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A Solution Method for Multistage Stochastic Programs with Recourse with Application to an Energy Investment Problem

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  • Francois V. Louveaux

    (CORE, Louvain-la-Neuve, Belgium and Facultes Universitaires Notre-Dame de la Paix, Namur, Belgium)

Abstract

We consider a multistage stochastic program with recourse, with discrete distribution, quadratic objective function and linear inequality constraints. We show that under reasonable assumptions, solving such a program is equivalent to solving a nested sequence of piecewise quadratic programs and we extend the algorithm presented in an earlier report to the multistage situation. Finally, we consider the application of the method to an energy investment problem and report on the results of numerical experiments.

Suggested Citation

  • Francois V. Louveaux, 1980. "A Solution Method for Multistage Stochastic Programs with Recourse with Application to an Energy Investment Problem," Operations Research, INFORMS, vol. 28(4), pages 889-902, August.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:889-902
    DOI: 10.1287/opre.28.4.889
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    Cited by:

    1. Maqsood, Imran & Huang, Guo H. & Scott Yeomans, Julian, 2005. "An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 208-225, November.
    2. Unai Aldasoro & María Merino & Gloria Pérez, 2019. "Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic," Annals of Operations Research, Springer, vol. 280(1), pages 151-187, September.
    3. Bülbül, Kerem & Noyan, Nilay & Erol, Hazal, 2021. "Multi-stage stochastic programming models for provisioning cloud computing resources," European Journal of Operational Research, Elsevier, vol. 288(3), pages 886-901.
    4. Ningyuan Chen & Steven Kou & Chun Wang, 2018. "A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure," Management Science, INFORMS, vol. 64(2), pages 784-803, February.
    5. John R. Birge & Charles H. Rosa, 1996. "Incorporating Investment Uncertainty into Greenhouse Policy Models," The Energy Journal, , vol. 17(1), pages 79-90, January.
    6. Semih Atakan & Suvrajeet Sen, 2018. "A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs," Computational Management Science, Springer, vol. 15(3), pages 501-540, October.
    7. Angelos Georghiou & Angelos Tsoukalas & Wolfram Wiesemann, 2019. "Robust Dual Dynamic Programming," Operations Research, INFORMS, vol. 67(3), pages 813-830, May.
    8. Zhenfang Liu & Yang Zhou & Gordon Huang & Bin Luo, 2019. "Risk Aversion Based Inexact Stochastic Dynamic Programming Approach for Water Resources Management Planning under Uncertainty," Sustainability, MDPI, vol. 11(24), pages 1-22, December.
    9. Xie, Fei & Huang, Yongxi, 2018. "A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 130-148.
    10. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    11. Pablo Salas, 2013. "Literature Review of Energy-Economics Models, Regarding Technological Change and Uncertainty," 4CMR Working Paper Series 003, University of Cambridge, Department of Land Economy, Cambridge Centre for Climate Change Mitigation Research.
    12. Weini Zhang & Hamed Rahimian & Güzin Bayraksan, 2016. "Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 385-404, August.

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