Modeling and solving line planning with integrated mode choice

We present a mixed-integer linear program (MILP) for line planning with integrated mode and route choice. In contrast to existing approaches, the mode and route decisions are modeled according to the passengers' preferences while commercial solvers can be applied to solve the corresponding MILP. The model aims at finding line plans that maximize the profit for the public transport operator while estimating the corresponding passenger demand with choice models. Both components of profit, revenue and cost, are influenced by the line plan. Hence, the resulting line plans are not only profitable for operators but also attractive to passengers. By suitable preprocessing of the passengers' utilities, we are able to apply any choice model for mode choices using linear constraints. We provide and test means to improve the computational performance. In experiments on the Intercity network of the Randstad, a metropolitan area in the Netherlands, we show the benefits of our model compared to a standard line planning model with fixed passenger demand. Furthermore, we demonstrate with the help of our model the possibilities and limitations for operators when reacting to changes in demand in an optimal way. The results suggest that operators should regularly update their line plan in response to changes in travel demand and estimate the passenger demand during optimization