An economic analysis of the future U.S. biofuel industry, facility location, and supply chain network

This paper presents a price-endogenous, dynamic, mixed-integer nonlinear programming (MINLP) model to determine the biofuel feedstock supply response in U.S. agriculture and future biorefinery locations that meet the mandated cellulosic biofuel production targets. With a large number of supply units and potential processing locations involved, the problem could not be solved directly using MINLP solvers. We developed a sequential two-stage solution procedure to cope with this computational difficulty. The original MINLP model is decomposed into a price-endogenous agricultural sector model that solves the supply response and equilibrium in agricultural product markets, and a dynamic linear mixed-integer programming (MIP) model that solves the optimum facility location and supply chain network. The two models are solved sequentially with feedback from each other. Because of the large number of binary variables involved, computational difficulty was also encountered when solving the MIP model. We employed a heuristic backward-recursive technique to cope with this difficulty. Using moderately large test problems, we demonstrate that the heuristic solution procedures are computationally convenient and produce near-optimal solutions. We then applied this method to solve the full-scale model where nearly 3,000 U.S. counties were considered both as spatial supply units and potential refinery locations over the 2007-2022 planning horizon. Empirical results show that: (i) the U.S. biofuel mandates would lead to a significant increase in food commodity prices; (ii) regional comparative advantage in producing biofuel feedstocks would be more important than proximity to biofuel demand locations when determining the optimum refinery locations; and (iii) incorporating biofuel refinery locations in land-use decisions makes a considerable difference in the regional biomass production pattern.