### Computational study of decomposition algorithms for mean-risk stochastic linear programs

*Lewis Ntaimo, Tanisha G. Cotton*

#### Abstract

Mean-risk stochastic programs include a risk measure in the objective to model risk averseness for many problems in science and engineering. This paper reports a computational study of mean-risk two-stage stochastic linear programs with recourse based on absolute semideviation (ASD) and quantile deviation (QDEV). The studywas aimed at performing an empirical investigation of decomposition algorithms for stochastic programs with quantile and deviation mean-risk measures; analyzing how the instance solutions vary across different levels of risk; and understanding when it is appropriate to use a given mean-risk measure. Aggregated optimality cut and separate cut subgradient-based algorithms were implemented for each mean-risk model. Both types of algorithms show similar computational performance for ASD whereas the separate cut algorithm outperforms the aggregated cut algorithm for QDEV. The study provides several insights. For example, the results reveal that the risk-neutral approach is still appropriate for most of the standard stochastic programming test instances due to their uniform or normal-like marginal distributions. However, when the distributions are modified, the risk-neutral approach may no longer be appropriate and the risk-averse approach becomes necessary. The results also show that ASD is a more conservative mean-risk measure than QDEV.

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