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Since 2019, Matheon's application-oriented mathematical research activities are being continued in the framework of the Cluster of Excellence MATH+
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Public transport

public transport
Changeover waiting times in a subway network

Nowadays, the use of mathematical planning methods is industry standard in the public transport sector. Matheon has made essentials contribution to that through its pioneering research on line planning and timetabling, vehicle and crew scheduling, work that has won multiple awards. Matheon's optimization tools have been adopted in standard market software systems as a result of diverse industrial cooperation projects and are used on a daily basis in many public transport companies at home and abroad.

There is even more potential for optimization in areas such as integrating planning steps that have so far been implemented sequentially, the creation of robust plans resistant to delays and failures, real-time optimization in scheduling, the incorporation of customer behavior, planning corporate strategies in competitive situations and the simultaneous consideration of multiple target criteria. Matheon spurs on these developments with the long-term objective of consistently establishing CAS (computer-aided scheduling) in public transportation planning in the same way as CAD/CAM in engineering.

New methods for solving large coupled integer programs and network flow problems as well as innovative procedures for robust optimization and algorithmic game theory form the mathematical basis. The focus here is on calculating solutions with optimum or verifiable quality.

Rail transport

rail transport

Diverse technical conditions need to be considered in rail transport, the planning problems are difficult to analyze, and there are very different requirements between intercity and regional passenger transport, or between block train and single wagon freight transportation. All these factors mean that railways are a system with high complexity.

The explosion in the effectiveness of mathematical optimization methods in the past 20 years has opened up new opportunities when it comes to optimizing railways. The Area B "Networks" developed by Matheon is a front runner in this field with important research contributions to track allocation, to rolling stock rostering and individual wagon freight transport optimization as well as to vehicle rotation planning and synchronized timetabling for intercity passenger transport.

Because careful coordination of detail and strategic planning is important for rail transport, Matheon develops methods for simulation-proof micro-macro transformation. The development of fundamental concepts for calculating robust timetables and rotation plans serves to handle delays in a better way. The consideration of train composition, in particular in conjunction with regularity requirements, leads to hypergraph-based network flow models. Matheon has extensive expertise in all the areas from process conception through to numerical solutions for large-scale systems.

Air transport

air transport
Anna-Valicek Medal of the AGIFORS

The use of operations research in air traffic is one of the major success stories in applied mathematics. Yield management, fleet, tail and crew assignment as well as rostering had and still have a significant influence on competition.

The increasingly advanced data situation and the availability of electronic sales routes allow ever more individual sales strategies when booking tickets. Methods for scenario reduction developed by Matheon allow the associated stochastic optimization models to be solved in a new dimension and quality.

The spread of delays along aircraft rotations can be reduced by the intelligent allocation of buffer times. The development of suitably robust optimization methods was singled out for an award in 2010 with the silver Anna-Valicek Medal of the Airline Group of the International Federation of Operational Research Societies (AGIFORS), one of the most prestigious awards in this field.

Individual transport

individual transport
Accelerated shortest path search

The wide-coverage expansion of navigation systems means that discrete optimization has become clearly visible in individual transport as well. Matheon has made important contributions to this with the development of super-fast shortest-path algorithms in large road networks. Our methods are used by major providers.

Individual transport is also confronted with the unique difficulty that individually optimal behavior does not necessarily lead to a so-called system optimum, as self-interested participants mutually hinder one another. Matheon develops new and innovative network flow models with game theory components to examine this "anarchic" user behavior. Such approaches can also provide a remedy for similar problems at toll checkpoints.

Further expertise involves, for one thing, decentralized, and distributed control systems for traffic light systems, for which Matheon develops methods of adaptive switching dependent on the traffic situation, instead of a fixed program. For another thing, the control of vehicles, for example in disabled transport or for breakdown assistance, as well as of automatic guided vehicles (AGVs) in factories or port facilities calls for rapid decisions without knowing the future. To this end, Matheon is developing online optimization methods with verifiable quality characteristics.


We have already implemented successful projects for various practice-relevant subjects with a range of prominent companies in the transport sector and areas directly related. A selection can be found here:
  • ADAC e.V.
  • Bundesamt für Güterverkehr
  • BVG Berliner Verkehrsbetriebe AöR
  • DB Fernverkehr AG
  • DB Schenker Rail Deutschland AG
  • IVU Traffic Technologies AG
  • Lufthansa Systems AG
  • PTV Planung Transport Verkehr AG
  • TomTom
  • ViP Verkehr in Potsdam GmbH
  • WSV – Wasser- und Schifffahrtsverwaltung des Bundes
Matheon has an extensive cooperation spectrum, extending from analyses, studies and consultations concerning model and algorithm development through to computer-assisted simulation and prototypical implementation of mathematical optimization methods. On request, we can convey spin-off companies for long-term software updating and maintenance.

Make the most of our expertise for a more efficient route to innovation!