Profit allocation mechanisms for carrier collaboration in pickup and delivery service

In collaborative logistics, multiple carriers may form an alliance by sharing their transportation requests and vehicle capacities in order to increase vehicle utilization rates and reduce empty back hauls. In this paper, a carrier collaboration problem in pickup and delivery service (CCPPD) is studied. CCPPD has two important issues which are the optimal reallocation of transportation requests among the carriers to maximize a total profit of the alliance and a fair allocation of the profit among the carriers so as to maintain the stability of the alliance. In this study, the profit allocation among carriers is addressed under a centralized collaboration framework. We propose three profit allocation mechanisms which are based on Shapley value, the proportional allocation concept, and the contribution of each carrier in offering and serving requests, respectively. All the mechanisms ensure that the allocation is in the core if the latter is not empty. They are evaluated and compared with numerical experiments on randomly generated instances.