Integrated line configuration and frequency determination with passenger path assignment in urban rail transit networks.

• An integrated model to jointly determine line configuration, line frequency and passenger assignment on a urban rail transit (URT) network is proposed by taking interplay between operator-oriented cost and passenger-oriented cost into account. It specifically considers (i) transfer waiting time, (ii) the use of the same tracks for trains belonging to different lines, and (iii) capacity restriction of trains. • The line planning problem in an URT network with passenger path assignment is formulated as a mixed-integer non-linear programming (MINLP) model with linear constraints. • An outer approximation method is developed to convert the original MINLP to mixed-integer linear programming (MILP). The experiment shows that approximation is actually very tight with a gap under 5.6 × 10–6. • A real case study based on the Hong Kong MTR network is conducted to test the performance of our approach. We also propose a method to determine the appropriate coefficients for the model and test the impacts of different candidate line pool size and the number of paths considered on the model. This paper considers a line planning problem in an urban rail transit (URT) network with passenger path assignment. The line planning problem involves both line configuration and frequency setting for the optimization of a combination of operator-oriented objective (minimization of operating costs or maximization of profits) and passenger-oriented objective (minimization of total travel times). The interplay between the line planning and the passenger assignment is explicitly taken into account and the problem is formulated as a mixed-integer non-linear programming (MINLP) model with linear constraints. In order to take advantage of existing commercial mix-integer linear programming (MILP) solvers, we propose an outer approximation method to linearize the objective. Finally, the model and solution algorithm are illustrated with a simplified version of the Hong Kong Mass Transit Railway (MTR) network. [ABSTRACT FROM AUTHOR]