6. Conclusions and further studies
The development of synchronized timetables for providing more user-oriented, system-optimal and well-connected public transport (PT) service is attracting ever-increasing attention. However, most previous studies on the PT timetable synchronization design problem are focused on maximizing the number of simultaneous arrivals (or arrivals within a time window) of vehicles at transfer stops, or on minimizing the total passenger transfer waiting time. Other operations activities and system performance measures are not explicitly taken into consideration, and nor has the impact of schedule changes on PT users’ route/trip choice behavior been well investigated. To bridge these gaps, this study provides a new multi-criteria optimization modelling framework using a systems approach for the integrated PT timetable synchronization and vehicle scheduling problem with passenger demand assignment. A new bi-objective, bi-level mathematical programming model that takes into account both PT user and operator interests is proposed. The nature of the overall mathematical formulations of the new model is bi-objective, bi-level integer programming, which is non-linear and non-convex. Based on the special structural characteristics of the model, a novel deficit function (DF)-based sequential search method, which is combined with a network-flow technique and a shifting departure time (route offset time) procedure, is proposed to solve the problem to obtain a set of Pareto-efficient solutions. The graphical features of the DF and the two-dimensional fleet-cost space can facilitate the decision-making process of PT schedulers in finding a desirable solution. Numerical results from a small PT network and a case study of the Spiess–Florian network demonstrate that the proposed model and solution method are effective and have potential for being applied to large scale and realistic networks.
