(773f) Multiobjective Stochastic Programming Models and Algorithms for Robust Design and Optimization of Biofuels Supply Chains

The growing concern about limited nonrenewable resources and severe pollution generated by traditional energy production triggers research on more sustainable energy resources. Hydrocarbon biofuels converted from biomass have been considered as promising alternatives.[1] Hydrocarbon biofuels can be used without significant changes of the current fuel distribution and utilization, and they provide vehicle performance similar to or better than their conventional counterparts.[2] Currently, several mathematical programming models, most of which are deterministic approaches, have been proposed to address the optimal design of hydrocarbon biorefinery supply chains.[3, 4] However, the final supply chain design is subject to various sources of uncertainty, such as seasonal and geographical fluctuation of biomass supplies, variability in biofuel demands due to unstable economic situations, population growth, the variability of feedstock purchase price and selling price of the hydrocarbon biofuels, and unexpected events. Deterministic model fails to consider these uncertain factors in the final solution. Thus it is of great importance to develop a comprehensive programming model which is robust from the economic performance perspective under the presence of uncertainties.[5] Stochastic programming model is an appropriate approach that optimizes the expected value of the objective function and obtains a solution performing well on average. When uncertainties are involved in, a critical issue is the existence of potentially high financial risk. Risk management should be taken into consideration in the final design of hydrocarbon biorefinery supply chain to reduce the impacts of unfavorable invent of uncertain parameters.[6] However, the standard stochastic programming methods usually do not provide control mechanisms on the unfavorable outcomes to implement risk management.[7] How to develop such a stochastic model that takes uncertainties into consideration while conducts financial risk management is a challenge. Another problem is that as the scenarios increase the resulting large scale model tends to be computationally expensive, how to solve it in a reasonable computational time needs to be addressed.

In this paper, a stochastic mixed-integer linear programming (MILP) model that predicts the optimal network design, technology selection, capital investment, production operations, and logistics management decisions under hydrocarbon biofuels demand and biomass supply uncertainties is developed. The design problem is formulated as a multi-objective optimization problem where the expected annualized cost of the supply chain network and a specific metric for financial risk are two objectives. The financial risk is measured by conditional value-at-risk and downside risk. A two-stage stochastic programming approach is used in formulation of the model.[6] In order to overcome the computational prohibition of the resulting MILP, an efficient decomposition approach is complemented, which is based on the multi-cut L-shaped method developed by You and Grossmann.[8] Finally, the modeling framework proposed and solution algorithm is illustrated by four cases studies in the State of Illinois. Optimal design of hydrocarbon biorefinery supply chain in deterministic case, stochastic cases with 4 scenarios, 100 scenarios and 1000 scenarios are presented. The comparison between deterministic and stochastic solutions, the conditional value-at-risk and downside risk, standard L-shaped method and multi-cut L-shaped method are discussed.

References

[1]        F. Q. You, L. Tao, D. J. Graziano, and S. W. Snyder, "Optimal design of sustainable cellulosic biofuel supply chains: Multiobjective optimization coupled with life cycle assessment and input-output analysis," AIChE Journal, vol. 58, pp. 1157-1180, 2012.

[2]        F. Q. You and B. Wang, "Life Cycle Optimization of Biomass-to-Liquid Supply Chains with Distributed-Centralized Processing Networks," Industrial & Engineering Chemistry Research, vol. 50, pp. 10102-10127, 2011.

[3]        A. Dunnett, C. Adjiman, and N. Shah, "A spatially explicit whole-system model of the lignocellulosic bioethanol supply chain: an assessment of decentralised processing potential," Biotechnology for Biofuels, vol. 1, pp. 1-17, 2008.

[4]        B. Aksoy, H. Cullinan, D. Webster, K. Gue, S. Sukumaran, M. Eden, and N. Sammons, "Woody biomass and mill waste utilization opportunities in Alabama: Transportation cost minimization, optimum facility location, economic feasibility, and impact," Environmental Progress & Sustainable Energy, vol. 30, pp. 720-732, 2011.

[5]        J. Kim, M. J. Realff, and J. H. Lee, "Optimal design and global sensitivity analysis of biomass supply chain networks for biofuels under uncertainty," Computers & Chemical Engineering, vol. 35, pp. 1738-1751, 2011.

[6]        F. Q. You, J. M. Wassick, and I. E. Grossmann, "Risk Management for a Global Supply Chain Planning Under Uncertainty: Models and Algorithms," AIChE Journal, vol. 55, pp. 931-946, 2009.

[7]        B. H. Gebreslassie, Y. Yao, and F. Q. You, "Design under Uncertainty of Hydrocarbon Biorefinery Supply Chains: Multiobjective Stochastic Programming Models, Decomposition Algorithm and A Comparison between CVaR and Downside Risk," Submited to AIChE Journal 2012.

[8]        F. Q. You and I. E. Grossmann, "Multicut Benders decomposition algorithm for process supply chain planning under uncertainty," Ann Oper Res, 2011.