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An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

  • Ali İrfan Mahmutoğulları
  • Özlem ÇavuşEmail author
  • M. Selim Aktürk
S.I.: Stochastic Modeling and Optimization, in memory of András Prékopa
  • 43 Downloads

Abstract

Risk-averse mixed-integer multi-stage stochastic programming problems are challenging, large scale and non-convex optimization problems. In this study, we propose an exact solution algorithm for a type of these problems with an objective of dynamic mean-CVaR risk measure and binary first stage decision variables. The proposed algorithm is based on an evaluate-and-cut procedure and uses lower bounds obtained from a scenario tree decomposition method called as group subproblem approach. We also show that, under the assumption that the first stage integer variables are bounded, our algorithm solves problems with mixed-integer variables in all stages. Computational experiments on risk-averse multi-stage stochastic server location and generation expansion problems reveal that the proposed algorithm is able to solve problem instances with more than one million binary variables within a reasonable time under a modest computational setting.

Keywords

Mixed-integer stochastic programming Risk-averse multi-stage stochastic optimization Dynamic mean-CVaR Group subproblem 

Notes

Acknowledgements

The authors would like to thank the editor and two anonymous reviewers for their comments and suggestions that have improved the manuscript significantly.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ali İrfan Mahmutoğulları
    • 1
  • Özlem Çavuş
    • 1
    Email author
  • M. Selim Aktürk
    • 1
  1. 1.Department of Industrial EngineeringBilkent UniversityAnkaraTurkey

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