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.