Modeling a Location and Routing Problem for Mobile Lockers in Last-Mile Delivery With Horizontal Collaboration

Due to the growth of e-commerce, promising last-mile delivery options have emerged to manage the rise in delivery frequency and small-volume deliveries. These delivery methods include mobile parcel lockers that are placed by electric vehicles, which enables customers to receive their packages at any time. This study presents a decision support model for enterprises that utilize mobile parcel lockers in last-mile delivery with pick-up and delivery under horizontal collaboration. The model aims to allocate parcel lockers and route the vehicles with the minimum cost, which encompasses the expenses associated with transportation and placement of the lockers, transportation of customer cargo, vehicle utilization, and payment of drivers. We propose an integer linear programming model for the location routing problem. We present an ILP-based decomposition heuristic and an iterative approach to larger-sized practical instances. A numerical analysis is conducted to see the cost and benefit of bilateral and trilateral collaborations in an illustrative case. According to the results, the total cost is reduced by up to 4.52% for companies in the trilateral collaboration scenario with single warehouses, and by up to 7.32% in the trilateral collaboration scenario with multiple warehouses. We examine the large problem sizes of up to 100 nodes to see the performance of the heuristic approaches compared to the model solutions. The two-stage heuristic achieves the optimal solutions for all instances with a node size 50 in a shorter solution time. The iterative approach allows us to deal with the problem complexity of instances with 75 and 100 nodes and yields 0.88% close solutions to the model on average.