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Quality evaluation of scenario-tree generation methods for solving stochastic programming problems

Author

Listed:
  • Julien Keutchayan

    (École Polytechnique de Montréal
    Logistics and Transportation (CIRRELT))

  • Michel Gendreau

    (École Polytechnique de Montréal
    Logistics and Transportation (CIRRELT))

  • Antoine Saucier

    (École Polytechnique de Montréal)

Abstract

This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the computational efficiency, the scenario trees must include only a finite (rather small) number of scenarios, therefore, they provide decisions only for some values of the random parameters. To overcome the resulting loss of information, we propose to introduce an extension procedure. It is a systematic approach to interpolate and extrapolate the scenario-tree decisions to obtain a decision policy that can be implemented for any value of the random parameters at little computational cost. To assess the quality of the scenario-tree generation method and the extension procedure (STGM-EP), we introduce three generic quality parameters that focus on the quality of the decisions. We use these quality parameters to develop a framework that will help the decision-maker to select the most suitable STGM-EP for a given stochastic programming problem. We perform numerical experiments on two case studies. The quality parameters are used to compare three scenario-tree generation methods and three extension procedures (hence nine couples STGM-EP). We show that it is possible to single out the best couple in both problems, which provides decisions close to optimality at little computational cost.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0279-4
    DOI: 10.1007/s10287-017-0279-4
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    References listed on IDEAS

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    1. Kouwenberg, Roy, 2001. "Scenario generation and stochastic programming models for asset liability management," European Journal of Operational Research, Elsevier, vol. 134(2), pages 279-292, October.
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    Cited by:

    1. Alexia Marchand & Michel Gendreau & Marko Blais & Jonathan Guidi, 2019. "Optimized operating rules for short-term hydropower planning in a stochastic environment," Computational Management Science, Springer, vol. 16(3), pages 501-519, July.
    2. Julien Keutchayan & Janosch Ortmann & Walter Rei, 2023. "Problem-driven scenario clustering in stochastic optimization," Computational Management Science, Springer, vol. 20(1), pages 1-33, December.

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