Computing the Cost of Stability in Periodic Microscopic Railway Timetabling via Logic-Based Benders Decomposition (Short Paper)

Abstract

Periodic railway timetables require stability in operation, but the cost of increasing stability in terms of total travel time remains unclear. We study this cost of stability in microscopic periodic timetabling using the realisable cycle time as a stability measure. To implement stability, we compress the timetable to a shorter realisable cycle time that remains feasible at the microscopic level, and then rescale it back to the nominal period used in regular operation. The difference between this nominal period and the realisable cycle time becomes the time supplement available for absorbing delays. We formulate an optimization problem that jointly considers realisable cycle time and total travel time, and solve it with Logic-Based Benders Decomposition. The master problem optimizes commercial timing variables, while the subproblem verifies microscopic feasibility with routing, periodicity, and resource-conflict constraints. Infeasible subproblems yield activity cuts that constrain the master. Experiments on two Swiss railway case studies show that the proposed decomposition substantially improves computational performance on the larger instance and reveals nonlinear cost-of-stability frontiers with topology-dependent infeasible cycle-time regions and exceptionally high marginal costs at certain stability levels.