Bi-objective stochastic model for the design of biofuel supply chains incorporating risk

The design of a biofuel supply chain network involves multiple uncertainty sources such as the biomass supply and quality. Most of the previous works took a risk-neutral approach by modeling this problem as two-stage stochastic formulation. However, most decision makers are not risk-neutral and a better understanding of the risk involved is germane. This study proposes a bi-objective two-stage stochastic optimization model that considers the expected total cost and the CVaR as objective functions. The first stage determines the location of biorefineries, and the second stage decides the flow between suppliers (counties) and biorefineries. We assume as non deterministic two features of switchgrass (biomass), the ash and moisture contents. To solve this problem, a hybrid method based on a Simulated Annealing algorithm and the augmented ε-constraint method is developed and tested using a realistic large-scale case study in the state of Texas. Based on the experimental results, we observe that the CVaR is not a suitable risk measure when the problem involves a third party because the cost of third-party does not imply risk for the decision makers (biorefinery owner). Therefore, the PVaR model is more suitable for the nature of this problem since PVaR includes the risk inherent to the third party in case this entity is not able to fulfill the demand of biofuel not covered by the supply chain network. As a result, we reformulate the original model by replacing the CVaR by PVaR to create a tailor-made formulation for the bi-objective two-stage stochastic programming problem including third party biofuel suppliers. Compared to existing solution procedures, the proposed hybrid method has merits in terms of computational burden and solution quality. Computational experiments show that the lower the confidence level in the third party (that is, a less reliable supplier needed to meet the bioethanol demand), the higher the expected costs and the PVaR (risk) for the supply chain design.