Robust design and planning of a bioenergy supply chain under multi-uncertainty

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 $ L_1 $ L1-norm ( $ L_1 $ L1-ball), $ L_2 $ L2-norm (ellipsoid), $ L_{\infty } $ L∞-norm (box) and D-norm (budgeted) are employed. All the models, except the $ L_2 $ L2-norm-based model, can be reformulated as mixed-integer linear programming (MILP) problems and easily solved. The $ L_2 $ 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.