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Case Studies Discrete Optimization (MA4512)
combined lecture and project work course

Advisors: Fabian Klemm, Jannik Matuschke
weekly hours: 4 hours
ECTS credits: 7



  • Feb 21, 2017: Registration deadline is March 5th, see also the information below. For information about the Case Studies in Nonlinear Optimization (MA4513), visit http://www-m1.ma.tum.de/bin/view/Lehrstuhl/LindemannCaseStudiesSS17.
  • Jan 19, 2017: There will be a preliminary meeting for this course (jointly with "Case Studies Nonlinear Optimization" on February 6th, 2017, at 16:15 hours in room MI 03.08.011.

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 klemmma.tum.de no later than March 5th, 2017.


Preliminary Meeting

slightly shortened version of the slides: pdf

A preliminary meeting took place on February 6h, 2017, at 16:15 hours in room MI 03.08.011. 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 March 5th, 2017 is mandatory! If you have any questions that are not answered here or at the preliminary meeting, please contact Fabian Klemm at klemmma.tum.de.


Registration is possible until March 5th, 2017, it is mandatory and binding. To register, please write a short mail to klemmma.tum.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)
  • list of optimization related lectures that you have attended (for lectures from other faculties or universities, 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, experience in using optimization software)
  • whether you speak (some) German (as some cooperation partners might only speak German; still, this will not exclude you from any project per default!)
  • ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects.
  • persons you would like to work with as a team
  • any additional information that might be relevant for the choice of your project or your partners
  • If you are registered for the companion seminar please be sure to mention that in your mail.
After March 5hth, 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 klemmma.tum.de. If not claimed, these places will be freed for applicants a few weeks before summer term starts. If this applies to you, we will inform you about that by email.

Course Schedule



All materials for this course will be provided in Moodle, registered participants will be granted access by their supervisors.

Project Summaries

Fare Evasion in Transit Networks

Fare evasion in public transit systems causes significant losses to the systems’ operators. In order to decrease evasion rates and reduce these losses, transportation companies conduct fare inspections to check traveling passengers for valid tickets. In turn, fare-evading passengers observe the distribution of inspections in the network and adapt their routes accordingly. The goal of this project is to optimize the inspection schedule in the Dutch railway system. In order to be effective, the optimization needs to take into account the reaction of the passengers. Therefore, the task is to solve a bilvel optimization problem that not only involves distributing the inspections in the network, but also optimizing the fare evaders’ routes so as to avoid the inspectors once they are placed.

Inventory Routing for Delivery of Liquid Oxygen in Healthcare

Air Liquide is a worldwide provider of gases for industry and healthcare. Its Healthcare section provides 7500 hospitals worldwide with bulk quantities of liquid oxygen. Such bulk customers are provided with on-site storage tanks that are refilled regularly by vehicles transporting the gases as cryogenic liquid. A remote telemetry system allows Air Liquide to forecast the demand of each bulk customer. In addition, smaller customers place “call-in” orders on demand. Roundtrips for vehicles have to be scheduled in such a way that each bulk customer is re-supplied before they run out of gas and each call-in request is fulfilled, while respecting additional constraints such as mandatory breaks for drivers. The goal of this project is to develop an algorithm that solves this complex inventory routing problem. This project is based on the ROADEF/EURO 2016 Challenge in cooperation with Air Lqiude.

Sequencing for Filling Lines in Dairy Production

Dairy factories produce a broad range of milk-based products such as milk, cream, or yogurts of many different flavors. These products are filled into the packaging in highly automatized filling lines. However, when changing between products of different types, setups have to be performed on the filling machinery. Furthermore, the equipment has to be cleaned within certain intervals to observe hygiene regulations. As setups and cleanings can be performed simultaneously, optimized sequencing of the products can reduce the total downtime of the system significantly, thus making the production more efficient. In mathematical terms, this results in a single-machine scheduling or sequencing problem with sequence-dependent setup times. The goal of this project is to develop optimization methods for the production at a local dairy factory.

Product Classification by Shopping Carts

Intelligent shopping carts in the very near future are to keep track of their current load. In order to achieve this, they keep track of certain parameters (an image of the current goods, their weight) which ware updated whenever the customers adds content to the cart. Of course, this yields a more or less classical classification/machine learning problem. While a bunch of algorithms have alread been tested by our project partner, students are to approach the topic with their knowledge about discrete and geometric optimization in order to finally provide a suitable recommondation of a reliable and sufficently fast classification method. This project will be in close cooperation with an external software company whose client will provide the necessary data and expertise about the issue on hands.

Charging-Station Allocation in Electrified Carsharing

The organization of charging electric vehicles in a free-floating carsharing business modell faces several challenges. This project will deal with the issue how to optimally strategically plan the allocation of charging stations, or hubs. Hubs are limited w.r.t. their capacity and cannot be allocated without restrictions such as costs or limited available locations. Still, they should be placed such that availability of vehicles of cars fits the demand by customers over the business area. The projects goal is thus to first provide a model that contains all restrictions as well as a suitable evaluates allocations of hubs. Second, this model shall be used in an algorithmic implemenation to provide possible optimal charging station allocations.

-- FabianKlemm - 19 Jan 2017

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.