Journal Article

A Robust Optimization Perspective on Stochastic Programming

Sim, Melvyn, Chen, Xin, Sun, Peng

2007

Overview

In this paper, 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.

• Publisher: INFORMS,Institute for Operations Research and the Management Sciences
• Subject: Analysis / Applied sciences / Approximation / Chebyshevs inequality / Decision theory. Utility theory / Determinism / Estimate reliability / Estimators / Exact sciences and technology / Gaussian distributions / Linear programming / Mathematical optimization / Mathematical programming / Mathematics / Operational research and scientific management / Operational research. Management science / Optimization / Optimization algorithms / programming / Random variables / Robust control / Robust optimization / Robust statistics / Standard deviation / stochastic / Stochastic models / Stochastic programming / Uncertainty / Uncertainty (Information theory)