Call center shift scheduling under uncertainty: a chance-constraint programming approach.
Résumé
We consider a workforce management problem arising in call centers, namely the shift-scheduling
problem. Its consists in determining the minimum-cost number of agents to be assigned to a set of predefined shifts so as to reach the required customer quality of service in each period of the scheduling horizon. We focus on explicitly taking into account in the problem the errors in forecasting the call arrival rates and model them as independent random variables following a continuous probability distribution. We formulate the resulting stochastic optimization problem as a joint chance-constraint program and exploit some of its specific features to reformulate it as an equivalent large-size mixed-integer linear program without resorting to a discretization of the probability distributions. Our preliminary computational results show that the proposed approach can efficiently solve real-size instances of the problem, enabling us to draw some useful managerial insights on the underlying risk-cost tradeoff.