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

NUS Business School, National University of Singapore, Singapore
NUS Business School and NUS Risk Management Institute, National University of Singapore, Singapore
NUS Business School and NUS Risk Management Institute, National University of Singapore, Singapore
NUS Business School, National University of Singapore, Singapore
chenwenqing{at}gmail.com
dscsimm{at}nus.edu.sg
jsun{at}nus.edu.sg
bizteocp{at}nus.edu.sg

We review and develop different tractable approximations to individual chance-constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional-value-at-risk (CVaR) measure. We extend the idea to joint chance-constrained problems and provide a new formulation that improves upon the standard approach. Our approach builds on a classical worst-case bound for order statistics problems and is applicable even if the constraints are correlated. We provide an application of the model on a network resource allocation problem with uncertain demand.

Subject classifications: decision analysis; risk; probability; application; programming; stochastic; nonlinear.
History: Received December 2007; revision received January 2009; accepted January 2009.