Compensation and profit distribution for cooperative green pickup and delivery problem

Cooperation is a powerful strategy to achieve the objective of the green pickup and delivery problem (GPDP) that minimizes carbon emissions of pickup and delivery service. However, the cooperative GPDP may not be accepted by all the partners, as the cost of cooperative GPDP may be higher than that of the non-cooperative minimum cost PDP. Therefore, a reasonable compensation mechanism is desired to form an acceptable cooperative GPDP, and a fair method of profit distribution, based on the mechanism, is needed to stabilize the cooperation. In this paper, we analyze the situations in which a compensation is needed and develop the lower bound of the compensation. Further, we propose an exact method to calculate the actual compensation and the profit distribution based on cooperative game theory. The proposed exact method can efficiently solve the largest scale instance in Li & Lim benchmarks, i.e., pdptw1000-LR1_10_1 with 1,054 customers and 19,306 products. The proposed compensation and profit distribution mechanism based on cooperative game theory is also applied to a real-world GPDP and achieve satisfactory performance. Some interesting and important managerial insights are found and discussed.