An Economic Analysis of the Future U.S. Biofuel Industry, Facility Location, and Supply Chain Network

Abstract

This paper presents a price endogenous, dynamic, nonlinear mixed integer programming (MINLP) model to determine the feedstock supply response and future biorefinery locations that meet the mandated cellulosic biofuel production targets in the U.S. With a large number of supply units and potential processing locations involved, these two problems cannot be solved simultaneously directly using MINLP solvers. We propose a sequential two-stage solution procedure with feedbacks from each other 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. Due to the large number of binary variables involved, computational difficulty was also encountered when solving the MIP model. We employed a heuristic backward progression technique to cope with the difficulty. Using a moderately large test problem we demonstrate that the proposed solution procedure is computationally convenient and produces near-optimal solutions. We then apply this method to solve a large-scale model where nearly 3,000 U.S. counties are considered both as spatial supply units and potential refinery locations. Empirical results show that biofuel mandates will lead to a significant increase in food commodity prices and the optimum refinery locations would be in those states that have comparative advantage in producing biofuel feedstocks. We also find that incorporating the biofuel refinery locations in the land use decisions makes a considerable difference in the regional biomass production pattern.