From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization

Melvyn Sim (dscsimmnus.edu.sg)
Chung Piaw Teo (bizteocpnus.edu.sg)
Wenqing Chen (chenwenqinggmail.com)
Sun Jie (jsunnus.edu.sg)

Abstract: In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon the standard approach. The standard approach decomposes the joint chance constraint into a problem with m individual chance constraints and then applies safe robust optimization approximation on each one of them. Our approach builds on a classical worst case bound for order statistics problem, and is applicable even if the constraints are correlated. We provide an application of the model on a network resource allocation network with uncertain demand. The new chance constrained formulation led to more than 8-12% improvement over the standard approach.

Keywords: robust optimization, chance constraint, stochastic programming, conditional value at risk

Category 1: Robust Optimization

Category 2: Stochastic Programming

Citation: Working paper, NUS Business School

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Entry Submitted: 01/12/2007
Entry Accepted: 01/13/2007
Entry Last Modified: 01/18/2007

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