A Job-Shop Scheduling Model for the Single-Track Railway Scheduling Problem

The Single-Track Railway Scheduling Problem can be modelled as a special case of the Job-Shop Scheduling Problem. This can be achieved by considering the train trips as jobs, which will be scheduled on tracks regarded as resources. A train trip may have many tasks that consist of traversing from one point to another on a track. Each of these distinct points can be a station or a signal placed along the track. Con icts may occur when the desired timetable would result in two trains occupying the same section of the track at the same time, and these are resolved by re-timing trains. The objective is to minimize the total delay. Here we consider the case where delays can only be introduced at the start of each trip. We show how the problem can be modelled using constraint programming and successfully solved. In addition, it discusses a group of practical constraints, incorporated into the software, that arise in real-life problems to which little attention has been paid hitherto. Results of solving 19 real-life problems gathered from literature are also presented.