A two-stage stochastic mixed-integer programming approach to the competition of biofuel and food production

The multi-attribute biomass and food production (BFP) problem facing farmers and co-operatives is further complicated by uncertainties in crop yield and prices. In this paper, we present a two-stage stochastic mixed-integer programming (MIP) model that maximizes the economic and environmental benefits of food and biofuel production. The uncertain parameters of yield amount and price level are calculated using real data. Economic aspects include revenue obtained from biomass and food crop sales as well as costs related to seeding, production, harvesting, and transportation operations at the farm level. Environmental effects include greenhouse gas (GHG) emissions, carbon sequestration, soil erosion, and nitrogen leakage to water. The first-stage variables define binary decisions for allocating various land types to food and energy crops, while the second-stage variables are operational decisions related to harvesting, budget allocation, and amounts of different yield types. We present a decomposition algorithm, which is enhanced with specialized Benders cuts for solving this stochastic MIP problem. The computational efficiency of the proposed model and approach is demonstrated by applying it to a real case study involving switchgrass and corn production in the state of Kansas. We measure the solution quality and speed of the decomposition method over stochastic and deterministic models. Results indicate the significant benefit of using the stochastic yield-level information in an optimization model. The proposed stochastic MIP model provides important strategies and insights into decision making for biofuel and food production under uncertainty.