Electric Vehicle Routing Problem with Simultaneous Pickup and Delivery: Mathematical Modeling and Adaptive Large Neighborhood Search Heuristic Method

Electric vehicles (EVs) are a promising option to reduce air pollution and shipping costs, especially in urban areas. To provide scientific guidance for the growing number of logistics companies using EVs, we investigated an electric-vehicle-routing problem with simultaneous pickup and delivery that also considers non-linear charging and load-dependent discharging (EVRPSPD-NL-LD). The objective was to minimize the total number of EVs and the total working time, including travel time, charging time, waiting time, and service time. We formulated the problem as a mixed integer linear program (MILP), and small-size problems could be solved to optimality in an acceptable amount of time using the commercial solver IBM ILOG CPLEX Optimization Studio (CPLEX). In view of the fact that the problem is NP-hard, an adaptive large neighborhood search (ALNS) metaheuristic method was proposed to solve large-size problems. Meanwhile, new operators and a time priority approach were developed to provide options for different scenarios. The results of our computational investigation and sensitivity analysis showed that the proposed methods are effective and efficient for modified benchmark instances.