Railway crew capacity planning problem with connectivity of schedules

• Integrating the connectivity of schedules in crew scheduling makes problems harder to solve.
• Path-based formulation and arc-based formulation are compared against each other.
• Arc-based formulation is better in both solution quality and computational effort.
• Optimal solutions for real-life problems can be obtained within reasonable computational time.
• The connectivity of schedules may affect crew capacity decisions significantly.

We study a tactical level crew capacity planning problem in railways which determines the minimum required crew size in a region while both feasibility and connectivity of schedules are maintained. We present alternative mathematical formulations which depend on network representations of the problem. A path-based formulation in the form of a set-covering problem along with a column-and-row generation algorithm is proposed. An arc-based formulation of the problem is solved with a commercial linear programming solver. The computational study illustrates the effect of schedule connectivity on crew capacity decisions and shows that arc-based formulation is a viable approach.