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    • On a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling
    Authors: Thuy Anh Ta; Tien Mai; Fabian Bastin; Pierre L’Ecuyer;  Advisor: -;  Co-Author: - (2021)

    We consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation. We study a sample average approximation (SAA) approach that uses nested sampling, in which at each stage, a number of scenarios are examined and a number of simulation replications are performed for each scenario to estimate the next-stage constraints. This approach provides an approximate solution to the multistage problem. To establish the consistency of the SAA approach, we first consider a two-stage problem and show that in the second-stage problem, given a scenario, the optimal values and solutions of the SAA converge to those of the true problem with probability one when the sample sizes go to infin...