An applied optimization based method for line planning to minimize travel time

The line planning problem in rail is to select a number of lines froma potential pool which provides sufficient passenger capacity and meetsoperational requirements, with some objective measure of solution linequality. We model the problem of minimizing the average passenger systemtime, including frequency-dependent estimates for switching between lines,working with the Danish rail operator DSB and data for Copenhagen commuters.We present a multi-commodity flow formulation for the problemof freely routing passengers, coupled to discrete line-frequency decisionsselecting lines from a predefined pool.

We show results directly applyingthis model to a Copenhagen commuter rail problem.