Convex Approximations of a Probabilistic Bicriteria Model with Disruptions

Abstract

We consider a multiperiod system operation problem with two con icting objectives, minimizing cost and risk. Risk stems from uncertain disruptions to the system during operation. While a general model would hedge against disruptions in each time period, we study special cases in which only a modest number of disruptions occur. To optimize for risk, we employ a convex approximation based on constraint sampling. We develop a strati ed sampling scheme based on distributional information on the time of disruption. We establish that our scheme yields signi cant savings in sampling costs|up to an order of magnitude in the number of time periods|over naive sampling. Moreover, in the absence of distributional information, we exhibit a sampling strategy that has comparable performance to optimal strati cation. We numerically demonstrate that strati cation improves cost over naive sampling, improving the solution's proximity to the e cient frontier of the bicriteria problem.