Enhanced column-and-constraint generation algorithm for robust logistics network design problem with capacity sharing

Achieving robustness has become an essential issue due to the significant volatility of the logistics networks. Current works prioritize the demand uncertainty, but not sufficiently consider the financial budget uncertainty in warehousing. This deficiency renders the collaborators with weak financial endurance intractable to maintain the scheme robustness, impairing the overall network resilience. Therefore, inspired by the Nash equilibrium, a logistics network design method focusing on capacity sharing is proposed. This method allows participants to share capacity in the distribution centers, improving resilience and reducing costs. Firstly, a two-stage robust model considering the uncertainty of demand and financial budget is established to minimize the operating costs of the logistics network. Then, the Nash equilibrium-based constraints are incorporated into the model to ensure a fair distribution of benefits and costs among participants. Subsequently, a two-stage method is designed with an enhanced column and constraint generation algorithm (C&CG) using optimal cut, and reverse Nash equilibrium-based constraints are proposed for the worst financial condition. The effectiveness of the algorithm and model is verified through a series of numerical benchmarks and sensitivity analysis for Nash equilibrium-based constraints, sharing restrictions, uncertainty of demand and financial budget. The results show that the proposed method is efficient and flexible when incorporating capacity sharing and highlighting the influence of the Nash equilibrium-based constraints. Finally, it presents that the Nash equilibrium-based constraints are more suitable for logistics networks through sharing alliances.