An optimization based method for line planning to minimize travel time

The line planning problem is to select a number of lines from a potential pool which provides sufficient passenger capacity and meets operational requirements, with some objective measure of solution line quality. We model the problem of minimizing the average passenger system time, 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 problem of freely routing passengers, coupled to discrete line-frequency decisions selecting lines from a predefined pool. We show results directly applying this model to the Copenhagen commuter rail problem.