This thesis deals with optimisation approaches for the train unit scheduling problem (TUSP). Given a train operator’s fixed timetables and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled units, with certain objectives achieved and certain constraints respected. From the perspective of a train unit, scheduling assigns a sequence of trains to it as its daily workload. The TUSP also includes some auxiliary activities such as empty-running generation, coupling/decoupling control, platform assignment, platform/siding/depot capacity control, re-platforming, reverse, shunting movements from/to sidings or depots and unit blockage resolution. It is also relevant with activities like unit overnight balance, maintenance provision and unit rostering. In general, it is a very complex planning process involving various aspects.
Current literature on optimisation methods for the TUSP is very scarce, and for those existing ones they are generally unsuitable for the UK railway industry, either due to different problem settings and operational regulations or simplifications on some critical factors in practice. Moreover, there is no known successful commercial software for automatically optimising train unit scheduling in the world as far as the author is aware, in contrast with bus vehicle scheduling, crew scheduling and flight scheduling. This research aims at taking an initial step for filling the above gaps.
A two-level framework for solving the TUSP has been proposed based on the connection-arc graph representation. The network-level as an integer multicommodity flow model captures the essence of the rail network and allocates the optimum amount of train unit resources to each train globally to ensure the overall optimality, and the station-level process (post-processing) resolves the remaining local issues like unit blockage. Several ILP formulations are presented to solve the network-level model. A local convex hull method is particularly used to realise difficult requirements and tighten LP relaxation and some further discussions over this method is also given. Dantzig-Wolfe decomposition is used to convert an arc formulation to a path formulation. A customised branch-and-price solver is designed to solve the path formulation.
Extensive computational experiments have been conducted based on real-world problem instances from ScotRail. The results are satisfied by rail practitioners from ScotRail and are generally competitive or better than the manual ones. Experiments for fine-tuning the branch-and-price solver, solution quality analysis, demand estimation and post-processing have also been carried out and the results are reported.
This research has laid a promising foundation leading to a continuation EPSRC funded project (EP/M007243/1) in collaboration with FirstGroup and Tracsis plc
