Optimal Rail Scheduling in Limited Flexibility Environments
Rail scheduling is a challenging problem given both its spatial and temporal characteristics. Rail lines can be hundreds of km long, while single line train crossing strategies are based on a station or passing loop level and require the analysis of the problem on a minute time scale. In mixed-use rail systems with limited passing loop infrastructure, trains have different passing priorities and lengths, thus differing in their ability to use passing loops. Most commercial software tools for simulating rail systems often resort to problem-specific rules and heuristics. They can typically only be used by highly specialized personnel but are still unable to solve complex rail configurations since the simulation approach is not well suited to optimize the train crossing problem. This paper presents an integer formulation for the detailed scheduling of trains on a single main line using the modeling elements/ equations presented as part of the Process Systems-based Unit-Operation-Port-State Superstructure (UOPSS) framework. This model is the basis of the patent-pending Hatch Rail Optimizer (HRO) software. Other approaches in the literature fail to address many of the intricacies solved by our work. This approach is demonstrated through a practical case study involving a 370 km rail corridor with five different train sizes over a week-long scheduling horizon. Interesting computational experiences comparing Mixed Integer Linear Programming (MILP) and Integer Programming (IP) formulations are also discussed.