A joint chance-constrained programming approach for call center workforce scheduling under uncertain call arrival forecasts

We study the call center shift scheduling problem under uncertain demand forecasts.Forecasting errors are seen as independent normally distributed random variables.The resulting stochastic problem is modeled as a joint chance-constrained program.A mixed-integer linear programming based solution approach is proposed.Numerical results based on a real case study and managerial insights are provided. We consider a workforce management problem arising in call centers, namely the shift-scheduling problem. It consists in determining the number of agents to be assigned to a set of predefined shifts so as to optimize the trade-off between manpower cost and customer quality of service. We focus on explicitly taking into account in the shift-scheduling problem the uncertainties in the future call arrival rates forecasts. We model them as independent random variables following a continuous probability distribution. The resulting stochastic optimization problem is handled as a joint chance-constrained program and is reformulated as an equivalent large-size mixed-integer linear program. One key point of the proposed solution approach is that this reformulation is achieved without resorting to a scenario generation procedure to discretize the continuous probability distributions. Our 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 trade-off.