Abstract
This research presents a two-stage stochastic programming model that is used to design and manage a biomass co-firing supply chain network under feedstock supply uncertainty. The model we propose extends current models by taking congestion effects into account. A non-linear cost term is added in the objective function representing the congestion factor which increases exponentially as flow of biomass approaches the capacity of multi-modal facility. We first linearize the model and then use a nested decomposition algorithm to obtain a feasible solution in a reasonable amount of time. The nested decomposition algorithm that we propose combine constraint Generation algorithm with a sample average approximation and Progressive Hedging (PH) algorithm. We apply some heuristics such as rolling horizon algorithm and variable fixing technique to enhance the performance of the PH algorithm. We develop a case study using data from the states of Mississippi and Alabama and use those regions to test and validate the performance of the proposed algorithm. Numerical experiments show that the proposed algorithm can solve large-scale problems with a larger number of scenarios and time periods to a near optimal solution in a reasonable amount of time. Results obtained from the experiments reveal that the delivery cost increases and less hubs with higher capacity are selected if we take congestion cost into account.
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An, H., Wilhelm, W. E., & Searcy, S. W. (2011). A mathematical model to design a lignocellulosic bio-fuel supply chain system with a case study based on a region in central Texas. Bioresource Technology, 102, 7860–7870.
Association of American Railroads. (2005). National rail infrastructure capacity and investment study. Available from: http://ops.fhwa.dot.gov/freight/freight_analysis/freight_story/congestion.htm.
Awudu, I., & Zhang, J. (2012). Uncertainty and sustainability concepts in biofuel supply chain management: A review. Renewable and Sustainable Energy Reviews, 16, 1359–1368.
Awudu, A., & Zhang, J. (2013). Stochastic production planning for a biofuel supply chain under demand and price uncertainties. Applied Energy, 103, 189–196.
Bai, Y., Hwang, T., Kang, S., & Ouyang, Y. (2011). Biofuel refinery location and supply chain planning under traffic congestion. Transportation Research Part B: Methodological, 45(1), 162–175.
Bai, Y., Li, X., Peng, F., Wang, X., & Ouyang, Y. (2015). Effects of disruption risks on biorefinery location design. Energies, 8(2), 1468–1486.
Balasubramanian, J., & Grossmann, I. (2004). Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty. Industrial and Engineering Chemistry Research, 43(14), 3695–3713.
Bioenergy Knowledge Discovery Framework (KDF). (2013). Available from: https://bioenergykdf.net/taxonomy/term/1036.
Camargo, R. S., Miranda, G, Jr., Ferreira, R., & Luna, H. P. (2009). Multiple allocation hub and spoke network design under hub congestion. Computers and Operations Research, 36(12), 3097–3106.
Carpentier, P. L., Gendreau, M., & Bastin, F. (2013). Long-term management of a hydroelectric multireservoir system under uncertainty using the progressive hedging algorithm. Water Resources Research, 49(5), 2812–2827.
Chang, M., Tseng, Y., & Chen, J. (2007). A scenario planning approach for the flood emergency logistics preparation problem under uncertainty. Transportation Research Part E: Logistics and Transportation Review, 43(6), 737–754.
Chen, C. W., & Fan, Y. (2012). Bioethanol supply chain system planning under supply and demand uncertainities. Transportation Research Part E, 48, 150–164.
Crainic, T. G., Fu, X., Gendreau, M., Rei, W., & Wallace, S. W. (2011). Progressive hedging-based metaheuristics for stochastic network design. Networks, 58, 114–124.
Cundiff, J. S., Dias, N., & Sherali, H. D. (1997). A linear programming approach for designing a herbaceous biomass delivery system. Bioresource Technology, 59, 47–55.
Demirbas, A. (2009). Biofuels from Agricultural Biomass. Energy Sources, Part A, 31, 1573–1582.
Eksioglu, S. D., Acharya, A., Leightley, L. E., & Arora, S. (2009). Analyzind the design and management of biomass-to-biorefinery supply chain. Computers and Industrial Engineering, 57, 1342–1352.
Eksioglu, S. D., Li, S., Zhang, S., Sokhansanj, S., & Petrolia, D. (2010). Analyzing impact of intermodal facilities on design and management of bio-fuel supply chain. Transportation Research Record, 2191, 144–151.
Elhedhli, S., & Hu, F. X. (2005). Hub-and-spoke network design with congestion. Computers and Operations Research, 32(6), 1615–1632.
Elhedhli, S., & Wu, H. (2010). A Lagrangean heuristic for hub-and-spoke system design with capacity selection and congestion. INFORMS Journal on Computing, 22(2), 282–296.
Gebreslassie, B. H., Yao, Y., & You, F. (2012). Design under uncertainty of hydrocarbon biorefinery supply chains: Multiobjective stochastic programming models, decomposition algorithm, and a comparison between CVaR and downside risk. AIChE Journal, 58(7), 2155–2179.
General Algebraic Modeling System (GAMS). (2013). Available from: http://www.gams.com/.
Giarola, S., Zamboni, A., & Bezzo, F. (2011). Spatially explicit multi-objective optimization for designing and planning of hybrid fast and second generation biorefineries. Computers and Chemical Engineering, 35, 1782–1797.
Gonzales, D., Searcy, E. M., & Eksioglu, S. D. (2013). Cost analysis for high-volume and long-haul transportation of densified biomass feedstock. Transportation Research Part A, 49, 48–61.
Grove, G. P., & OKelly, M. E. (1986). Hub networks and simulated schedule delay. Papers in Regional Science, 59, 103–119.
Gul, S., Denton, B., & Fowler, J. W. (2012). A multi-stage stochastic integer programming model for surgery planning. Michigan Engineering.
Hajibabai, L., & Ouyang, Y. (2013). Integrated planning of supply chain networks and multimodal transportation infrastructure expansion: Model development and application to the biofuel industry. Computer-Aided Civil and Infrastructure Engineering, 28(4), 247–259.
Helgason, T., & Wallace, S. W. (1991). Approximate scenario solutions in the progressive hedging algorithm. Annals of Operations Research, 31, 425–444.
Huang, Y., Chen, C. W., & Fan, Y. (2010). Multistage optimization of the supply chains of bio-fuels. Transportation Research Part E, 46(6), 820–830.
Huang, Y., Fan, Y., & Chen, C.-W. (2014). An integrated bio-fuel supply chain against feedstock seasonality and uncertainty. Transportation Science, 48(4), 540–554.
Hubbard, R. (2014). Bnsf railway to put $6 billion toward relieving congestion. Available from: http://www.omaha.com/money/bnsf-railway-to-put-billion-toward-relieving-congestion/article_f00f7b1d-353e-58e3-abd5-3967d8f2c474.html.
Hvattum, L. M., & Lokketangen, A. (2009). Using scenario trees and progressive hedging for stochastic inventory routing problems. Journal of Heuristics, 15, 527–557.
Kara, B. Y., & Tansel, B. C. (2001). The latest arrival hub location problem. Management Science, 47(10), 1408–1420.
Kim, J., Realff, M. J., & Lee, J. H. (2011). Optimal design and global sensitivity analysis of biomass supply chain networks for bio-fuels under uncertainty. Computers and Chemical Engineering, 35, 1738–1751.
Kleywegt, A. J., Shapiro, A., & Homem-De-Mello, T. (2001). The sample average approximation method for stochastic discrete optimization. SIAM Journal of Optimization, 12, 479–502.
Kostina, A. M., Guillen-Gosalbeza, G., Meleb, F. D., Bagajewiczc, M. J., & Jimeneza, L. (2011). A novel rolling horizon strategy for the strategic planning of supply chains. Application to the sugar cane industry of Argentina. Computers and Chemical Engineering, 35, 2540–2563.
Li, X., Peng, F., Bai, Y., & Ouyang, Y. (2011 January). Effects of disruption risks on biorefinery location design: Discrete and continuous models. In proceeding of the 90th TRB annual meeting, Washington D.C..
Magnanti, T. L., & Wong, R. T. (1981). Acclerating benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research, 29, 464–484.
Mahmudi, H., & Flynn, P. (2006). Rail vs. truck transport of biomass. Applied Biochemistry and Biotechnology, 129(1), 88–103.
Mak, W. K., Morton, D. P., & Wood, R. K. (1999). Monte Carlo bounding techniques for determining solution quality in stochastic programs. Operations Research Letters, 24, 47–56.
Marianov, V., & Serra, D. (2003). Location models for airline hubs behaving as M/D/c queues. Computers and Operations Research, 30, 983–1003.
Marufuzzaman, M., & Ekşioğlu, S. D. (2016). Designing a reliable and dynamic multimodal transportation network for biofuel supply chains. Transportation Science. doi:10.1287/trsc.2015.0632.
Marufuzzaman, M., Eksioglu, S. D., & Huang, Y. (2014). Two-stage stochastic programming supply chain model for biodiesel production via wastewater treatment. Computers and Operations Research, 49, 1–17.
Marufuzzaman, M., Eksioglu, S. D., Li, X., & Wang, J. (2014). Analyzing the impact of intermodal-related risk to the design and management of bio-fuel supply chain. Transportation Research Part E, 69, 122–145.
Memişoğlu, G., & Üster, H. (2015). Integrated bioenergy supply chain network planning problem. Transportation Science, 50(1), 35–56.
Miranda, G, Jr., de Camargo, R. S., Pinto, L. R., Conceicao, S. V., & Ferreira, R. P. M. (2011). Hub location under hub congestion and demand uncertainty: The Brazilian case study. Pesquisa Operacional, 31(2), 319–349.
Mulvey, J. M., & Vladimirou, H. (1991). Applying the progressive hedging algorithm to stochastic generalized networks. Annals of Operations Research, 31, 399–424.
Norkin, V. I., Ermoliev, Y. M., & Ruszczynski, A. (1998). On optimal allocation of indivisibles under uncertainty. Operations Research, 46, 381–395.
Norkin, V. I., Pflug, G. C., & Ruszczynski, A. (1998). A branch and bound method for stochastic global optimization. Mathematical Programming, 83(3), 425–450.
Parker, N., Tittmann, P., Hart, Q., Lay, M., Cunningham, J., Jenkins, B., & Schmidt, A. (2008). Strategic assessment of bioenergy development in the west spatial analysis and supply curve development. Final report. University of California, Davis. http://www.westgov.org/component/docman/doc_download/215-wgabioenergy-assessment-spatial-analysis?Itemid=.
Persson, T., Garcia, A., Paz, J., Jones, J., & Hoogenboom, G. (2009). Maize ethanol feedstock production and net energy value as affected by climate variability and crop management practices. Agricultural Systems, 100, 11–21.
Poudel, S., Marufuzzaman, M., & Bian, L. (2016). Designing a reliable biofuel supply chain network considering link failure probabilities. Computers and Industrial Engineering, 91, 85–99.
Rockafellar, R. T., & Wets, R. J.-B. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119–147.
Roni, M. S., Eksioglu, S. D., Searcy, E., & Jha, K. (2014). A supply chain network design model for biomass co-firing in coal-fired power plants. Transportation Research Part E, 61, 115–134.
Santos, M. L. L., da Silva, E. L., Finardi, E. C., & Goncalves, R. E. C. (2009). Practical aspects in solving the medium-term operation planning problem of hydrothermal power systems by using the progressive hedging method. International Journal of Electrical Power and Energy Systems, 31, 546–552.
Santoso, T., Ahmed, S., Goetschalckx, M., & Shapiro, A. (2005). A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 167, 96–115.
Schutz, P., Tomasgard, A., & Ahmed, S. (2009). Supply chain design under uncertainty using sample average approximation and dual decomposition. European Journal of Operational Research, 199, 409–419.
SteadieSeifi, M., Dellaert, N. P., Nuijten, W., Woensel, T. V., & Raoufi, R. (2014). Multimodal freight transportation planning: A literature review. European Journal of Operational Research, 233, 1–15.
The National Energy Technology Laboratory. (2005). Coal-fired power plants in the United States. Available from: http://www.netl.doe.gov/energyanalyses/hold/technology.html.
United States Energy Information Administration. (2014). State energy data system (seds): 2012 (updates). Available from: http://www.eia.gov/state/seds/seds-data-fuel.cfm?sid=US.
Verweij, B., Ahmed, S., Kleywegt, A. J., Nemhauser, G., & Shapiro, A. (2003). The sample average approximation method applied to stochastic routing problems: A computational study. Computational Optimization and Applications, 24, 289–333.
Vidyarthi, N., & Jayaswal, S. (2014). Efficient solution of a class of location allocation problems with stochastic demand and congestion. Computers and Operations Research, 48, 20–30.
Wallace, S. W., & Helgason, T. (1991). Structural properties of the progressive hedging algorithm. Annals of Operations Research, 31, 445–456.
Wang, X., & Ouyang, Y. (2013). A continuous approximation approach to competitive facility location design under facility disruption risks. Transportation Research Part B, 50, 90–103.
Watson, J. P., & Woodruff, D. L. (2011). Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Computational Management Science, 8, 355–370.
Williams, J. L. (2007). Information theoretic sensor management. Available from: http://dspace.mit.edu/handle/1721.1/38534.
Xie, F., Huang, Y., & Eksioglu, S. D. (2014). Integrating multimodal transport into cellulosic bio-fuel supply chain design under feedstock seasonality with a case study based on California. Bioresource Technology, 152, 15–23.
Xie, W., & Ouyang, Y. (2013). Dynamic planning of facility locations with benefits from multitype facility colocation. Computer-Aided Civil and Infrastructure Engineering, 28(9), 666–678.
You, F., Tao, L., Graziano, D. J., & Snyder, S. W. (2012). Optimal design of sustainable cellulosic bio-fuel supply chains: Multiobjective optimization coupled with life cycle assessment and input-output analysis. AIChE Journal, 58(4), 1157–1180.
Zamboni, A., Bezzo, F., & Shah, N. (2009). Spatially explicit static model for the strategic design of future bioethanol production systems. 2. Multi-objective environmental optimization. Energy and Fuels, 23(10), 5134–5143.
Zamboni, A., Shah, N., & Bezzo, F. (2009). Spatially explicit static model for the strategic design of future bioethanol production systems. 1. Cost Minimization. Energy and Fuels, 23(10), 5121–5133.
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Poudel, S.R., Quddus, M.A., Marufuzzaman, M. et al. Managing congestion in a multi-modal transportation network under biomass supply uncertainty. Ann Oper Res 273, 739–781 (2019). https://doi.org/10.1007/s10479-017-2499-y
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DOI: https://doi.org/10.1007/s10479-017-2499-y