Benders Decomposition for Robust Tactical Railway Crew Scheduling

We consider robust tactical crew scheduling for a large passenger railway operator, who aims to inform crew early on about their work schedules while also maintaining the ability to respond to changes in the daily timetables. To resolve this conflict, the operator considers a template-based planning process, templates being time windows during which duties can later be scheduled. The goal is to select a cost-efficient set of templates that is robust with respect to uncertainty in the work to be performed in the operational phase. A set of templates is deemed robust when few excess duties are required to cover all work in the operational planning phase. To enable the construction of efficient template-based rosters, we impose several template rostering constraints that proxy the actual rostering rules of later planning steps. We propose a two-phase accelerated Benders decomposition algorithm that can incorporate these restrictions. Computational experiments on real-life instances from Netherlands Railways, featuring up to 948 tasks per day, show that historical planning information can be used to obtain robust templates and that parsimonious solutions can be obtained at negligible extra costs. Compared to a literature benchmark, our Benders decomposition method solves three times as many instances without rostering constraints to optimality.