The Vehicle Routing Problem with Simultaneous Pickup and Delivery Considering the Total Number of Collected Goods

As a consequence of e-commerce development, large quantities of returned goods are shipped every day. The vehicle routing problem with simultaneous delivery and pickup (VRPSDP) has become one of the most important areas of logistics management. Most related studies are aimed at minimizing travel time. However, the total number of collected goods is also very important to logistics companies. Thus, only considering the traveling time cannot reflect actual practice. To effectively optimize these operations for logistics companies, this paper introduces the vehicle routing problem with simultaneous pickup and delivery considering the total number of collected goods. Based on the principles of considering the number of collected goods, a bi-objective vehicle routing model minimizing the total travel time and maximizing the total number of collected goods simultaneously is developed. A polynomial time approximation algorithm based on the ε-constraint method is designed to address this problem, and the approximation ratio of the algorithm is analyzed. Finally, the validity and feasibility of the proposed model and algorithm are verified by test examples, and several managerial insights are derived from the sensitivity analysis.