Mathematical methods play a key role in numerous problems in traffic optimization. For planning and operating public transportation networks, often discrete optimization techniques are employed.

The lecture deals with the mathematical modeling and algorithmic investigation of the following applications:
* Shortest routes in public transportation networks
* Network and infrastructure planning
* Line planning
* Timetabling
* Railway track allocation

This includes the following mathematical problems and techniques:
* Shortest paths in graphs, time-dependent and resource-constrained
* Multi-commodity network flows
* Cycle bases in graphs
* Mixed integer linear programming, cutting planes and column generation
* Steiner trees
* Facility Location
* Periodic Event Scheduling

Prerequisites: Basics of graph theory, e.g., Discrete Mathematics I. A background in optimization (e.g., Optimization I) is desirable, but not obligatory.

Literature: will be announced in the lecture

As a complement, you may optionally visit the lecture Optimierung II or the seminar on Optimization in Public Transport.