TUM – TUM – Menü


Case Studies Discrete Optimization (MA4512)

combined lecture and project work course

supported through study contributions%SBBANNER%


Advisors: Michael Ritter, Fabian Klemm, Wolfgang Riedl
weekly hours: 4 hours
ECTS credits: 7


  • June 23, 2014: Some preliminary information on the upcoming final workshop is now available at the SCoNDO VI website. In particular, you can find some images of our conference venue. More information will be posted on that site over the coming days.
  • Feb 02, 2015: There will be a programming course for discrete optimization at the end of the upcoming semester break, more information below.
  • Jan 29, 2015: A shortened version of the slides used in the preliminary meeting is available below in Course Materials.
  • Jan 20, 2015: Some information on last year's case studies courses is available at the SCoNDO V conference website.
  • Jan 12, 2015: There will be a preliminary meeting for this course (jointly with Case Studies Nonlinear Optimization) on January 28th, 2015, at 16:30 hours in room MI 00.07.014.
  • Jan 12, 2015: We offer an optional companion seminar for the case studies, see here for further information.

There is a limit on the number of participants for this course with a small number of places being reserved for incomings from abroad and for students from other universities starting their master's courses at TUM this summer. If you want to participate in the case studies course, please register by writing an email to michael.rittertum.de no later than March 1st, 2015.


Preliminary Meeting

A preliminary meeting will take place on January, 28th, 2015 at 16:30 hours in room MI 00.07.014. At this meeting, we will give you some information about the case studies courses in general, what to expect during the courses, this year's projects, important dates and the registration process. This is a joint meeting for both the "Case Studies Discrete Optimization" and the "Case Studies Nonlinear Optimization". If you cannot come to this meeting but would still like to take the course, some more information will be published here after the meeting. Please note that registration by March1st, 2015 is mandatory! If you have any questions that are not answered here or at the preliminary meeting, please contact Michael Ritter at michael.rittertum.de.


Registration is possible until March 1st, 2015, it is mandatory and binding. To register, please write a short mail to michael.rittertum.de providing the following information:
  • last name, first name
  • your master's program (Mathematics, Mathematics in Bioscience, Mathematics in Science and Engineering, Mathematical Finance and Actuarial Science, Mathematics in Operations Research, others)
  • curriculum (of your master's studies and anything that might be related to optimization from your bachelor's studies)
  • ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects (project list will be made available after the preliminary meeting).
  • list of optimization related lectures that you have attended (for lectures from other faculties or univiersities, please give a short description of the topics covered so that we know about your expertise in the field)
  • programming skills (programming languages and other programming related skills)
  • persons you would like to work with as a team
  • If you are registered for the companion seminar please be sure to mention that in your mail.
After March 1st, we still have a limited number of places available for incomings from abroad and for master students coming from other universities and starting at TUM this summer. If this applies to you, please write an email to michael.rittertum.de.

Programming Course Discrete Optimization

There will be a programming course for discrete optimization from April 8th to 10th. This course's goal will be the application of the theory in linear and integer-linear programming (that you have learned in lectures such as the Discrete Optimization (MA 3502)) by learning how to deal with professional optimization software. More precisely, the course will give an introduction to the optimization suite Fico Xpress and the modelling language Mosel. This will be used for modelling and solving some practical example problems on your own.

We strongly recommend to attend this course in case you do not have any experience in using optimization software for discrete optimization problems. For more information, see the course's website. Registration is possible at http://ferienkurse.ma.tum.de

Course Materials

Preliminary Meeting

  • shortened version of the slides used for the preliminary meeting: pdf


Below is a short description of each of the projects planned for this year's case studies. As we are still talking to some of our partners, most of these projects are still subject to change depending on the feedback we get from our partners. Of course, projects may also be adapted to better suit your preferences, e.g. if there is overwhelming interest in one of the topics. Your objective will generally consist of the following tasks: Based on some practical problem, develop a suitable abstraction and a mathematical model. Use extensive analysis of the problem and discrete and integer optimization tools to come up with an algorithmic approach for solving the problem. Implement your solution and analyze the results.


Designing timetables is a very complex problem with a plethora of different constraints, e.g. available rooms, distances between those, curricula of different classes/degree programs, preferences of teaching staff, the sequence of courses within each day and within the week and many more. In this project, you will develop a model that encompasses all relevant requirements of a specific planner, research relevant literature and algorithms on timetabling and adapt/extend it using different integer linear programming techniques.

Car Sharing

The market of car sharing is quite new, highly competitive and hence offers a range of challenges for the providers. For example, market leaders in Munich offer a fully flexible carsharing concept, which allows users to (almost) arbitrarily choose the starting and destination point of their trips. This may lead to unpleasant vehicle allocations and therefore results in the necessity of reallocating the vehicle fleet, which may increase the vehicle's workload but comes along with tremendous labor costs. Thus, the issue of scheduling this process of redistribution in a cost efficient way and regarding the (uncertain) demand needs to be solved.

Bicycle Sharing Systems

Bicycle sharing systems usually use a station-based model, so there needs to be a sufficient supply of bikes as well as enough free spaces at each station for the system to be accepted by customers. To balance the distribution of bikes among the different stations, frequent redistribution trips are necessary. These trips need to comply with a number of constraints: Supply/demand needs to be taken into account, driving times, loading/unloading times and capacity of the vehicle used the relocation are of importance, and different vehicles should get relocation routes of roughly equal duration. In this project, you will adapt/extend a model for this problem and come up with algorithmic approaches to compute good relocation routes.

Discrete Tomographic Reconstruction

In material science, an analysis of different materials is often performed by directing a flow of particles at the target to be analyzed and then capturing the particle streams emitted/reflected from the sample. One regularly employs discrete measurements that capture information about particle positions in different projections (think of taking photographs with two or three cameras from different perspectives). The task of this project is to reconstruct the actual particle trajectories in space from the discrete projections.

Integrated Scheduling and Logistics

Modern production chains are often highly integrated and tightly scheduled. For this reason, failure of a single component regularly results in severe problems for a large number of production lines. A key feature of such complex systems is a tight integration of production scheduling and logistics. These systems do not only arise in industrial production, but also in mobile health care and other fields. The aim of this project is to develop and implement a model that can help in case of disruptions, e.g. by rescheduling, relocating production to different plants, shipping parts or tools necessary to produce certain parts or - depending on the actual application context - changing staff schedules or transportation routes.

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. Stefan Weltge
Discrete Mathematics

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


April 2018
Case Studies 2018: Save the date: Case Studies poster presentation on May 25th, 2018, final workshop on July 7th, 2018.