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Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR

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  • Mahmutoğulları, Ali İrfan
  • Çavuş, Özlem
  • Aktürk, M. Selim

Abstract

Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions, and the objective function is nonlinear in general. We propose a scenario tree decomposition approach, namely group subproblem approach, to obtain bounds for such problems with an objective of dynamic mean conditional value-at-risk (mean-CVaR). Our approach does not require any special problem structure such as convexity and linearity, therefore it can be applied to a wide range of problems. We obtain lower bounds by using different convolution of mean-CVaR risk measures and different scenario partition strategies. The upper bounds are obtained through the use of optimal solutions of group subproblems. Using these lower and upper bounds, we propose a solution algorithm for risk-averse mixed-integer multi-stage stochastic problems with mean-CVaR risk measures. We test the performance of the proposed algorithm on a multi-stage stochastic lot sizing problem and compare different choices of lower bounds and partition strategies. Comparison of the proposed algorithm to a commercial solver revealed that, on the average, the proposed algorithm yields 1.13% stronger bounds. The commercial solver requires additional running time more than a factor of five, on the average, to reach the same optimality gap obtained by the proposed algorithm.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:595-608
    DOI: 10.1016/j.ejor.2017.10.038
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    References listed on IDEAS

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