Speeding up call center simulation and optimization by Markov chain uniformization

Staffing and scheduling optimization in large multi-skill call centers is time-consuming, mainly because it requires lengthy simulations to evaluate performance measures and their sensitivity. Simplified models that provide tractable formulas are unrealistic in general. In this paper we explore an intermediate solution, based on an approximate continuous-time Markov chain model of the call center. This model is more accurate than the commonly used approximations, and yet can be simulated faster than a more realistic simulation (based on non-exponential distributions and additional details). To speed up the simulation, we uniformize the Markov chain and simulate only its discrete-time version. We show how performance measures such as the fraction of calls of each type answered within a given waiting time limit can be recovered from this simulation, how to synchronize common random numbers in this setting, and how to use this in the first phase of an optimization algorithm based on the cutting plane method. We also discuss various implementation issues and provide empirical results.