We propose heuristic and exact algorithms for the (periodic and non-periodic) train timetabling problem on a corridor that are based on the solution of the LP relaxation of an ILP formulation in which each variable corresponds to a full timetable for a train. This is in contrast with previous approaches to the same problem, which were based on ILP formulations in which each variable is associat...

The energy consumption of trains is highly efficient due to the low friction between steel wheels and rails, although the efficiency is also influenced largely by the driving strategy applied and the scheduled running times in the timetable. Optimal energy-efficient driving strategies can reduce operating costs significantly and contribute to a further increase of the sustainability of railway ...

The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for nonperiodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinato...

The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach t...

The railway planning process is a complex activity which is usually decomposed into a succession of stages, traditionally network design, line design, timetabling, rolling stock, and personnel planning. In this paper, we study the design and optimization of train timetables adapted to a dynamic demand environment. The objective is to minimize passenger waiting times at the stations. We first de...

We introduce, discuss, and solve a hard practical optimization problem which we call the ship traffic control problem (STCP). Since we plan bi-directional traffic, STCP relates to, and in fact generalizes train timetabling on single-track networks. The objective of finding quickest routes motivates the integration of recent algorithmic ideas from dynamic collision-free routing of automated guid...