Heterogeneous vehicle pickup and delivery problems: Formulation and exact solution

The heterogeneous green pickup and delivery problem (GPDP) aims to minimize carbon emissions of pickups and deliveries by a fleet of heterogeneous vehicles. We propose the first exact algorithm for solving the heterogeneous GPDP. This exact algorithm is based on a set partitioning model and the key characteristics of its optimal solution. We prove that the optimal solution is composed of the optimal trips of heterogeneous vehicles; thus, the solution space is significantly reduced by cutting the non-optimal trips. The proposed exact algorithm can rapidly find the optimal solution of the largest-scale instance from Li & Lim benchmarks and three types of vehicles. The exact algorithm is also validated by solving a practical case of heterogeneous GPDP in China. Based on the extensive experiments, we conclude an interesting managerial insight that heterogeneous vehicles can always effectively reduce carbon emissions except for two situations.