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A robust optimization perspective on stochastic programming. (English) Zbl 1167.90608
Summary: We introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a tractable approximation approach for solving a class of multistage chance-constrained stochastic linear optimization problems. An attractive feature of the framework is that we convert the original model into a second-order cone program, which is computationally tractable both in theory and in practice. We demonstrate the framework through an application of a project management problem with uncertain activity completion time.

MSC:
90C15 Stochastic programming
90C31 Sensitivity, stability, parametric optimization
Software:
SDPT3
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