Double-type player games and proportional cross-evaluation allocation method for collaborative logistics

Abstract

In collaborative logistics, multiple shippers may collaborate with each other by consolidating their transportation requests and negotiate a contract with a single carrier to serve the requests at a favorable tariff. In this collaboration, agents of one type (the shippers) cannot increase their payoffs without the participation of an agent of the other type (the carrier). One key issue for such collaboration is the cost allocation among the shippers. Motivated by this real need, we introduce a new class of games called double-type player games and propose a cost/payoff allocation method for them. Each double-type player game has two types of players or agents: service requestors and service providers. We prove that the core of any game in this class is not empty and apply the concept of cross-evaluation originating from data envelopment analysis to generate a fair cost/payoff allocation among the players in such a game. More particularly, we propose a new and simple method called proportional cross-evaluation method for generating an allocation in the semi-core with some important properties. It is based on self-evaluation and peer-evaluations of the contribution of each player to the grand coalition. As applications, this method is applied to the cost allocation of double-type player games appearing in shipper collaboration in both truckload transportation and less-than-truckload transportation. It is compared with several popularly used allocation methods by numerical experiments. The results show that our method outperforms those methods in generating an allocation in the core.