Conclusions
We have proposed a mathematical model to tackle the supplier selection and operation planning problem in biomass supply chains to help decision-makers facing uncertainty of biomass feedstock supply. The objective is to minimize the total system cost of a biomass supply chain. We have applied an enhanced and regularized L-shaped method to solve the two-stage stochastic programming model. This technique allows us to decompose a high dimensional stochastic model into subproblems of reasonable size. These sub-problems could be solved on a personal computer with limited memory. Moreover, our proposed method could find an optimal solution faster than the standard L-shaped decomposition method and commercial MILP solver Gurobi. Besides, we have analyzed the impacts of critical parameters on the optimal expected cost of the system and supplier selection. Several directions for future research may be pursued as considering other uncertainties (price, quality, external demand, conversion technology). Another possibility is to integrate a more detailed transportation planning with the number of truck trips as a decision variable in each period. For this extension, the second stage problem may become a MILP model which imposes a high computational challenge. More effective algorithms may be developed to solve the complex and high dimensional model. Our ultimate goal is to develop a decision-making support tool for biomass supply chain management.
