Sustainable multi-objective location-routing problem with time windows: a case study in China

In response to intense market competition and the growing need for sustainable development, logistics companies must balance economic, environmental, and social objectives. This study investigates a sustainable multi-objective location-routing problem (MLRP) in urban e-commerce logistics, aiming to minimise total costs, CO2 emissions, and vehicle time window violation durations. The proposed model incorporates practical constraints, including flow balance, depot and vehicle capacity, hard time windows at depots, and soft time windows at service stations. Due to the NP-hard nature of the problem, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to solve the multi-objective issue. Real-world case data from China are used to validate the model, producing a Pareto frontier and enabling detailed analysis of extreme solutions. The results reveal inherent conflicts among the three objectives, requiring decision-makers to select appropriate strategies from the Pareto frontier based on their specific needs and goals. Finally, sensitivity analyses of key parameters were conducted to provide strategic guidance for urban logistics decisions to express enterprises.