Solving the Shared Capacity Vehicle Routing Problem with Simultaneous Pick-Up and Delivery in Omni-Channel Retailing Using a Modified Differential Evolution Algorithm

This study examines the logistical challenges arising in omni-channel retailing, where the interaction between traditional stores and online channels requires flexible and efficient transportation planning. In particular, the growth of Buy-Online-and-Pick-up-in-Store (BOPS) services has intensified the need to manage both forward deliveries and customer returns, the latter being a costly component of reverse logistics. To address these challenges, this study introduces the Shared Capacity Vehicle Routing Problem with Simultaneous Pickup and Delivery (SCVRP-SPD), which minimizes total operational cost by considering both transportation costs and the additional transfer costs incurred when reallocating store visits to more efficient delivery paths. In the SCVRP-SPD, stores are designed to serve a dual role as both pickup and return points, and a shared-capacity mechanism is incorporated to utilize leftover capacity in pre-planned trips, improving efficiency while reducing overall logistics cost. A mixed-integer programming model is developed for the problem, and solutions are obtained using GUROBI (version 11.0) and a newly designed Modified Differential Evolution (MDE) algorithm. Numerical experiments are conducted to evaluate the performance of the proposed MDE algorithm and to generate managerial insights, showing that the SCVRP-SPD is a promising strategy for omni-channel retailers seeking to reduce transportation costs, streamline reverse logistics, and better utilize resources.