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

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      Author
      Mahmutoğulları, A. İ.
      Çavuş, Ö.
      Aktürk, M. S.
      Date
      2018
      Source Title
      European Journal of Operational Research
      Print ISSN
      0377-2217
      Publisher
      Elsevier B.V.
      Volume
      266
      Issue
      2
      Pages
      595 - 608
      Language
      English
      Type
      Article
      Item Usage Stats
      129
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      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.
      Keywords
      Bounding
      CVaR
      Dynamic measures of risk
      Mixed-integer multi-stage stochastic programming
      Stochastic programming
      Permalink
      http://hdl.handle.net/11693/49868
      Published Version (Please cite this version)
      https://doi.org/10.1016/j.ejor.2017.10.038
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