Branch and Price for Railway Crew Scheduling: Benchmark Instances and Computational Study

Abstract

Railway crew scheduling consists of assigning a set of tasks to crew members in the form of feasible duties so as to minimise costs, and is one of the key planning problems faced by railway operators. While column generation is the dominant solution method, literature on exact branch-and-price approaches is scarce. Moreover, few publicly available benchmark instances exist. We present a state-of-the-art branch-and-price algorithm and conduct a systematic computational study of its components, including branching rules, primal heuristics, and reduced cost fixing techniques. To this end, we introduce a novel library of 100 benchmark instances, ranging in size from 90 to 3,016 tasks. The instances are generated by mimicking the railway planning process, validated against data from Netherlands Railways, and publicly available with best known solutions and a solution checker. We report average optimality gaps below 1% across all instance sizes, driven primarily by the strong performance of primal heuristics, whereas branching and reduced cost fixing contribute little to closing the gap. Branch and price also outperforms a multi-commodity flow formulation, which fails to find a feasible solution on many of the smallest instances. Our findings provide support for the popularity of column generation-based primal heuristics, and show that improving the dual bound remains the main challenge for exact methods in railway crew scheduling.