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. This paper was accepted by Yinyu Ye, optimization.

Graph Coloring based Heuristic for Crew Rostering

In the last years personnel cost became a huge factor in the financial management of many companies and institutions.The firms are obligated to employ their workers in accordance with the law prescribing labour rules. The companies can save costs with minimizing the differences between the real and the expected worktimes. Crew rostering is assigning the workers to the previously determined shifts, which has been widely studied in the literature. In this paper, a mathematical model of the problem is presented and a two-phase graph coloring method for the crew rostering problem is introduced. Our method has been tested on artificially generated and real life input data. The results of the new algorithm have been compared to the solutions of the integer programming model for moderate-sized problems instances.