Biofuel supply chain design under competitive agricultural land use and feedstock market equilibrium

The rapid expansion of the biofuel industry diverts a large amount of agricultural crops as energy feedstocks, and in turn affects farm land allocation, feedstock market equilibrium, and agricultural economic development in local areas. In this paper, we propose game-theoretic models that incorporate farmers' decisions on land use and market choice into the biofuel manufacturers' supply chain design problem. A noncooperative bi-level Stackelberg leader–follower game model and a cooperative game model are developed respectively to address possible business partnership scenarios between feedstock suppliers and biofuel manufacturers. The models determine the optimal number and locations of biorefineries, the required prices for these refineries to compete for feedstock resources, as well as farmers' land use choices between food and energy. Using corn as an example of feedstock crops, spatial market equilibrium is utilized to model the relationship between corn supply and demand, and the associated price variations in local grain markets. With linear corn demand functions, we develop a solution approach that transforms the original discrete mathematical program with equilibrium constraints (DC-MPEC) into to a solvable mixed integer quadratic programming (MIQP) problem based on Karush–Kuhn–Tucker (KKT) conditions. The proposed methodology is illustrated using an empirical case study of the Illinois State. The computation results reveal interesting insights into optimal land use strategies and supply chain design for the emerging “biofuel economy”.