Finding robust periodic timetables by integrating delay management


Julius Pätzold

Document Type

Journal Article

Publication Date


Subject Area

operations - scheduling, planning - methods


Periodic Timetabling, Delay Management, Robust Optimization, Adjustable Robustness, Periodic Event Scheduling Problem


This paper defines and solves a mathematical model for finding robust periodic timetables by proposing an extension of the Periodic Event Scheduling Problem (PESP). In order to model delayed and non-nominal travel times already in the timetabling step, the aim of this paper is to integrate delay management into the periodic timetabling problem and investigating the resulting problem (RPT). After revisiting both (PESP) and delay management individually, we introduce a periodic delay management model – an auxiliary model capable of evaluating periodic timetables with respect to delay resistance. Having introduced periodic delay management, we define the robust periodic timetabling problem (RPT). Due to the high complexity of the robust periodic timetabling problem we propose two different simplifications of the problem and introduce solution algorithms for both of them. These solution algorithms are tested against timetables found by standard procedures for periodic timetabling with respect to their delay-resistance. The computational results show that our algorithms yield timetables which can cope better with occurring delays, even on large-scale datasets and with low computational effort.


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