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One of the greatest challenges in the public transportation network is the optimization of the passengers waiting time, where it is necessary to find a compromise between the satisfaction of the passengers and the requirements of the transport companies. This paper presents a detailed review of the available literature dealing with the problem of passenger transport in order to optimize the passenger waiting time at the station and to meet the requirements of companies (maximize profits or minimize cost). After a detailed discussion, the paper clarifies the most important objectives in solving a timetabling problem: the requirements and satisfaction of passengers, passenger waiting time and capacity of vehicles. At the end, the appropriate algorithms for solving the set of optimization models are presented.