فرزاد بهرامی

Objective : This study introduces a location-routing model tailored for parcel delivery in large, sparsely populated regions with limited infrastructure. It aims to minimize system costs by optimizing hub placement, city-to-hub assignments, routing paths, and fleet composition. The model accounts for real-world complexities such as diverse vehicle types, flexible delivery time windows, and multiple pickup/delivery paths, offering a strategic planning tool for logistics operations in challenging environments.  Methodology: To solve this NP-hard problem, the researchers reformulated a mixed-integer nonlinear program (MINLP) into a more computationally efficient mixed-integer programming (MIP) model. For larger instances, they developed a two-stage hybrid metaheuristic: the first stage uses an Artificial Bee Colony (ABC) algorithm to explore hub locations and initial allocations, while the second stage applies Simulated Annealing (SA) with local search to optimize routing and assignments. Validation was performed using CPLEX for small instances and benchmarked against a published SA-based method across 75 test scenarios and two real-world case studies from an Iranian parcel delivery company. Results : The hybrid method achieved optimal or near-optimal solutions faster than CPLEX for minor problems and outperformed the SA benchmark for larger ones, improving solution quality by 4% and reducing routes by 11%. The model also increased 24-hour deliveries by 4% without raising costs. The SA phase alone contributed a 1.6% cost reduction by restructuring the network. Case studies confirmed the model’s practical value, consistently identifying robust hub configurations across diverse network scales and operational strategies. Conclusion : This study presents a strategic planning tool for parcel delivery in challenging geographic and infrastructural conditions. It enables logistics managers to minimize operational costs while maintaining stable hub configurations during network expansion. A case study in Iran highlights its long-term value: a four-hub network with a 680 km line-haul limit offers superior nationwide coverage compared to a three-hub setup with a 510 km limit focused on major cities.