On a Cost Allocation Problem Arising from a Star-Star Capacitated Concentrator Location Problem

Abstract

We analyze a cost allocation problem associated with the Star-Star Capacitated Concentrator Location (SSCCL) problem. The problem is formulated as a cost cooperative game in characteristic function form to be referred to as the SSCCL game. The characterization and computation of game theoretic solution concepts associated with this game are investigated. We show that, in general, the core of this cooperative game may be empty. However, we provide a polynomial representation of the core of the SSCCL game. In case of nonemptiness of the core we provide an efficient method to find the nucleolus. For the case when the core is empty, we propose the least weighted e-core as a concept for fair cost allocation for the SSCCL problem and give its polynomial characterization. Moreover, certain 'central' point of the least weighted e-core is also efficiently characterized.