Quantifying and enforcing robustness in staff rostering

Employee absences are inevitable in practice due to illness, heavy workloads or accidents. These unforeseen events result in the disruption of employee shift rosters, which are then typically repaired using re-rostering methods. Despite their widespread use, repair methods often require last-minute changes to rosters, negatively affecting employees’ personal lives. Robust rosters are thus crucial when it comes to minimizing the negative impact of these unforeseen events. The academic literature, however, currently lacks a metric capable of measuring the robustness of staff rosters. This study introduces two complementary approaches for quantifying roster robustness without the use of simulation. The first metric enables an a priori estimation of how well unexpected employee absences can be accommodated, while the second metric approximates the costs incurred by repair methods. An integer programming-based methodology is proposed for generating robust rosters in a controlled manner. A computational study using public instances based on real-world scenarios demonstrates the effectiveness of the proposed methodology. A significant reduction of costs is observed when enforcing an appropriate level of robustness, compared against when robustness is ignored.