Vehicle rotation planning is the assignment of vehicles to trips of a given schedule and the concatenation of these trips to rotations. Mathematical optimization of especially vehicle resources and deadhead trip lengths can achieve significant savings and derive optimality bounds. In this project we deal with a very complex vehicle rotation planning problem for long distance passenger railways.

We integrate several aspects in one model. It includes the following components:

• selection of vehicle groups for scheduled and deadhead trips, i.e. single and multiple units and passenger cars can be represented
  
• allowance for multiple maintenance intervals for each vehicle
• optimization of "regular" rotations, in simple terms this means that, e.g., similar turns are desired for the same trip on different weekdays
  
• robust optimization by the optimization of planed turning times
  

To produce feasible rotations all components are modeled in great detail. For example, it is possible to distinguish orientations and positions of vehicles in a vehicle groups, whereby very complex rules can be represented.

We work in a close cooperation with our partner DB Fernverkehr AG, for whom we optimize the vehicle rotation planning for ICE and IC trains in Germany. This allows us to adjust our model and our solution methods to the requirements of real world problems.

The employed methods for solving the mathematical problem are Integer and Dynamic Programming. Besides using commercial solvers we implement specialized high performance algorithms to solve the vehicle rotation planning problem from scratch.