STAFFING AND SCHEDULING FLEXIBLE CALL CENTERS BY TWO-STAGE ROBUST OPTIMIZATION

We study the shift scheduling problem in a multi-shift, flexible call center where moving agents between front end and back office is allowed to follow the actual demand. Differently from previous approaches, the staffing levels, required to provide a service with desired quality, are considered uncertain. This perspective naturally leads to a two-stage robust integer program with right-hand-side uncertainty (R-IP-RSHU). Three different uncertainty sets are investigated, also including correlations between consecutive time slots. In contrast to the general R-LP-RSHU problem, we show that the associated LP relaxation is polynomially solvable. A branch-and-cut algorithm based on a Benders type reformulation is also devised to solve the integer problem and tested on real-world data from a large Italian call center. The algorithm turns out to be effective and suitable to support relevant managers decisions. In fact, a high level of protection is achieved with a limited additional cost. 3