Annals of Operations Research

, Volume 273, Issue 1–2, pp 739–781 | Cite as

Managing congestion in a multi-modal transportation network under biomass supply uncertainty

  • Sushil R. Poudel
  • Md Abdul Quddus
  • Mohammad MarufuzzamanEmail author
  • Linkan Bian
  • Reuben F. Burch V
OR in Transportation


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.


Biomass supply chain network Multi-modal facilities Constraint-generation algorithm Sample average approximation Progressive Hedging algorithm Rolling horizon heuristics 


  1. 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.CrossRefGoogle Scholar
  2. Association of American Railroads. (2005). National rail infrastructure capacity and investment study. Available from:
  3. Awudu, I., & Zhang, J. (2012). Uncertainty and sustainability concepts in biofuel supply chain management: A review. Renewable and Sustainable Energy Reviews, 16, 1359–1368.CrossRefGoogle Scholar
  4. Awudu, A., & Zhang, J. (2013). Stochastic production planning for a biofuel supply chain under demand and price uncertainties. Applied Energy, 103, 189–196.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. Bai, Y., Li, X., Peng, F., Wang, X., & Ouyang, Y. (2015). Effects of disruption risks on biorefinery location design. Energies, 8(2), 1468–1486.CrossRefGoogle Scholar
  7. 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.CrossRefGoogle Scholar
  8. Bioenergy Knowledge Discovery Framework (KDF). (2013). Available from:
  9. 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.CrossRefGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. Chen, C. W., & Fan, Y. (2012). Bioethanol supply chain system planning under supply and demand uncertainities. Transportation Research Part E, 48, 150–164.CrossRefGoogle Scholar
  13. 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.Google Scholar
  14. 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.CrossRefGoogle Scholar
  15. Demirbas, A. (2009). Biofuels from Agricultural Biomass. Energy Sources, Part A, 31, 1573–1582.CrossRefGoogle Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.CrossRefGoogle Scholar
  18. Elhedhli, S., & Hu, F. X. (2005). Hub-and-spoke network design with congestion. Computers and Operations Research, 32(6), 1615–1632.CrossRefGoogle Scholar
  19. 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.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. General Algebraic Modeling System (GAMS). (2013). Available from:
  22. 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.CrossRefGoogle Scholar
  23. 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.CrossRefGoogle Scholar
  24. Grove, G. P., & OKelly, M. E. (1986). Hub networks and simulated schedule delay. Papers in Regional Science, 59, 103–119.CrossRefGoogle Scholar
  25. Gul, S., Denton, B., & Fowler, J. W. (2012). A multi-stage stochastic integer programming model for surgery planning. Michigan Engineering.Google Scholar
  26. 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.CrossRefGoogle Scholar
  27. Helgason, T., & Wallace, S. W. (1991). Approximate scenario solutions in the progressive hedging algorithm. Annals of Operations Research, 31, 425–444.CrossRefGoogle Scholar
  28. 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.CrossRefGoogle Scholar
  29. 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.CrossRefGoogle Scholar
  30. Hubbard, R. (2014). Bnsf railway to put $6 billion toward relieving congestion. Available from:
  31. Hvattum, L. M., & Lokketangen, A. (2009). Using scenario trees and progressive hedging for stochastic inventory routing problems. Journal of Heuristics, 15, 527–557.CrossRefGoogle Scholar
  32. Kara, B. Y., & Tansel, B. C. (2001). The latest arrival hub location problem. Management Science, 47(10), 1408–1420.CrossRefGoogle Scholar
  33. 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.CrossRefGoogle Scholar
  34. 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.CrossRefGoogle Scholar
  35. 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.CrossRefGoogle Scholar
  36. 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..Google Scholar
  37. Magnanti, T. L., & Wong, R. T. (1981). Acclerating benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research, 29, 464–484.CrossRefGoogle Scholar
  38. Mahmudi, H., & Flynn, P. (2006). Rail vs. truck transport of biomass. Applied Biochemistry and Biotechnology, 129(1), 88–103.CrossRefGoogle Scholar
  39. 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.CrossRefGoogle Scholar
  40. Marianov, V., & Serra, D. (2003). Location models for airline hubs behaving as M/D/c queues. Computers and Operations Research, 30, 983–1003.CrossRefGoogle Scholar
  41. 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.
  42. 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.CrossRefGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. Memişoğlu, G., & Üster, H. (2015). Integrated bioenergy supply chain network planning problem. Transportation Science, 50(1), 35–56.Google Scholar
  45. 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.CrossRefGoogle Scholar
  46. Mulvey, J. M., & Vladimirou, H. (1991). Applying the progressive hedging algorithm to stochastic generalized networks. Annals of Operations Research, 31, 399–424.CrossRefGoogle Scholar
  47. Norkin, V. I., Ermoliev, Y. M., & Ruszczynski, A. (1998). On optimal allocation of indivisibles under uncertainty. Operations Research, 46, 381–395.CrossRefGoogle Scholar
  48. Norkin, V. I., Pflug, G. C., & Ruszczynski, A. (1998). A branch and bound method for stochastic global optimization. Mathematical Programming, 83(3), 425–450.Google Scholar
  49. 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.
  50. 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.CrossRefGoogle Scholar
  51. 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.CrossRefGoogle Scholar
  52. Rockafellar, R. T., & Wets, R. J.-B. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119–147.CrossRefGoogle Scholar
  53. 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.CrossRefGoogle Scholar
  54. 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.CrossRefGoogle Scholar
  55. 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.CrossRefGoogle Scholar
  56. 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.CrossRefGoogle Scholar
  57. 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.CrossRefGoogle Scholar
  58. The National Energy Technology Laboratory. (2005). Coal-fired power plants in the United States. Available from:
  59. United States Energy Information Administration. (2014). State energy data system (seds): 2012 (updates). Available from:
  60. 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.CrossRefGoogle Scholar
  61. 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.CrossRefGoogle Scholar
  62. Wallace, S. W., & Helgason, T. (1991). Structural properties of the progressive hedging algorithm. Annals of Operations Research, 31, 445–456.CrossRefGoogle Scholar
  63. 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.CrossRefGoogle Scholar
  64. 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.CrossRefGoogle Scholar
  65. Williams, J. L. (2007). Information theoretic sensor management. Available from:
  66. 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.CrossRefGoogle Scholar
  67. 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.CrossRefGoogle Scholar
  68. 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.CrossRefGoogle Scholar
  69. 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.CrossRefGoogle Scholar
  70. 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.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Sushil R. Poudel
    • 1
  • Md Abdul Quddus
    • 1
  • Mohammad Marufuzzaman
    • 1
    Email author
  • Linkan Bian
    • 1
  • Reuben F. Burch V
    • 1
  1. 1.Department of Industrial and Systems EngineeringMississippi State UniversityStarkvilleUSA

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