Cross-Evaluation Cost Allocation for Vehicle Routing Games
Résumé
In this paper, we study a cost allocation problem that arises in goods distribution by vehicles. This problem can be formulated as a vehicle-routing game (VRG), where the total distribution cost must be divided among all customers visited by the vehicles. We apply our recently developed solution concept for cooperative games, cross-evaluation value, to the cost allocation. In the solution concept, the allocation of the total cost of a VRG among its players is based on self-evaluation and peer-evaluations of the cost contribution of each player to the grand coalition, subject to the core constraints when the core of the game is not empty. Since the vehicle-routing game may have an empty core, an extended core concept is also proposed for the game, and the cross-evaluation value is then applied to its cost allocation. Numerical examples are presented and discussed.