Enhanced models and improved solution for competitive biofuel supply chain design under land use constraints

This paper studies the effect of government regulation on farmland use to balance food and energy production in a competitive biofuel supply chain design framework. We propose a Stackelberg–Nash game model with a direct land-use constraint that captures farmland, food, and fuel market equilibrium. To provide farmers with incentives to comply with the land-use regulation, we implement the land-use constraint through a cap-and-trade mechanism which we show attains equivalent land-use patterns. We further prove the existence of optimal solutions of the two equivalent discretely constrained mathematical program with equilibrium constraints (DC-MPEC) models. Two adaptive “relax-and-tighten” schemes, integrality and Lagrangian duality based relaxation, are proposed to handle the binary variables in a mixed integer formulation of the models. The proposed methodology is tested in a case study for the State of Illinois. The computational results demonstrate the superiority of our customized algorithms to publicly available solvers for solving problems with realistic sizes. Finally, the efficiency of the cap-and-trade mechanism is demonstrated through comparisons of scenarios with and without regulation as well as a sensitivity analysis on the cap-and-trade level. The cap-and-trade policy is found to effectively reduce biomass farmland use and profits of the biofuel industry. It may have different impacts on social welfare depending on problem settings and market parameters. Cap-and-trade levels also affect system behavior and thus should be carefully selected.