A robust location-routing model with self-service lockers and micro-hubs for last-mile logistics under uncertainty

The rapid expansion of e-commerce has increased the need for cost-effective last-mile delivery, particularly in regions with fragmented demand. This study develops a robust location-routeing model, termed the Vehicle Routeing Problem with Self-Service Parcel Lockers and Micro-Hub Locations (VRP-SPMH), integrating self-pickup service and en-route replenishment. The model jointly determines facility locations, customer service modes, and vehicle routes while accounting for customer willingness and finite facility capacities. Parcel-locker operating-cost uncertainty is modelled using a multi-interval robust formulation, while demand uncertainty is addressed through a protected-demand extension. Additional sensitivity analyses examine demand scale and travel-time variation. Tailored hybrid heuristics based on tabu search and modified Clarke-Wright savings are developed. Computational experiments include ablation and an independent Variable Neighbourhood Search (VNS) benchmark. The proposed heuristic achieves solution quality close to VNS with substantially less computational effort and reaches competitive solutions earlier under short-to-medium time budgets. Out-of-sample tests further reveal the trade-off between nominal cost and robustness. A rural case study in China shows that coordinating parcel lockers and micro-hubs reduces total operating cost by 7.82% relative to traditional home delivery.