A Column Generation Approach for the Integrated Crew Re-Planning Problem

Planned maintenance and construction activities are crucial for heavily used railway networks to cope with the ever increasing demand. These activities lead to changes in the timetable and rolling stock schedule (often for multiple days) and can have a major impact on the crew schedule, as the changes can render many planned duties infeasible. In this paper, we propose a novel integrated approach to crew re-planning, i.e., the construction of new duties and rosters for the employees given changes in the timetable and rolling stock schedule. In current practice, the feasibility of the new rosters is ‘assured’ by allowing the new duties to deviate only slightly from the original ones. This allows the problem to be solved on a day-by-day basis. In the Integrated Crew Re-Planning Problem (ICRPP), we loosen this requirement and allow for more flexibility: The ICRPP considers the re-scheduling of crew for multiple days simultaneously, thereby explicitly taking the feasibility of the rosters into account. By integrating the scheduling and rostering decisions, we can allow for larger deviations from the original duties. We propose a mathematical formulation for the ICRPP, strengthen it using a family of valid cover inequalities, and develop a column generation approach to solve the problem. We apply our solution approach to practical instances from Netherlands Railways, and show the benefits of integrating the re-planning process.