An Optimization Framework for Transit Network Design and Scheduling

In this study, we propose a mixed integer linear programming (MILP) model as an optimization framework for transit network design and timetabling. The framework has high flexibility and compatibility because it can be used to solve three major categories of transit network problems, bus network design problems, bus timetabling problems, and bus network and timetabling problems, considering most of the constraints and objectives adopted in the related studies. For bus network design problems, the optimization framework is compatible with all the linear and a great majority of nonlinear constraints and objective functions appeared in the past studies. Moreover, we found that the linear objective functions of bus network design problems in the literature can be classified into six major types. For bus timetabling problems, there are two major types of objectives and constraints in the related studies: passenger-based and bus-based. Since the major purpose of transit systems is to serve passengers, the former is chosen in the framework. As a result, the framework is almost fully compatable with the passenger-based objectives and constraints. It is also found that the passenger-based objectives in the literature can be categorized into two major types. In the case study, all categories of objective functions above are tested using the same numerical example. The results show that various types of operator or user costs and constraints in bus network design and timetabling are effectively considered. Furthermore, because the optimization framework integrates network design and timetabling, it often provides better overall results than the individual network design models and timetabling models. Therefore, the proposed framework is a useful tool for decision-makers under different objectives and constraints and has potential for improving the efficiency of urban transit systems.