Is equality always desirable? Analyzing the trade-off between fairness and attractiveness in crew rostering

Millions of employees around the world work in irregular rosters. The quality of these rosters is of utmost importance. High-quality rosters should be attractive on an individual level, but also divide the work fairly over the employees. We develop novel methodology to compute the trade-off between fairness and attractiveness in crew rostering. First, we propose an intuitive fairness scheme for crew rostering and analyze its theoretical performance. To do so, we introduce the approximate resource-allocation problem. This extension of the resource-allocation problem provides a framework for analyzing decision making in contexts where one relies on approximations of the utility functions. Fairness is a typical example of such a context due to its inherently subjective nature. We show that the scheme has "optimal" properties for a large class of approximate utility functions. Furthermore, we provide a tight bound on the utility loss for this scheme. We then present a unified approach to crew rostering. This approach integrates our proposed fairness scheme with a novel mathematical formulation for crew rostering. We call the resulting problem the Fairness-Oriented Crew Rostering Problem and develop a dedicated exact Branch-Price-and-Cut solution method. We conclude by applying our solution approach to practical instances from Netherlands Railways, the largest passenger railway operator in the Netherlands. Our computational results confirm the importance of taking the fairness- attractiveness trade-off into account.