Network-wide synchronized scheduling of public transport services

Bus line timetabling is a part of the tactical planning phase which consists ofthe following stages: (i) frequency settings; (ii) timetable design; (iii) vehicleand crew scheduling ([7], [3], [1]).Timetables are usually determined with the objective of minimizing pas-senger waiting times at stops [4]. Several studies have considered also the min-imization of the waiting times of passengers at transfer stops as an additionalmetric for reducing the total travel time of passengers.The problem of timetable synchronization has been addressed by [2], [6],[11], [10] with the objective of reducing the waiting time of passengers at thetransfer stops while maintaining even dispatching headways among the dailytrips. Most works in the literature have decoupled the timetabling synchro-nization from the other tactical planning problems, except the work of [12]that tried to minimize also the total number of required vehicles and the totaldeadheading time of all daily trips. This was achieved by solving each objectiveseparately, using bi-level programming where the number of the required ve-hicles was solved rst and the total transfer time of passengers was minimizedusing a heuristic algorithm at the second stage.Transport and Plannin