Synergistic modeling of call center operations

We synergistically apply queueing theory, integer programming, and stochastic simulation to determine an optimal staffing policy for a repair call handling center. A stationary Markovian queueing model is employed to determine minimal staffing levels for a sequence of time intervals with varying call volumes and mean handling times. These staffing requirements populate an integer program model for determining the mix of call agent shifts that will achieve service quality standards at minimum cost. Since the analytical modeling requires simplifying assumptions, expected performance of the optimal staffing policy is evaluated using stochastic simulation. Computational efficiency of the simulation is improved dramatically by employing the queueing model to generate an analytic control variate.