Staffing and scheduling flexible call centers by two-stage robust optimization

We study the shift scheduling problem in a multi-shift, flexible call center. Differently from previous approaches, the staffing levels ensuring the desired quality of service are considered uncertain, leading to a two-stage robust integer program with right-hand-side uncertainty. We show that, in our setting, modeling the correlation of the demands in consecutive time slots is easier than in other staffing approaches. The complexity issues of a Benders type reformulation are investigated and a branch-and-cut algorithm is devised. The approach can efficiently solve real-world problems from an Italian call center and effectively support managers decisions. In fact, we show that robust shifts have very similar costs to those evaluated by the traditional (deterministic) method while ensuring a higher level of protection against uncertainty.