Simultaneous frequency and capacity setting for rapid transit systems with a competing mode and capacity constraints

The railway planning problem consists of several consecutive phases: network design, line plan- ning, timetabling, personnel assignment and rolling stocks planning. In this paper we will focus on the line planning process. Traditionally, the line planning problem consists of determining a set of lines and their frequencies optimizing a certain objective. In this work we will focus on the line planning problem context taking into account aspects related to rolling stock and crew operating costs. We assume that the number of possible vehicles is limited, that is, the problem that we are considering is a capacitated problem and the line network can be a crowding net- work. The main novelty in this paper is the consideration of the size of vehicles and frequencies as variables as well as the inclusion of a congestion function measuring the level of in-vehicle crowding. Concretely, we present the problem and an algorithm to solve it, which are tested via a computational experience.