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Scenario decomposition of risk-averse multistage stochastic programming problems

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  • Ricardo Collado

    ()

  • Dávid Papp

    ()

  • Andrzej Ruszczyński

    ()

Abstract

For a risk-averse multistage stochastic optimization problem with a finite scenario tree, we introduce a new scenario decomposition method and we prove its convergence. The main idea of the method is to construct a family of risk-neutral approximations of the problem. The method is applied to a risk-averse inventory and assembly problem. In addition, we develop a partially regularized bundle method for nonsmooth optimization. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Ricardo Collado & Dávid Papp & Andrzej Ruszczyński, 2012. "Scenario decomposition of risk-averse multistage stochastic programming problems," Annals of Operations Research, Springer, vol. 200(1), pages 147-170, November.
  • Handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:147-170:10.1007/s10479-011-0935-y
    DOI: 10.1007/s10479-011-0935-y
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    References listed on IDEAS

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    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    2. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Conditional Risk Mappings," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 544-561, August.
    3. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    4. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    5. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. Naomi Miller & Andrzej Ruszczyński, 2011. "Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition," Operations Research, INFORMS, vol. 59(1), pages 125-132, February.
    8. Birge, John R. & Louveaux, Francois V., 1988. "A multicut algorithm for two-stage stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 34(3), pages 384-392, March.
    9. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
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    Citations

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    Cited by:

    1. 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).
    2. Mahmutoğulları, Ali İrfan & Çavuş, Özlem & Aktürk, M. Selim, 2018. "Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR," European Journal of Operational Research, Elsevier, vol. 266(2), pages 595-608.
    3. Schur, Rouven & Gönsch, Jochen & Hassler, Michael, 2019. "Time-consistent, risk-averse dynamic pricing," European Journal of Operational Research, Elsevier, vol. 277(2), pages 587-603.
    4. Alois Pichler, 2017. "A quantitative comparison of risk measures," Annals of Operations Research, Springer, vol. 254(1), pages 251-275, July.
    5. Alonso-Ayuso, Antonio & Escudero, Laureano F. & Guignard, Monique & Weintraub, Andres, 2018. "Risk management for forestry planning under uncertainty in demand and prices," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1051-1074.
    6. Collado, Ricardo & Meisel, Stephan & Priekule, Laura, 2017. "Risk-averse stochastic path detection," European Journal of Operational Research, Elsevier, vol. 260(1), pages 195-211.
    7. Andre Luiz Diniz & Maria Elvira P. Maceira & Cesar Luis V. Vasconcellos & Debora Dias J. Penna, 2020. "A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning," Annals of Operations Research, Springer, vol. 292(2), pages 649-681, September.

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