A two stage optimization model for sustainable location routing problem with capacity and time window constraints in smart parcel lockers

The rapid expansion of e-commerce has significantly increased the demand for sustainable delivery methods to mitigate urban congestion, emissions, and rising logistical costs. Addressing the challenges of last-mile delivery requires logistics providers to respond to operational demands and market dynamics with both urgency and efficiency. Smart parcel lockers, as a known solution, reduce the negative externalities of urban transportation while improving delivery performance. This research introduces a sustainable location-routing model for smart parcel lockers using a two-stage optimization approach. The model aims to minimize operational costs, fuel consumption, and CO₂ emissions while ensuring customer demand is met. Exact solution techniques are applied, and multiple scenarios are evaluated through extensive sensitivity analysis. The model is validated using a real-world case study in Tehran, Iran. In addition, metaheuristic algorithms, such as the Keshtel, Genetic, and Simulated Annealing methods, were benchmarked to evaluate model performance under varying problem scales, with the Keshtel algorithm showing superior scalability and runtime efficiency in large instances. Findings indicate that optimally positioned lockers combined with efficient routing can lead to substantial reductions in both transportation costs and environmental impacts. Practical implications for logistics managers include the integration of electric vehicles and renewable-powered lockers to further advance sustainability goals.