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.
Working paper, NUS Business School
View From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization