Methodological and computational framework of stochastic programming and decisions under uncertainty (2019)
We study the Sample Average Approximation method for different types of problems. We discuss the implications of using different schemes of sampling (Uniform, Random and Importance sampling) and different risk measurements (CVaR and EDR). We illustrate this by applying these methods to two problems: the newsvendor problem and the San Francisco Bay Area bridge retrofit problem. We show that Uniform sampling does not exhibit asymptotic behavior as well as underestimate the CVaR measure. In addition, Importance sampling besides being a good estimator of the objective function of the problems can reduce the variance for rare event scenarios.