A Two-Stage Location Problem with Lockers and Mini-Depots Under Crowdsourced Last Mile Delivery in E-Commerce Logistics

With the rapid growth of e-commerce and rising demand for faster, reliable last mile delivery, optimizing the spatial layout of terminal logistics facilities is critical. This paper proposes a two-stage location framework for mini-depots and lockers considering spatiotemporal customer demand. In the first stage, Affinity Propagation (AP) clustering identifies candidate mini-depot locations and locker layouts based on temporal and spatial demand characteristics. In the second stage, an Adaptive Heuristic Electric Eel Foraging Optimization (AHEEFO) determines the optimal mini-depot location strategy to minimize total cost. A dataset of 1157 Beijing customer points, including latitude, longitude and demand information, is used for model validation. Results show that Scenario 2, with dispersed demand, outperforms Scenario 1 and traditional strategies in both total cost and customer satisfaction; dispersed demand can be effectively supported via crowdsourced delivery and locker layout, whereas concentrated demand requires more professional courier resources. Comparative experiments reveal AP clustering is more stable, reducing clustering-stage cost by 13.57% compared with K-means, and AHEEFO outperforms other algorithms in cost optimization, computational efficiency, and significance tests under random demand surges. Finally, the sensitivity analysis highlights the effects of different algorithmic and operational parameters, offering valuable insights for both managerial practice and academic research.