03:30 PM - 03:55 PM
A new approach for generating scenario trees for stochastic programming problems
We present a framework for generating efficient scenario trees for solving stochastic programming problems. We argue that a scenario tree should not only provide a good discretization of the stochastic process, but should also take into account the variations of the objective function with respect to the random parameters in order to better suit the problem. Based on this idea, we develop a figure of merit for scenario trees leveraging on recent advances in quasi-Monte Carlo methods. We illustrate its use for two- and multi-stage problems.
03:55 PM - 04:20 PM
On the Sample Average Approximation of the Two-Stage Chance-Constrained Staffing Problem in Call Centers
We consider a chance-constrained two-stage stochastic staffing problem for multi-skill call centers with arrival rate uncertainty. The aim is to minimize the total cost of agents under some chance constraints, defined over the randomness of the service level in a given time period. We use the Monte Carlo method to generate M scenarios of arrival rates and we perform N simulation runs to get the estimates of probabilities that the service level is satisfied. We then obtain a sample average approximation (SAA) of the problem. We investigate the convergence of the optimal solution of the SAA to that of the original problem when the sample size increases and present numerical illustrations on the sample sizes M and N.