Dynamic Railway Crew Planning with Fairness over Time

Railway operators typically employ large numbers of drivers and guards, and are interested in providing them with fair and attractive working conditions. At Netherlands Railways (NS), the largest passenger railway operator in the Netherlands, this challenge is addressed through the use of Sharing-Sweet-and-Sour rules, which specify a fair allocation of sweet (attractive) and sour (unattractive) work over the different crew bases. While these rules are currently implemented at the crew base level and in the tactical planning phase, NS is considering formulating these rules at the individual level, in the operational planning phase, and over a given planning period. This gives rise to a new problem, which we call the dynamic railway crew planning problem with fairness over time. We propose a rolling horizon approach with a penalty-based feedback mechanism and a column generation heuristic to solve this problem. On several real-life instances from NS, including up to 572 unique crew members, this method is able to satisfy the individual rules for on average 95.2% of the employees.