ABSTRACTIn public transport (PT) operations planning, timetable synchronization is a useful strategy to reduce inter-route or inter-modal passenger transfer waiting time and provide a well-connected service. This work addresses the integrated PT timetable synchronization with vehicle scheduling problem for a given PT network. A new bi-objective integer programming model is developed for the problem. The objectives are to maximize the number of simultaneous vehicle arrivals at the transfer nodes of a PT network, and to minimize the required fleet size. A novel two-stage deficit function (DF)-based method is developed to solve the mathematical model using a human–machine interactive approach. At the first stage, some existing optimizers are employed to quickly generate an initial solution. At the second stage, a DF-based graphical optimization technique is utilized to generate alternative Pareto-efficient solutions by reducing the fleet size. Numerical results demonstrate that the proposed model has the pot...