A Sample Average Approximation Approach for Event-Driven Probabilistic Constraint Programming

In this work we augment a known Monte Carlo simulationbased approach to stochastic discrete optimization problem, the so called Sample Average Approximation (SAA) method, with a new criterion to decide when the search has to be stopped. Our approach exploits a well known and effective sampling technique, Latin Hypercube Sampling (LHS), and confidence interval analysis, a well established approximation method in statistics. We apply SAA augmented with LHS and the new stopping criterion we defined to an Event-Driven Constraint Programming model for scheduling under uncertainty. Our computational experience shows how this technique can not only quickly converge to near optimal solutions by analyzing small sample sets, but also promptly decide when the chances of improving the current optimal solution by analyzing larger sample sets are sufficiently low to justify the interruption of the search process.