Application Process
Please send your application, including a CV, your examination report, and your preference for a certain topic (see below for a list of topics), to Maximilian von Aspern (maximilian.aspern@tum.de). If you are interested in multiple topics, please only send one application and include a ranking of all topics you are interested in.
If you have already formed a team, each participant must apply separately and indicate their preferred team mates in their application. If you apply as an individual or an incomplete team, we will match you to other students interested in the same topic.
Priority is given to students who have successfully completed the lecture “Applied Discrete Optimization”, though all applications are encouraged. If you apply as a team, at least 2 team members must have a sufficient background in (discrete) mathematical optimization.
Requirements
- Teams consist of 3-4 students
- The project studies are completed over a period of 3-6 months
- Your work is assessed based on a final presentation (45 minutes) and a written project report (20-40 pages)
- For more details, check the Project Studies Information Sheet or your FPSO
Topics
It is also possible to propose your own topic, though such proposals are only accepted if they align with our chair's interest in mathematical optimization.
Charity Fund Allocation (Bachelor)
While there are many charitable causes worthy of being supported, the available funding is unfortunately quite limited in most cases. Therefore, it is important to maximize the social impact of the available funds, while also taking fairness aspects into account. In this project, we will explore how mathematical optimization can be used to maximize the positive impact of charitable work. As a team, you will be able to choose which “area” of charitable work your project focuses on (e.g., treatment of neglected diseases, environmental preservation, education) based on your personal interests. The goal of the project is to gather data on charitable projects and to build a mathematical model used to make funding decisions (and to evaluate its performance and shortcomings).
Food Delivery Optimization (Bachelor)
With the explosive growth of the food delivery industry in recent years, routing decisions for delivery companies with dozens of riders and hundreds of customers are becoming increasingly complex. To keep delivery times and costs down, it is important to identify “good” routes out of exponentially many options. Of course, there are several legal and practical constraints which make this problem even harder to solve. In this project, you will use mixed integer linear programming to solve such a problem based on real-world data provided by the company Delivery Hero.
Meal Planning (Master)
Commonly cited as the first ever problem to be solved as a Linear Program, the diet problem asks which annual diet minimizes total cost while meeting a number of nutritional requirements. However, the solution computed by George Stigler in 1945, consisting of 170kg of wheat, 57 cans of evaporated milk, 50kg of cabbage, 10kg of spinach, and 129kg of dried beans, does not exactly make an appetizing meal plan.
In a modern version of this problem, we want to look at many more possible ingredients and a more sophisticated nutritional profile as well as sustainability aspects, such as CO2 production and water usage. Finally, we want to generate meal plans with realistic meal options and a healthy and appetizing variety, which significantly increases the difficulty of the problem. To tackle this problem, you will use real-world food data taken from large databases and advanced optimization methods.
Last Mile Delivery Routing (Master)
Last Mile Delivery describes the final leg of a delivery journey, in which items are delivered from a regional distribution hub directly to the customers. This part of the delivery contributes significantly to the overall shipping cost, so finding optimal route essential. Many customers have to be served (some of them in predefined time windows) by any of several vehicles starting at the same distribution hub. Finding short delivery routes is crucial in minimizing the delivery cost. You will use sophisticated mathematical tools to calculate optimal (or near-optimal) solutions to these routing problems on real historical data from Amazon deliveries in the United States in 2018.
Nurse Rostering (Master)
In the Nurse Rostering Problem, a team of nurses needs to be scheduled such that the patients' needs are fulfilled. But of course, work shifts are constrained by labor laws, hospital policies, employee availability, employee qualifications, etc. Some of these constraints are hard (i.e., they must not be violated) whereas others are soft (i.e., a violation of such constraints is allowed but will be penalized in the objective function). These constraints make this problem notoriously difficult to solve by standard techniques (or even human planners), which calls for the use of advanced optimization methods. You will implement, test, and compare these methods on realistic data sets with up to 150 employees.