Designing an optimal contract mechanism in a cellulosic biofuel enterprise

Energy security and environmental concerns resulting from fossil fuel consumption have led to important changes in the U.S. energy policy in the past two decades. One of those is the Renewable Fuel Standard that mandates blending biofuels, especially cellulosic biofuels, with conventional transportation fuels. This requires producing substantial amounts of biomass for which currently there is no established market. Potential producers would grow energy crops only if appropriate guarantees and economic incentives are provided. Similarly, cellulosic biorefineries need a guaranteed and steady flow of biomass at a low price. Biorefinery managers and biomass producers are independent decision-makers operating in a hierarchical order and have conflicting economic interests. We hypothesize a contracting mechanism between biomass producers and biorefineries to address this complexity and formulate the problem as a two-level optimization model. While being a realistic representation, the model is computationally challenging. To address this issue, we introduce a search algorithm based on the optimization theory to solve the optimal biomass price and biorefinery size. We apply this approach to a hypothetical cellulosic biorefinery located in the U.S. Midwest. We present numerical results of the model along with sensitivity analysis on some key parameters. The results show that: (1) current cellulosic biofuel subsidy provided by the US government is highly inadequate to support an economically viable enterprise, (2) distances between biomass producers and the biorefinery and risk-taking behavior of farmers are crucial factors, and (3) under the estimated yield and production costs, Miscanthus would be the main source of biomass.