A stochastic programming approach for staffing and scheduling call centers with uncertain demand forecasts following continuous distributions

We consider a workforce management problem arising in call centers, namely a staffing and shift-scheduling problem. It consists in determining the minimum-cost number of agents to be assigned to each shift of the scheduling horizon so as to reach the required customer quality of service. We assume that the mean call arrival rate in each period of the horizon is a random variable following a continuous distribution. We model the resulting optimization problem as a stochastic program involving joint probabilistic constraints. This allows to manage the risk of not reaching the required quality of service at the horizon level rather than on a period by period basis. We propose a solution approach based on linear approximations to provide approximate solutions of the problem. We finally give numerical results carried out on a real-life instance. These results show that the proposed approach compares well with previously published approaches both in terms of risk management and cost minimization.