A novel time-dependent electric vehicle pickup and delivery problem with time windows in cold supply chains

In order to alleviate the environmental impact of greenhouse gas, electric vehicles (EVs) have been widely employed in cold supply chains. Many researchers have focused on the pickup and delivery problem with time windows (PDPTW) to design the optimal routing plan satisfying the specified precedence constraints and time windows. However, few studies considered the time-dependent travel time and product spoilage in electric vehicle PDPTW. Therefore, this study proposes a novel time-dependent electric vehicle PDPTW model in cold supply chains. Support vector machine is employed to train the travel speed predictor so that the time-dependent travel time can be obtained through the predicted travel speed. The traditional linear loss function for product spoilage is extended by taking into account the customers’ sensitivity to product spoilage. To solve the proposed model, a new deep reinforcement learning with paired embedding and graph attention network (DRL-PE-GAT) algorithm is proposed. The paired embedding and graph attention network (GAT) are integrated to capture the intrinsic relationship between pickup and delivery customer nodes and obtain the spatial dependencies between nodes, respectively. Further, several experiments are conducted with the proposed algorithm and three baseline algorithms to validate the performance of the proposed algorithm.