Staffing optimization with chance constraints for emergency call centers

We consider a staffing problem with probabilistic constraints in an emergency call center. The aim is to minimize the total cost of agents while satisfying chance constraints defined over the service level and the average waiting time, in a given set of time periods. We provide a mathematical formulation of the problem in terms of probabilities and expectations. We define a sample average approximation (SAA) version of this problem whose solution converges to that of the exact problem when the sample size increases. We also propose a quick and simple simulation-based (heuristic) algorithm to compute a good (nearly optimal) staffing solution for the SAA problem. We illustrate and validate our algorithm with a simulation model based on real data from the 911 emergency call center of Montreal, Canada.