Smart modular lockers for last-mile delivery: Integrated optimization for parcel allocation and locker configuration

The rapid growth of e-commerce has intensified pressure on last-mile logistics, motivating the deployment of smart parcel lockers to improve delivery efficiency and service accessibility. Compared with traditional fixed-compartment designs, modular locker, such as the system supported by Physical Internet (PI) containers, offers greater adaptability by enabling reconfigurable storage capacity. However, their operational optimization has received limited attention. Existing studies typically address locker configuration and parcel allocation separately, overlooking their real-time interdependence in modular systems. This study develops a mixed-integer programming framework that jointly optimizes parcel allocation and locker configuration, with dual objectives of minimizing operational costs and customer walking distances. The problem is decomposed into two sequentially dependent processes: the master problem allocates parcels to couriers or lockers, while the sub-problem verifies and configures locker layouts. A heuristic solution framework is proposed by integrating the Strength Pareto Evolutionary Algorithm 2 (SPEA2) for the master problem with a Contour Line Algorithm (CLA) for the sub-problem. Computational experiments on benchmark datasets and a real-world urban delivery case demonstrate the superior convergence and solution diversity of SPEA2 over NSGA2, and show CLA effectively reduces both locker space waste and computation time. Sensitivity analysis on locker modes (fixed and modular) and operational parameters (locker width and parcel ratio) reveals that modular configurations significantly enhance robustness under high-demand conditions. The findings advance methodological research on modular locker optimization and provide actionable insights for last-mile delivery operators. In particular, they highlight the value of modularity and adaptability in achieving cost-efficient and resilient parcel delivery networks.