(305c) Optimal Design and Operations of Cellulosic Biofuel Supply Chains Under Uncertainty

Concerns about climate change, energy security, and the diminishing supply of fossil fuels are causing our society to search for new renewable sources of transportation fuels. Domestically available biomass has been proposed as part of the solution to our dependence on fossil fuels. Biofuels, especially liquid transportation fuels produced from cellulosic materials, have the benefits of significantly reducing greenhouse gas (GHG) emissions and leading to new jobs and greater economic vitality in rural areas. Renewable Fuels Standard (RFS), part of the Energy Independence and Security Act of 2007, establishes a target of 16 billion gallons of cellulosic biofuel annual production by 2022 [1, 2], although the United States produced less than 1 billion gallons of liquid fuels from cellulosic materials in 2010 [3, 4]. In observance of this mandatory production target, many new cellulosic biomass-to-biofuels supply chains will be designed and developed in the coming decade for better economic, environmental and social performances. However, uncertainty resulting from supply and demand variations may have significant impact on the biofuel supply chain. Therefore, an efficient optimization strategy is urgently needed to for the design and operations of sustainable and robust cellulosic biofuel supply chains.

In this work, we address the optimal design and planning of cellulosic biofuel supply chains under supply and demand uncertainty. A two-stage stochastic mixed-integer linear programming (SMILP) model combined with Monte Carlo sampling and the associated statistical analysis [4, 5] is proposed to deal with different types of uncertainty, and it is incorporated into a multi-period planning model that takes into account the main characteristics of the biofuel supply chains, such as seasonality of feedstock supply, biomass deterioration with time, geographical diversity and availability of biomass resources, feedstock density, diverse conversion technologies and byproducts, infrastructure compatibility, demand distribution, regional economic structure, and government incentives. In the two-stage framework, the supply chain network design and capacity planning decisions are made “here-and-now” prior to the resolution of uncertainty, while the production, transportation and storage decisions for each time period are postponed in a “wait-and-see” mode. The SMILP model integrates decision making across multiple temporal and spatial scales and simultaneously predicts the optimal network design, facility location, technology selection, capital investment, production operations, inventory control, and logistics management decisions. In order to solve the resulting large scale SMILP problems effectively, a decomposition algorithm based on sampling average approximation [5] and multi-cut L-shaped method [6, 7] is proposed by taking advantage of the problem structure.

In addition to the economic objective of minimizing the annualized net present cost, the SMILP model is also extended to integrate with life cycle assessment (LCA) and regional economic input-output (EIO) analysis through a multiobjective optimization scheme to include two other objectives: the environmental objective measured by life-cycle greenhouse gas emissions and the social objective measured by the number of accrued local jobs resulting from the construction and operation of the cellulosic biofuel supply chain. The multiobjective optimization framework allows the model to establish tradeoffs among the economic, environmental, and social performances of the cellulosic biofuel supply chains in a systematic way. The multiobjective optimization problem is solved with an ε-constraint method and produces Pareto-optimal curves that reveal how the optimal annualized cost and the supply chain network structure change with different environmental and social performance of the entire supply chain [10, 11].

The proposed optimization model and solution method is illustrated through county-level case study for the state of Illinois. Three major types of biomass, including crop residues, energy crops, and wood residues, and three major conversion pathways, including biochemical conversion, gasification followed by Fischer-Tropsch synthesis and fast pyrolysis followed by hydroprocessing are considered. Uncertainty information is generated from the time series analysis [8] based on the historical data of biomass feedstock supply [9] and liquid fuel demand [1]. County-level results will be presented that provide regionally-based insight into transition pathways of biomass production and conversion. Computational results also demonstrate the effectiveness of the proposed decomposition algorithm for the solution of large-scale SMILP problems.

References:

[1]     Biomass Program Multi-Year Program Plan 2010; EERE, U.S. DOE, March 2010.

[2]     National Biofuels Action Plan; Biomass Research and Development Board: U.S. U.S. Energy Information Administration.

[3]     National Renewable Fuel Standard Program for 2010 and Beyond; U.S. EPA, February 2010

[4]     Department of Agriculture and U.S. Department of Energy: 2008.

[5]     Shapiro, A.; Homem-de-Mello, T., A simulation-based approach to two-stage stochastic programming with recourse, Mathematical Programming, 1998, 81, 301-325

[6]     Birge, J.R.; Louveaux, F., Introduction to Stochastic Programming, Springer Verlag, New York, 1997

[7]     You, F.; Wassick, J. M.; Grossmann, I. E., Risk management for global supply chain planning under uncertainty: models and algorithms. AIChE Journal 2009, 55, 931-946.

[8]     Enders, W., Applied Econometric Time Series. Wiley: Hoboken, NJ, 2004.

[9]     National Agricultural Statistics Service.

[10] You, F.; Tao, L.; Graziano, D. J.; Snyder, S. W., Optimal Design of Sustainable Cellulosic Biofuel Supply Chains: Multi-objective Optimization Coupled with Life Cycle Assessment and Input-Output Analysis. AIChE Journal 2011, In press, DOI: 10.1002/aic.12637.

[11] You, F.; Wang, B., Life Cycle Optimization of Biomass-to-Liquids Supply Chains with Distributed-Centralized Processing Networks. Industrial & Engineering Chemistry Research 2011, Submitted.