Collaborative Mechanism for Pickup and Delivery Problems with Heterogeneous Vehicles under Time Windows

The sustainability and complexity of logistics networks come from the temporally and spatially uneven distributions of freight demand and supply. Operation strategies without considering the sustainability and complexity could dramatically increase the economic and environmental costs of logistics operations. This paper explores how the unevenly distributed demand and supply can be optimally matched through collaborations, and formulates and solves a Collaborative Pickup and Delivery Problem under Time Windows (CPDPTW) to optimize the structures of logistics networks and improve city sustainability and liverability. The CPDPTW is a three-stage framework. First, a multi-objective linear optimization model that minimizes the number of vehicles and the total cost of logistics operation is developed. Second, a composite algorithm consisting of improved k-means clustering, Demand-and-Time-based Dijkstra Algorithm (DTDA) and Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) is devised to solve the optimization model. The clustering algorithm helps to identify the feasible initial solution to INSGA-II. Third, a method based on improved Shapley value model is proposed to obtain the collaborative alliance strategy that achieves the optimal profit allocation strategy. The proposed composite algorithm outperforms existing algorithms in minimizing terms of the total cost and number of electro-tricycles. An empirical case of Chongqing is employed to demonstrate the efficiency of the proposed mechanism for achieving optimality for logistics networks and realizing a win-win situation between suppliers and consumers.