Case Studies Optimization

The modules Case Studies Discrete Optimization (MA4512) and Case Studies Nonlinear Optimization (MA4513) are a combination of lectures, project work, presentation and soft skills courses: Experience real world optimization problems and apply the skills you have acquired during your degree program to design and implement an optimal solution.

In the Case Studies a small team of students is presented a challenging problem by one of our cooperation partners. Your task is to understand the problem, work out the details together, find a viable way to attack the problem and implement a solution. To do this, you will also have to organize your work as a team, discuss possible solutions and obstacles with your partner and present your challenges and results to a broad audience. Of course, your advisors will be ready to help and guide you through that learning experience. They provide mathematical and methodological input in the form of lecture units and individual consulting sessions and also help you with your presentations and provide constant feedback.


  • Feb 9th, 2018: Application is now open until March 1st, 2018. Please see the detailed information below. A short description of all projects is also available below.
  • Jan 26th, 2018: There will be a preliminary meeting for both case studies courses on Thursday, February 8th, at 16:00 in room MI 02.04.011.

Preliminary Meeting

Slighty shortened version of the slides for the information event.

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 application 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 application by March1st, 2018 is mandatory! If you have any questions that are not answered here or at the preliminary meeting, please contact Michael Ritter at or Florian Lindemann at, respectively.


Application is possible until March 1st, 2018. It is mandatory and binding. To register, please write a short mail to (Discrete Optimization) or (Nonlinear Optimization) 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) and your current semester (counting from the beginning of your master's program).
  • 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)
  • language skills, especially 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. (You can also submit an application with a "mixed" ranking including all projects from discrete and nonlinear optimization, we will then assign you to one of the courses while trying to respect your individual ranking.)
  • persons you would like to work with as a team (please ask all these persons to give your name in their application, too)
  • any additional information that might be relevant for the choice of your project or your partners

You may also submit a joint application by ranking all projects for both Case Studies courses. We will then try to fit you into one of the courses according to your project preferences. In that case, please send the application email to both Mr Lindemann and Mr Ritter.

We will send you a short message when we have received your email. If you do not receive an acknowledgement within a week, please resubmit your application.

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 mention that in your email. 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.

Project Summaries

Order Batching in Intralogistics (Discrete Optimization)

In a warehouse, orders coming in from customers have to be fetched, packed and sent to the right destinations. To fetch the required articles of an order, in many storages commissioners collect articles by making tours through the storage with carts. They usually have a fixed start and end point and are able to work off several different orders in one tour. In every storage these tour lengths are supposed to be minimized: Reduced length directly corresponds to a smaller amount of time needed and less time implies either a higher throughput in the storage or reduced working cost.

Therefore, orders should be batched to create short tours. However, at the start of the day only a few orders are known. The rest of the orders arrives at the storage step by step and the batching strategy should find the best solution for the whole day. Another issues are priorities: All orders have a deadline and the most important way to measure the efficiency of a warehouse is the amount of orders that go out in time.

This NP-hard problem is of general interest for many warehouses. In this project, you will get to know and visit one specific storage and test your algorithms against their real world data. Based on a master thesis on order batching, you will develop and implement a model for solving the order batching problem with one or both of the side constraints. With a given simulation tool, your algorithm(s) can be tested and evaluated. This project is a cooperation with Heureka Business Solutions.

Class Scheduling (Discrete Optimization)

Designing timetables for a school is a very complex problem with a plethora of different constraints, e.g. available rooms, curricula of different classes, preferences of teaching staff, the sequence of courses within each day and within the week, availability of specialized teaching staff, cooperative teaching, and many more. In this project, you will develop a model that encompasses all relevant requirements for scheduling the classes of our cooperation partner, research relevant literature and algorithms and adapt/extend it to the specific situation at hand. Our partner will furnish you with data to test your approach and provide extensive feedback. This project is a cooperation with SFZ München Mitte 1.

Coating Printed Circuit Boards (Discrete Optimization)

As a protection against harmful environmental influences, many printed circuit boards are partially coated using a robotic coating machine. This device applies spray coating by means of moving a nozzle along pre-programmed paths over the printed circuit board. These paths must not lead to overlapping coating on the board, certain areas need to stay free from coating and the nozzle has to be steered clear of large components. In addition, there are a number of technological constraints due to the operation of the machine and the board layout. The objective of this project is automating and optimizing the path programming for these coating machines. This project is a cooperation with Siemens AG.

Routing and Schedule in Mobile Healthcare (Discrete Optimization)

In mobile healthcare operations, a number of patients need to be visited by nursing staff on different days and times of day for different periods. The scheduling and routing of the nursing staff depends on such factors as medical qualifications, patients' preferences, working time regulations, and a number of additional factors. The objective of this project is to analyze the connection between the two problems of routing and scheduling the nursing staff and identifying constraints that tend to have a high influence on the outcome. This project is a cooperation with acuila and unternehmerTUM.

Bus Chartering (Discrete Optimization)

Bus companies that offer chartering services get inquiries from potential customers that would like to rent a bus ride for one-time services. The challenge for such a company lies within fulfilling the requests in a cost-minimal way.

The customers’ inquiries include origin and destination locations, time constraints as well as requirements on the type of bus. This data might not necessarily be available from the beginning but arrives only in an online fashion. Additionally, regulations by the law limit the operating times of drivers. The goal is to assign available busses and drivers to the requested trips fulfilling aforementioned restrictions.

This problem involves routing as well as scheduling techniques. You will develop and implement an algorithm which computes feasible assignment and schedules for the busses of small operational cost. On data provided by the business partner, you will evaluate the quality of your solutions. This project is a cooperation with Flixbus Mieten.

Cargo Train Timetabling (Discrete Optimization)

The high demand for cargo shipments leads to high congestion of the rail network. The operators try to maximize the number of cargo trains which are routed through the network.

Requests for transportation of cargo are known beforehand for the considered time horizon and include specifications regarding origin and destination, time windows, and type of train. These trains have to be scheduled without interfering with passenger trains. Furthermore, the created timetables must obey certain constraints like safety distances between trains and should take into account that overtakes are possible at certain locations in the network only.

In this project, you will analyze small networks provided by our partner based on a real-world instance. You will develop and implement a scheduling scheme which maximizes the through-put. Your solution will then be compared to existing approaches. This project is a cooperation with DB Netze.

Motion Planning in Robotics (Nonlinear Optimization)

A key element in industry 4.0 is flexible production hardware; several tasks can be automated by using robotic arms. Due to changing task sequences the motion planning for such robots have to be done online. The pose of the gripper mounted on the robotic arm is the combination of a positon in R^3 and an orientation in SO(3). Since solving the full dynamic optimal control problem in real-time is only feasible in some special cases, the optimization of a sub-problem is the focus of this case study: Given the poses and velocity at start and end, the optimization problem is to find a trajectory between the two minimizing some cost function like time. The goal of the case study is solving this problem fast enough for real-time control. This project is a cooperation with Siemens AG.

Motion Interpolation and Sensor Fusion (Nonlinear Optimization)

Measuring the 6 degrees of freedom for a general rigid motion in space is an important task for many Computer Vision as well as Robotic applications. Knowing where an object is located in space is important to interact with it e.g. to manipulate or grasp it. There are many current systems that estimate the location and orientation of an object of interest by using a variety of sensors such as cameras, inertial measurement units (IMU) or tactile systems. All of them have advantages and drawbacks which is why a oftentimes a suitable approach is to use them hybridly together.

In order to calculate a pose (rotation & translation) given the different modalities a fusion of the data is needed. This project aims to fuse input streams of IMU and vision which work at very different frequencies and with different accuracy levels - and ultimately find the smooth trajectory describing the underlying motion via nonlinear optimization in pose space. For this, a pose stream can be viewed as a sequence of data points on the (dual) quaternion manifold, which is a parametric representation of the space of rotations (3D motions). With the help of interpolation techniques on pose space (e.g. LERP, SLERP), the different pose sequences are combined and a continuous trajectory is approximated by efficient spline interpolation on the manifold. For an example see this video. This project is a cooperation with FRAMOS.

Adaptive Pose Graph Optimization for Visual SLAM (Nonlinear Optimization)

One fundamental challenge in Computer Vision is to map the surrounding scene for self-localization. This is commonly referred to as Simultaneous Localization and Mapping (SLAM). Many SLAM algorithms, like the famous ORB-SLAM (, are able to detect loops within a sequence and subsequently close them, while adapting the map accordingly. During long sequences drift can occur, due to accumulating small errors in the map and the camera position. Loop closures allow for minimizing the accumulated drift by manipulating the map and camera positions. Here is an example video Pfeil for SLAM. Current algorithms are able to perform loop closures efficiently, but lack the capability to take the frequency distribution of the camera location over time into account. This may lead to inadequate solutions after performing the loop closure due to the highly inconsistent representation of the scene. While some structures may be over-represented (e.g. long enduring image sequence of a room), others may be under-represented (e.g. subsequent sequence of passing a hallway in a fast motion). Goal of this case study is to develop a robust optimization scheme which overcomes this issue. This project is a cooperation with FRAMOS.

Mixed-integer models and heuristics for portfolio optimization (Nonlinear Optimization)

The central question in portfolio optimization is how to allocate wealth across assets to gain maximum profit while minimizing the associated risk. Therefore, Markowitz proposed to compute the portfolio with minimum variance within the ones for which a certain return can be expected. This approach is often extended to use the conditional value-at-risk as alternative risk measure. Typically, this leads to distributing the wealth over many assets to exploit diversification benefits. However, this can cause high transaction costs or management costs may be high when the assigned weight is very small. To avoid this, optimal portfolios which contain only a fixed, small number of assets (cardinality constraint) and optimal portfolios with a minimum amount of money to invest in each asset (minimal allocation constraint) shall be computed in this project. This leads to mixed-integer problems, for which alternative formulations/heuristics (l1-penalization, clever rounding etc.) shall be investigated and compared based on real data. This project is a cooperation with risklab GmbH.

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