Efficient Simulation for Linear Programming Under Uncertainty

We consider a problem of estimating the probability that the optimal value of a stochastic linear program exceeds a large threshold. Inspired by the classical theory of linear programming, we partition the sample space of random components so that the optimal value can be generated without solving a linear program for each sample. This enables us to develop an efficient importance sampling scheme for computing the said probability when the random components are jointly normal. We prove its asymptotic efficiency under the regime where the threshold increases. Our numerical experiments reveal that the proposed method significantly outperforms the existing simulation techniques in the literature.