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Worst-Case-Expectation Approach to Optimization Under Uncertainty

Author

Listed:
  • Alexander Shapiro

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Wajdi Tekaya

    (Cambridge Systems Associates, Cambridge CB5 8AF, United Kingdom)

  • Murilo Pereira Soares

    (Operador Nacional do Sistema Elétrico, Rio de Janeiro, RJ 20211-160, Brazil)

  • Joari Paulo da Costa

    (Operador Nacional do Sistema Elétrico, Rio de Janeiro, RJ 20211-160, Brazil)

Abstract

In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation where the data process can be naturally separated into two components: one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst-case) point of view. We formulate this in a time consistent way and derive the corresponding dynamic programming equations. To solve the obtained multistage problem, we develop a variant of the stochastic dual dynamic programming method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.

Suggested Citation

  • Alexander Shapiro & Wajdi Tekaya & Murilo Pereira Soares & Joari Paulo da Costa, 2013. "Worst-Case-Expectation Approach to Optimization Under Uncertainty," Operations Research, INFORMS, vol. 61(6), pages 1435-1449, December.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:6:p:1435-1449
    DOI: 10.1287/opre.2013.1229
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    References listed on IDEAS

    as
    1. Shapiro, Alexander & Tekaya, Wajdi & da Costa, Joari Paulo & Soares, Murilo Pereira, 2013. "Risk neutral and risk averse Stochastic Dual Dynamic Programming method," European Journal of Operational Research, Elsevier, vol. 224(2), pages 375-391.
    2. Shapiro, Alexander, 2012. "Minimax and risk averse multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 219(3), pages 719-726.
    3. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    4. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Homem-de-Mello, Tito & Pagnoncelli, Bernardo K., 2016. "Risk aversion in multistage stochastic programming: A modeling and algorithmic perspective," European Journal of Operational Research, Elsevier, vol. 249(1), pages 188-199.
    2. Meloni, Carlo & Pranzo, Marco & Samà, Marcella, 2021. "Risk of delay evaluation in real-time train scheduling with uncertain dwell times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    3. Angelos Georghiou & Angelos Tsoukalas & Wolfram Wiesemann, 2019. "Robust Dual Dynamic Programming," Operations Research, INFORMS, vol. 67(3), pages 813-830, May.
    4. Guigues, Vincent, 2017. "Dual Dynamic Programing with cut selection: Convergence proof and numerical experiments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 47-57.
    5. Borgonovo, E. & Cappelli, V. & Maccheroni, F. & Marinacci, M., 2018. "Risk analysis and decision theory: A bridge," European Journal of Operational Research, Elsevier, vol. 264(1), pages 280-293.
    6. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    7. Haodong Yu & Jie Sun & Yanjun Wang, 2021. "A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure," Computational Optimization and Applications, Springer, vol. 79(1), pages 67-99, May.
    8. Wang, Fan & Zhang, Chao & Zhang, Hui & Xu, Liang, 2021. "Short-term physician rescheduling model with feature-driven demand for mental disorders outpatients," Omega, Elsevier, vol. 105(C).

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