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Dynamic generation of scenario trees

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  • Georg Pflug
  • Alois Pichler

Abstract

This paper presents new algorithms for the dynamic generation of scenario trees for multistage stochastic optimization. The different methods described are based on random vectors, which are drawn from conditional distributions given the past and on sample trajectories. The structure of the tree is not determined beforehand, but dynamically adapted to meet a distance criterion, which measures the quality of the approximation. The criterion is built on transportation theory, which is extended to stochastic processes. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Georg Pflug & Alois Pichler, 2015. "Dynamic generation of scenario trees," Computational Optimization and Applications, Springer, vol. 62(3), pages 641-668, December.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:3:p:641-668
    DOI: 10.1007/s10589-015-9758-0
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    References listed on IDEAS

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    1. Alexander Shapiro, 2003. "Inference of statistical bounds for multistage stochastic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 57-68, September.
    2. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    3. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    4. Michal Kaut & Stein Wallace, 2011. "Shape-based scenario generation using copulas," Computational Management Science, Springer, vol. 8(1), pages 181-199, April.
    5. Holger Heitsch & Werner Römisch, 2009. "Scenario tree reduction for multistage stochastic programs," Computational Management Science, Springer, vol. 6(2), pages 117-133, May.
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    Cited by:

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    2. Torres-Rincón, Samuel & Sánchez-Silva, Mauricio & Bastidas-Arteaga, Emilio, 2021. "A multistage stochastic program for the design and management of flexible infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
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    4. Delgado, Felipe & Trincado, Ricardo & Pagnoncelli, Bernardo K., 2019. "A multistage stochastic programming model for the network air cargo allocation under capacity uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 292-307.
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    9. Veraguas, Julio Backhoff & Beiglböck, Mathias & Eder, Manu & Pichler, Alois, 2020. "Fundamental properties of process distances," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5575-5591.
    10. Séguin, Sara & Fleten, Stein-Erik & Côté, Pascal & Pichler, Alois & Audet, Charles, 2017. "Stochastic short-term hydropower planning with inflow scenario trees," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1156-1168.
    11. Castro, Jordi & Escudero, Laureano F. & Monge, Juan F., 2023. "On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 268-285.
    12. Seljom, Pernille & Kvalbein, Lisa & Hellemo, Lars & Kaut, Michal & Ortiz, Miguel Muñoz, 2021. "Stochastic modelling of variable renewables in long-term energy models: Dataset, scenario generation & quality of results," Energy, Elsevier, vol. 236(C).
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    15. Raimund M. Kovacevic, 2019. "Valuation and pricing of electricity delivery contracts: the producer’s view," Annals of Operations Research, Springer, vol. 275(2), pages 421-460, April.
    16. Zhe Yan & Zhiping Chen & Giorgio Consigli & Jia Liu & Ming Jin, 2020. "A copula-based scenario tree generation algorithm for multiperiod portfolio selection problems," Annals of Operations Research, Springer, vol. 292(2), pages 849-881, September.
    17. Cadarso, Luis & Escudero, Laureano F. & Marín, Angel, 2018. "On strategic multistage operational two-stage stochastic 0–1 optimization for the Rapid Transit Network Design problem," European Journal of Operational Research, Elsevier, vol. 271(2), pages 577-593.
    18. Ksciuk, Jana & Kuhlemann, Stefan & Tierney, Kevin & Koberstein, Achim, 2023. "Uncertainty in maritime ship routing and scheduling: A Literature review," European Journal of Operational Research, Elsevier, vol. 308(2), pages 499-524.
    19. Escudero, Laureano F. & Monge, Juan F. & Rodríguez-Chía, Antonio M., 2020. "On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 262-279.
    20. Yu Mei & Zhiping Chen & Jia Liu & Bingbing Ji, 2022. "Multi-stage portfolio selection problem with dynamic stochastic dominance constraints," Journal of Global Optimization, Springer, vol. 83(3), pages 585-613, July.
    21. Julien Keutchayan & Michel Gendreau & Antoine Saucier, 2017. "Quality evaluation of scenario-tree generation methods for solving stochastic programming problems," Computational Management Science, Springer, vol. 14(3), pages 333-365, July.

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