Re-supplying autonomous mobile parcel lockers in last-mile distribution

This paper investigates a practical last-mile delivery scenario where a fleet of trucks replenishes autonomous mobile parcel lockers (AMPLs) in an urban setting. The lockers move along specified paths within restricted zones to reach customers’ locations. Ensuring seamless coordination between trucks and AMPLs requires the identification of suitable locations to exchange empty or loaded modular lockers. We first introduce a mixed-integer linear programming (MILP) formulation for the investigated problem. The proposed formulation establishes the basis for optimizing meeting point selection and routing decisions. Additionally, the study introduces a cluster-based simulated annealing (CSA) algorithm tailored for addressing larger-scale instances of the studied problem. The CSA algorithm incorporates the K-means clustering method with specialized operators rooted in an extensive neighborhood search, aiming to improve the effectiveness of solution discovery. We generated a new set of benchmark instances to assess the MILP formulation’s efficiency and the proposed metaheuristic algorithm and conducted comprehensive numerical experiments.