Robust design and planning of a bioenergy supply chain under multi-uncertainty
针对生物乙醇需求、转化率和生物质供应等多重不确定性，提出基于范数不确定集的鲁棒优化框架，并开发高效算法求解，适用于不同风险偏好的生物燃料生产商。
This paper addresses a robust design and planning problem for a bioenergy supply chain with uncertain bioethanol demand, conversion rates, and biomass supply. We propose a general robust optimisation (RO) framework with norm-based uncertainty sets to handle multiple uncertainties, offering a universal approach suitable for biofuel producers with varying risk preferences and levels of prior knowledge of uncertainties. Four uncertainty sets based on the L1-norm (L1-ball), L2-norm (ellipsoid), L∞-norm (box) and D-norm (budgeted) are employed. All the models, except the L2-norm-based model, can be reformulated as mixed-integer linear programming (MILP) problems and easily solved. The L2-norm-based model can be reformulated as a mixed-integer second-order cone programming (MISOCP) problem and solved via the proposed exact generalised Benders decomposition-outer approximation (GBD-OA) algorithm. This algorithm combines the generalised Benders decomposition (GBD) and outer approximation (OA) algorithms. We derive two classes of valid inequalities, Benders cuts and OA cuts, to increase the efficiency of the method. The extensive computational results demonstrate the superior performance of the GBD-OA algorithm over both the B&C algorithm of CPLEX and the GBD algorithm in solving the MISOCP model. A case study using data from Henan Province, China, is presented to demonstrate the applicability of the proposed model, and managerial insights related to designing and planning the bioenergy supply chain under multiple uncertainties are explored.