A Biofuel Supply Chain Equilibrium Analysis with Subsidy Consideration

Abstract

Growing environmental concerns in the last few decades along with the energy security issues have led governments to take actions to reduce their dependence on fossil fuels and enhance renewable energy usage, including biofuels. Enforcement of federal or state mandates and regulations that obligate a certain amount of biofuel production are one of the main levers that governments use to achieve their goals. In the U.S. as an example, Renewable Fuel Standard (RFS) requires the production of 36 billion gallons of ethanol by 2022, 21 billion gallons of which should be advanced biofuels derived from biostocks other than corn starch. In parallel with making regulations, governments also incentivize the biofuel producers and farmers who provide the input biomass by paying subsidies to promote the industry. In this research, one of our main goals is to study the government’s role as both a regulator and incentive payer in the biofuel production industry. In the first chapter we consider a pilot biofuel supply chain problem, in which a farmer supplies two downstream refineries with non-identical crops (corn and energy crop). The problem has been modeled as a multi-leader-single-follower game to derive the farmer’s decisions on land allocation as well as refineries’ proposed prices to the farmer for their raw materials. We consider subsidizing the farmer and the refinery that uses the energy crop to study whether a subsidy plan can enhance the advanced biofuel production and meet the existing mandate. We solve the problem under four cases based on the willingness of the farmer to sell corn to the food market as well as the availability of farming land expansion. The Nash Equilibrium (NE) is derived for all cases, and parametric analyses are used to study the effect of subsidies on the profit of the players and the total social welfare of the supply chain. We observe that a government’s expenditure can be offset by the increase of the social welfare under certain circumstances. We find the minimum budget requirement to meet the EPA’s mandate and show that a specific budget can be distributed to the farmer and the refineries in different ways while obtaining the same results. In Chapter 3, we extend the above equilibrium analysis by relaxing a simplifying assumption regarding the capacity of the refineries, which assumes that the refineries can process any amount of crop from the land that the farmer may allocate to them. Relaxing this assumption gives us the possibility of analyzing the problem under more general circumstances, although the assumption may be acceptable in a relatively small regional scope. We obtain closed form solutions for the supply chain equilibrium under the existence of the new capacity constraints and find that refineries offer lower prices under the new condition, while their profit is larger. However, this is not the case for the farmer, and her profit diminishes under this capacitated problem. In Chapter 4, we extend the scope of our problem by generalizing the model to consider multiple players and make conclusions more general. Our bilevel supply chain is modeled as an equilibrium problem with equilibrium constraints (EPEC) and solved using a linearization method and a commercial solver of GAMS. We perform several analyses including the effect of the farmer’s cost structure and the number of the refineries on a few socio-economic measures. We also perform a sensitivity analysis on a few critical industry and market parameters. Through our analyses, we first find that the budget requirement to meet the government’s goal is higher than what other similar works have estimated. Second, we find that as new refineries are built, the government should spend more on the subsidy to obtain the goal; however, the total social welfare increases because of an increase in the biofuel market consumer surplus from lower fuel price. We show that the government’s expenditure will not be offset by the increase of the social welfare in this multi-player case as the required conditions found from Chapter 2 do not hold. Finally, we find that the advanced biofuel technology improvement is the most important factor among the considered industry related factors in reducing the subsidy requirements. Finally, in Chapter 5, we summarize the introduced models in previous chapters, the effect of the capacity constraint, and the effect of the competition.