Joint location and pricing optimization of self-service in urban logistics considering customers’ choice behavior

Self-services by widely-deployed stations allow customers to pick up their packages themselves and have great potential to reduce last-mile delivery cost by aggregating spatial demands. An efficient self-service design for the locations of self-service stations and the service price will help to shift customers from the home-delivery service to the cost-effective self-service, thus reducing the vehicle routing cost of the dedicated fleet. This study proposes a comprehensive modeling and optimization framework for the joint self-service station location and service price (SLSP) optimization problem considering customers’ choice behavior and vehicle routing in order to maximize the profit of the logistics service providers in the last-mile delivery system. Logit equilibrium and Wardrop equilibrium conditions are employed to characterize the delivery service choice and route choice behavior of customers. A convex optimization model is developed to capture the distribution of customers opting for home-delivery service and self-services at various locations, who aim to maximize their expected utilities. We then formulate the SLSP problem as a mathematical program with complementarity constraints. An active set algorithm is proposed to solve the model effectively. Numerical experiments based on the Nguyen-Dupuis and Sioux Falls networks are conducted to demonstrate the proposed framework and derive managerial insights.