Modeling and Solving Line Planning with Mode Choice

We present a mixed-integer linear program (MILP) for line planning with mode and route choice. In contrast to existing approaches, the mode and route decisions of passengers are modeled depending on the line plan and commercial solvers can be applied to solve the corresponding MILP. The model aims at finding line plans that maximize the profit for the railway operator while estimating the corresponding passenger demand with aggregate choice models. Hence, the resulting line plans are not only profitable for operators but also attractive to passengers. By suitable preprocessing we are able to apply any aggregate choice model for mode choices using linear constraints. We provide and test means to improve the computational performance. Our experiments on the Intercity network of the Randstad, a metropolitan area in the Netherlands, show that models which assume a fixed passenger assignment to modes cannot attract the passenger numbers they were designed for and therefore lead to inferior profit compared with our new model.