Evaluation of recoverable-robust timetables on tree networks

In the context of scheduling and timetabling, we study a challenging combinatorial problem which is interesting from both a practical and a theoretical point of view. The motivation behind it is to cope with scheduled activities which might be subject to unavoidable disturbances, such as delays, occurring during the operational phase. The idea is to preventively plan some extra time for the scheduled activities in order to be “prepared” if a delay occurs, and to absorb it without the necessity of re-scheduling the activities from scratch. This realizes the concept of designing so called robust timetables. During the planning phase, one has to consider recovery features that might be applied at runtime if delays occur. Such recovery capabilities are given as input along with the possible delays that must be considered. The objective is the minimization of the overall needed time. The quality of a robust timetable is measured by the price of robustness, i.e. the ratio between the cost of the robust timetable and that of a non-robust optimal timetable. The considered problem is known to be NP-hard. We propose a pseudo-polynomial time algorithm and apply it on random networks and real case scenarios provided by Italian railways. We evaluate the effect of robustness on the scheduling of the activities and provide the price of robustness with respect to different scenarios. We experimentally show the practical effectiveness and efficiency of the proposed algorithm.