An exact decomposition method to save trips in cooperative pickup and delivery based on scheduled trips and profit distribution

Abstract

Compared to the non-cooperative mode, the cooperative mode is a powerful way to reduce operational cost in pickup and delivery service. In order to protect business sensitive information, sometimes participants are unwilling to open the customer's detailed information. Thus, we utilize the publishable trip scheduled results to compute the saved trips brought by cooperation. A mathematical model minimizing trips of cooperation is proposed. To obtain the exact solution, we define the cooperative trip set. We prove that only when cooperative trip set exists it is possible to save trips by cooperation. For a two-trip cooperative trip set, we exactly obtain the saved trips by enumerating all feasible cooperative cases. For a K-trip cooperative trip set, we propose an exact method to obtain the saved trips by decomposing it to at most K-1 two-trip cooperative trip sets. Computational complexity of the based-on-decomposition exact algorithm is O(N), where N is the total number of trips. Using the based-on-decomposition algorithm, we calculate the exact Shapley value to distribute profit. To empirically verify the exact method, we perform the extensive experiment cases of the real cooperative pickup and delivery service, i.e., “picking up and delivering customers to airport service” (PDCA).