A mathematical model proposal for mobile parcel lockers utilized in last mile delivery under horizontal collaboration

Along with growing e-commerce effect, increasing delivery frequencies and small volume deliveries led to innovative and efficient last mile transportation solutions. In this context, mobile parcel lockers, which are dynamically located via electric vehicles and enabling customers to receive their cargo at any time of the day, have emerged as an innovative mode of delivery. The aim of this study is to propose a decision support model to organizations using these lockers in last mile transportation. A mixed-integer linear programming model is proposed in this study for the location routing problem with pick-up and delivery under horizontal collaboration using mobile parcel lockers. The objective of the model is to minimize the total cost including the costs of mobile parcel locker transportation and placement, customer cargo transportation, vehicle usage and driver. The model involves decisions to establish a route plan to depart the full parcel lockers and collect expired lockers while selecting right location for the full lockers, and load lockers with various cargo sizes. The model is first solved for the operations of three hypothetical organizations without collaboration; then solutions are obtained for scenarios in which organization have bilateral and trilateral horizontal collaboration. Cost benefits of horizontal collaboration are evaluated in the results. The scenario solutions have demonstrated that a crucial factor in determining the benefits of horizontal collaboration is the physical proximity of collaborating organizations' working regions. It has been revealed that horizontal trilateral collaborations are more cost-effective for organizations. Sensitivity analyses are also performed on these scenarios to reveal the impact of changes in the number of common customers and the parcel lockers' capacity on the outcomes. The findings demonstrated that as the number of common customers between the organizations increases, the advantage of horizontal collaboration increases, and as mobile parcel locker capacities increase, the total cost and locker occupancy rates decrease.