Optimizing a new robust bi-level closed-loop supply chain network problem by tailored Benders decomposition method

Globalized closed-loop supply chains (CLSC) struggle to balance economic efficiency and delivery reliability under uncertainty. Existing research often prioritizes speed over quantity reliability and cannot effectively model capacity uncertainty with partial distribution information. A new distributionally robust optimization (DRO) model for CLSC network design is proposed, featuring simultaneous optimization of upper-level total profit and lower-level on-time delivery, distributionally robust chance constraints with sub-Gaussian ambiguity sets to handle facility capacity uncertainty strictly, providing probabilistic feasibility guarantees, and an accelerated Benders decomposition algorithm for large-scale mixed integer linear programming. Applied to Ontario’s mobile phone industry, the model achieves CAD 92.55 million profit and 97.16% on-time delivery under 5% capacity fluctuation. It incurs only 1.6% cost loss versus deterministic models while preventing capacity violations at five facilities. It shows superior robustness to sample average approximation (SAA), maintaining a 2% constraint violation probability across sample sizes.