Journées de l'optimisation 2007 Optimizations days

Combining several variance reduction techniques can make simulation quicker and more accurate, which is especially useful for simulation-based optimization of complex systems. We show several ways stratification with respect to uniform random variates can be combined with a control variate. This exhibits nontrivial synergies between the two techniques. We illustrate this with a telephone call center simulation.

We present models for the arrival process in a call center. We used different approaches: nonhomogeneous Poisson process (NHPP), doubly stochastic process (Cox process), and a model with dependence structure. We also propose a nonparametric estimation for the rate function using cubic splines. We compare different models via the simulation of a call center. The results show superiority of models with dependence structure.

We compare simulation-based algorithms for the agent scheduling problem in multiskill call centers. This problem consists in minimizing the total costs of agents under constraints on the expected service level per call type, per period, and aggregated. We propose a solution approach that combines simulation with integer or linear programming, with cut generation.

In this talk, we will present the optimization algorithms that we developed to solve the staffing problem for multi-skill call centers. Our goal is to minimize the cost of agents while maintaining a minimum threshold on the service level for each call type as well as globally for the whole call center. Solving the multi-skill problem is much more difficult than the single-skill version for several reasons such as the presence of skill overlaps, complex routing policies and the stochastic elements which, unfortunately, can only be approximated accurately by simulations most of the time.