Biomass Logistics Network Design Under Price-Based Supply and Yield Uncertainty

We consider an integrated supply pricing and biomass logistics network design problem in which yield rates are uncertain. The base supply amount is modeled via a farmers’ decision model that estimates the amount of land dedicated to biomass production under a given biomass wholesale price. We develop a two-stage stochastic integer program for integrated design of a network as well as biomass pricing decisions under yield uncertainty. To efficiently solve our model, we suggest a Benders decomposition–based algorithm in which the Benders cuts, one for each scenario, are aggregated by utilizing a scheme that takes into account yield rates as well as the geographical nature of the underlying problem. With further strengthening of the cuts, we present a significantly improved approach for solving relatively large instances and illustrate its performance via a computational study. We further present an extensive case study in Texas using realistic data to test our model’s capabilities and to demonstrate its effectiveness in capturing the relationships between total cost, biomass wholesale price, network structure, and various input parameters. Finally, we examine the relationship between farmers’ decision model parameters, which dictate the risk profile of farmers, and the expected total system cost, as well as the biomass wholesale price.