problem.