A bilevel approach for sustainable warehouses location with inventory decisions

Growing environmental concerns have placed increasing pressure on supply chains to reduce greenhouse gas (GHG) emissions while maintaining economic efficiency. However, strategic and operational decisions in sustainable supply chains are often optimized separately, despite their strong interdependence and combined impact on environmental performance. This paper addresses this gap by integrating strategic and operational decisions within a sustainable supply chain framework aimed at reducing GHG emissions. Strategic decisions are handled by a higher-level decision-maker (leader) and involve locating warehouses to satisfy the demand of a set of customers, with the objective of minimizing environmental pollution generated by delivery, order placement, and inventory processes. Operational decisions are managed by a lower-level decision-maker (follower), who focuses on inventory management and minimizes traditional economic costs. This hierarchized decision-making structure is modeled using a bilevel programming approach, resulting in a single-objective problem with multiple independent nonlinear follower problems, which poses significant computational challenges. To obtain high-quality solutions within reasonable computational times, two component-based metaheuristic algorithms are proposed. The first metaheuristic combines four commonly used and effective components for solving bilevel problems: random solution generation, solution recombination, random modification, and competition among solution sets. The second metaheuristic enhances this framework by incorporating a local search procedure at each iteration to further improve newly generated solutions. The effectiveness of the proposed methods is assessed by comparing their solutions with those obtained from an exact approach when instance sizes allow. Robustness is further demonstrated through computational experiments on a benchmark set of instances, showing good solution stability and low computational times. Finally, the proposed approach is applied to a realistic case study from the Mexican steel industry, where a sensitivity analysis provides valuable managerial insights and reveals several counterintuitive results.