Recoverable Robust Timetables on Trees

In the context of scheduling and timetabling, we study a challenging combinatorial problem which is very interesting for both practical and theoretical points of view. The motivation behind it is to cope with scheduled activities which might be subject to unavoidable disruptions, 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 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 disruptions occur. Such recovery capabilities are given as input along with the possible disruptions that must be considered. As in standard delay management problems, the main objective still remains the minimization of the overall needed time. We show that finding an optimal solution for this problem is NP-hard even though the topology of the event activity network, which models dependencies among activities, is restricted to trees. However, we manage to design a pseudo-polynomial