A new robust bi-level optimization framework for biomass supply chain network and its accelerated Benders decomposition

The biomass supply chain (BSC) encompasses the entire biomass lifecycle from resource procurement to energy transformation. As a viable alternative to fossil fuels, BSC promotes renewable biomass energy utilization. However, its large-scale implementation is impeded by various operational uncertainties. This study develops a novel globalized robust bi-level (GRB) optimization model with probabilistic guarantees to manage multi-source uncertainties in BSC design. Methodologically, we integrate globalized robust optimization (GRO) with distributionally robust optimization (DRO), translating uncertain constraints into solvable forms via sub-Gaussian ambiguity sets. The bi-level structure can capture producer-farmer Stackelberg interactions and can be reformulated as a mixed-integer linear programming (MILP) model through follower decision enumeration. To enhance computational tractability, an accelerated Benders decomposition (ABD) algorithm is designed. A case study on Illinois’ BSC network demonstrates the proposed framework’s efficacy: ( i ) the price of robustness (the increase in the objective value when passing from the nominal solution to the robust solution) increases by only 0.8% over deterministic model; ( ii ) robust optimal solutions are ensured under 1%, 10% and 20% parameter perturbations; and ( iii ) solution times reduced by 40%–50% for large scale networks compared to commercial solvers. Additionally, we provide decision-makers with managerial insights for sustainable bioenergy managements. • Developed a novel globalized bi-level optimization framework for the BSC in renewable energy. • Constructed a pair of uncertainty sets to capture uncertain model parameters. • Established a posteriori probabilistic guarantee for obtained robust optimal solution. • Designed an accelerated BD algorithm for the resulting MILP model. • Verified the superiority of the proposed methods via a practical case in Illinois.