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Main research areas and research projects


Water distribution
Forest exchange
Choice of conveyance
Power management
Land consolidation
Foto Automat

Optimal operation of water distribution networks
Foto Network A water distribution network is a system containing engineered hydraulic components to provide water supply to consumers. The main task in operating a water distribution network is to choose different sources of water and determine a configuration of pumps and valves to satisfy reliable customer demands. The cost of water, energy, and the number of pump switches should be minimized. Mathematically, the operation problem can be modeled as a mixed integer nonlinear program (MINLP) involving nonconvex constraints and objective. We aim at solving them to global optimality.
People: Prof. Dr. Raymond Hemmecke, Dipl.-Math. Dipl.-Inf. Wei Huang
Partners: Dr. Harald Held (Siemens AG, Corporate Technology, Munich)
Period: 2011 - today

Voluntary land exchange in forests - project "ArborChange" with "ArborEval" and "ArborOpt"
iph.png The voluntary land exchange of forest lots owners is a new tool to improve on problems in the cost-effective structure of forest regions owned by private owners. Some of the methods for land consolidation (read more...) are helpful, but there are many new challenges to overcome in forestry regions, like an extreme numbers of different owners, badly shaped lots, and read more...
People: Dr. Steffen Borgwardt
Partners: Bayerische Staatsministerium für Ernährung, Landwirtschaft und Forsten, Bayerische Forstverwaltung, Dr. Stefan Schaffner, Holger Hastreiter
Period: R&D project Arborchange April 2012 - July 2013, transition into regular use of the Staatsministerium and Forstverwaltung 2013 - today

Routing under choice of conveyance
Sight-Seeing We investigate several typical routing problems in the situation where it may be of some advantage for the travelers to change the conveyances from time to time. In many settings this may not be reduced back to the orginal problem. read more...
People: Dr. René Brandenberg, Dr. Michael Ritter
Partners: Institut für Produktionswirtschaft und Logistik, Universität für Bodenkultur Wien 
Period: 2010 - 2015

DFG Research Project: Geometric reconstruction in refraction- and diffraction-based tomography
Refraction Tomography Computerized tomography (CT), the process of obtaining the density distribution within a specimen from multiple X-ray projections, has revolutionized diagnostic radiology over the past three decades. While standard CT is based on the principle of absorption, we focus on three novel read more...
People: Prof. Dr. Peter Gritzmann, Dr. Andreas Alpers
Partners: Prof. Dr. Franz Pfeiffer (TU München, Germany), Prof. Henning Friis Poulsen (DTU, Denmark) , Prof. Gabor T. Herman (CUNY, USA) , Prof. Rafal Dunin-Borkowski (Research Centre Jülich, Germany) 
Period: 2011 - today

Geometric and Constrained Clustering: Gravity Bodies and Power Diagrams
powerdiagram.png The studies of special geometric bodies tied to constrained clustering of high-dimensional point sets lead to new and improved algorithms for the associated clustering read more...
People: Prof. Dr. Peter Gritzmann, Dr. Steffen Borgwardt
Partners: Prof. Dr. Andreas Brieden 
Period: 2005 - today

Modelling and Optimizing the General Power System
© Kalle Pihlajasaari 
The efficient integration of renewable energy into the existing infrastructure poses a multitude of challenges, many of which have not been brought to a satisfactory conclusion so far, such as the power grid and its expansion, unit commitment in systems with intermittent renewable energy units, and the impact of renewable energy on the power market read more...
People: Prof. Dr. Peter Gritzmann, Dr. René Brandenberg, Dr. Michael Ritter
Partners: Lehrstuhl für Energiewirtschaft und Anwendungstechnik (Fakultät für Elektrotechnik und Informationstechnik, TUM)
Fachgebiet Elektrische Energieversorgungsnetze (Fakultät für Elektrotechnik und Informationstechnik, TUM)
Period: 2009 - today

Optimal Containment
10 center solution A central point of this project is the combination of some recent results on so called core-sets with geometric inequalities and typical techniques from combinatorial optimization. We obtained new and significantly faster approximation routines for read more...
People: Dr. René Brandenberg
Prior Funding: 5/2005 - 4/2006
Prizes: Walther-von-Dyck-prize, December 2006

Clustering Models and Algorithms for Land Consolidation
land_consolidation.jpg In many agricultural regions, a small number of farmers cultivates a large number of small lots that are scattered over an extended area. Due to this, they have high driving costs, and cannot used heavy machinery profitably. Using methods of combinatorial optimization, mathematical models are derived that do not share the issues of a classical land consolidation process. The central idea is read more...
People: Prof. Dr. Peter Gritzmann, Dr. Steffen Borgwardt
Partners: Prof. Dr. Andreas Brieden , Dr. Paul-Michael Rintelen
Period: 2003 - today

eXIST Start-up Project: Optimal storage of differently sized rectangular packages on round storage disks
Foto Automat Automated warehouse systems with shelves have one major downside, they have a poor utilization of space. The Munich based startup Magazino developed a storage system which reduces this problem by eliminating the area for the handling system. The storage of various goods, usually differently sized rectangular packages, will be on round storage disks. One way of increasing the utilization of space, is an optimized algorithm of how to position differently sized rectangular packages on the round disks.
People: Prof. Dr. Raymond Hemmecke
Partners: Magazino – simple storage  (startup of TUM), Institute for Industrial Design, Institute for Materials Handling, Material Flow, Logistics
Period: 2012 - today


TUM Hall of Science and Technology
Graph Im Rahmen des Projekts TUM@School.School@TUM sollen die Schnittstellen zwischen Schule und Universität intensiviert werden und somit für eine exzellente Ausbildung von Lehrkräften an der TU München gesorgt werden. Als Forschungsraum zur Übersetzung komplexer fachwissenschaftlicher Erkenntnisse in den Schulbetrieb ("didaktische Rekonstruktion") soll hierbei die TUM Hall of Science and Technology dienen. Read more...
People: Dr. René Brandenberg, Dr. Michael Ritter
Partners: Prof. Dr. Kristina Reiss, Matthias Bernhard
Funding: Deutsche Telekom Stiftung 
Period: 2012 - 2013

Automatisiertes Kopiertreiben
Kopiertreiben In sheet metal forming there are two production methods used in most industrial applications: Hydraulic presses are used for mass production where the batch sizes justify the necessary investments. For individual parts, on the other hand, mostly manual processes using tools like the "Kraftformer" are employed. With more and more individualization demanded by the customers, there is an increasing need for a production method for very small batch sizes that is more efficient than a purely manual production. The method of "automated driving" combines the Kraftformer with an industrial robot and clever mathematical algorithms to significantly reduce the amount of manual labour needed for small batch size productions.
People: Prof. Dr. Peter Gritzmann, Dr. Michael Ritter, Dipl.-Math. Felix Schmiedl
Partners: Lehrstuhl für Umformtechnik und Gießereiwesen, Fakultät für Maschinenwesen, TU München
Funding: research project AiF 16895N of the Europäische Forschungsgesellschaft für Blechverarbeitung e.V. financed through the Arbeitsgemeinschaft industrieller Forschungsvereinigungen "Otto von Guericke" e.V. as part of the program for the advancement of the Industrielle Gemeinschaftsforschung by the Bundesministerium für Wirtschaft und Technologie
Period: 2011 - 2013

Optimal Slot Scheduling for Long-Term Flight Planning
Flughafen Frankfurt am Main
© Sven Teschke 
Most major airports suffer from restricted capacity, requiring the use of an allocation mechanism for scheduling flight requests. This project investigates means of allocating slots such as to make optimal use of the available capacities. read more...
People: Andreas Brieden, Peter Gritzmann, Matthias Hähre, Gunter Heinrich, Michael Ritter
Partners: Fraport AG Frankfurt Airport Services Worldwide, Frankfurt
Period: 2003 - 2008

  • Analysis of production strategies for cataloging construction components

  • Phenomena in High Dimensions: in analysis, combinatorics, convexity, probability and mathematical physics 
    Drittmittel: European Network, MRTN-CT-2004-511953
    Zeitraum: 2005 - 2008
  • Modeling and optimization of correction measures for human extremities
    Drittmittel: Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, 03 GRNGM 1
    Partner: Chirurgische Klinik und Poliklinik, Ludwig-Maximillians-Universität München;
    Zeitraum: 2000 - 2008
  • Neue kombinatorische Algorithmen für die Logistik-Optimierung
    Partner: Axxom AG, München
    Zeitraum: 2004 - 2007
  • Kombinatorische Optimierungsverfahren zur Reduktion von Bewirtschaftungskosten in der Landwirtschaft
    Partner: Bayerischer Bauernverband und Bayerische Landesanstalt für Landwirtschaft, Institut für Ländliche Strukturentwicklung, Betriebswirtschaft und Agrarinformatik, München
    Zeitraum: 2002 - 2007
  • Koexistenz von Gentechnik, konventioneller Landwirtschaft und Ökolandbau in Bayern: Mathematische Optimierung
    Partner: Bayerisches Staatsministerium für Landesentwicklung und Umweltfragen, München
    Zeitraum: 2003 - 2005
  • Kreise in großen Graphen (DFG-Schwerpunktprogramm Algorithmik großer und komplexer Netzwerke)
    Drittmittel: Deutsche Forschungsgemeinschaft, Gr 993/8-1, Gr 993/8-2
  • Kombinatorische Untersuchungen Diskreter Inverser Probleme (mit Prof. Dr. Alberto Del Lungo, Università di Siena, Italien)
    Drittmittel: Deutscher Akademischer Austauschdienst, 314-vigoni-dr
  • Allokation von Ressourcen im Kreditgeschäft
    Partner: Deutsche Bank, München
    Zeitraum: 2000 - 2001
  • Verifikation von Schaltkreisen
    Partner: Infineon Technologies AG, München
    Zeitraum: 1999 - 2001
  • Diskrete Tomographie
    Partner: Dr. Peter Schwander, Institut für Halbleiterphysik, Frankfurt/O.
    Drittmittel: Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, 03 GR 7 TM 1
  • Mathematische Verfahren zur Auswertung von Bilddaten der Transmissionselektronenmikroskopie
    Partner: Institut für Halbleiterphysik, Frankfurt/O.
    Industriepartner: Lesswire AG, Frankfurt/O.
    Zeitraum: 1996 - 2001
  • Forschungsprojekt Computational Convexity and its Applications (mit Prof. Dr. Dr. h.c. mult. Victor Klee , University of Washington)
    Drittmittel: Deutscher Akademischer Austauschdienst & National Science Foundation, 315/PPP/ru-ab.
  • Forschungsprojekt Repräsentation, Visualisierung und mathematische Analyse semiotischer Räume (Kooperation mit Prof. Dr. Burghard Rieger, Computerlinguistik, Universität Trier)
    Drittmittel: Deutsche Forschungsgemeinschaft, Gr 993/7-1.
  • Forschungsprojekt Algorithmische Theorie konvexer Körper
    Drittmittel: Forschungsfond des Landes Rheinland-Pfalz.
  • Forschungsprojekt Research in Computational Convexity (mit Prof. Dr. Dr. h.c. mult. Victor Klee , University of Washington)
    Drittmittel: Collaborative Research Grant CRG 950220, NATO
  • Computational Convexity (DFG-Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung)
    Drittmittel: Deutsche Forschungsgemeinschaft, Gr 993/3-1, Gr 993/3-2.
  • Computational Convexity (mit Prof. Dr. Dr. h.c. mult. Victor Klee , University of Washington)
    Drittmittel: Deutsche Forschungsgemeinschaft, Gr 993/1-1

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.