In many industrial sectors, energy consumption represents a significant cost factor and is therefore the subject of possible optimization measures. The redesign of technical processes or adjustments to product portfolios or production programs, for example, offer approaches for energy optimization. Due to the nature of energy as a supporting resource, various technical and economic constraints as well as different objectives must be taken into account. In the energy industry, issues arise in particular in the context of the energy transition that suggest the application of optimization models and methods. Sector coupling is based on the networking of a large number of players with different functions and individual objectives. The increasing decentralization in generation due to many small generation plants and the volatility of renewable energies ensure a high level of complexity. Energy grids are designed with the objectives of security of supply, economic efficiency and environmental sustainability in mind. The conflicting relationship between these objectives requires the determination of appropriate compromise-based solutions. Final theses can focus on optimizing the operation of smart grids or individual systems and pursue the goal of minimizing costs or emissions. In addition to the implementation of such a model, a component of such a thesis is the evaluation and analysis of the results of an exemplary case study. The specific topic is developed in consultation with the supervisor.

In the aftermath of natural disasters and other emergency situations, finding missing people quickly and efficiently is often critical to their survival. Search and Rescue (SAR) operations face the challenge of operating under significant time pressure, often in difficult to access terrain. The integration of drones into SAR missions offers promising opportunities to cover search areas more quickly and effectively. To use this combination efficiently and purposefully, optimization models are needed that can coordinate SAR operations and maximize success rates based on often uncertain data. Key questions include: What uncertainties have the greatest impact on the coordination of SAR operations? What are the options for combining humans and drones in SAR operations, and how can they be modeled? What approaches are appropriate for real-world scenarios? Research in this area will focus on addressing these questions, as well as analyzing and possibly further developing quantitative models that have been proposed in the literature for search and rescue problems.

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Would you like to work on a question from this subject area in your project or final thesis? If you are interested, please approach:
Tobias Klein

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For each type of new Mobility Service, there are different questions that can be answered with the help of optimization methods.
In the case of stationary or free-floating bike sharing, the routes of the service transporters for replacing and repairing the bicycles or the question of optimal new locations for bicycle stations are topics that can be mathematically optimized.
Car sharing offers similar research topics to bike sharing. An additional question is, for example, the optimization of the refueling (with fuel or electricity) of the vehicles in terms of time and/or location.
Ridesharing, which includes ridehailing (taxi rides), carpooling (commuter communities) and ridepooling (collective taxi rides), can benefit in different ways from methods of Operations Research. For example, vehicle routing and matching between vehicles and customers can be optimized, or dynamic pricing can be used to maximize revenue. On the Uber Engineering Blog you can find some articles and papers on the topic, e.g. "Dynamic Pricing and Matching in Ride-Hailing Platforms".
The probably most recent mobility service in Germany is E-Scooter sharing. E-Scooters are electrically driven scooters. Scientific literature on the optimization of this mobility service is still scarce. A research object is, for example, the optimization of evening rides, which are necessary to collect the scooters and charge them over night. E-Scooter sharing providers include myTaxi with the brand Hive, Bird, Lime or Tier Mobility.
The implementation of mathematical models, which is usually part of every thesis, and/or the analysis and evaluation of data can be done in GUSEK or Python.
The concrete topic is to be developed in consultation with the supervisor.

Container terminals (CTs) are the interface between sea-bound and hinterland transportation. However, the quay space is a critical resource on CTs as its capacity is limited by the quay’s length and the terminals working hours. Therefore, in order to use the quay optimally, terminal operators assign the berths to specific container vessels beforehand. The corresponding planning problem is called the Berth Allocation Problem (BAP). The aim of the BAP is to decide when and where to berth an incoming vessel and whether a vessel has to be rejected due to low quay capacity. This involves the efficient use of the limited quay resource by determining optimal berth times and positions for all incoming ships. Depending on the perspective, the objective may be maximizing the CTs returns or, e.g., maximizing the service level and the customer satisfaction respectively. The main goal of the thesis will be the identification of basic mathematical models representing the model formulations from the relevant literature. Therefore, an (1) overview of the relevant literature will be provided, (2) similar models will be grouped based on their formulation and (3) and a general, basic model formulation for each group will be presented. Moreover, the basic models of each group will be applied to a case study and analyzed with regard to computational effort and the resulting objective function values.

In both practice and research, there is a growing effort to develop innovative transport solutions that combine traditional trucks with drones or autonomous delivery vehicles to address the challenges of last-mile or inter-location logistics. The aim is to effectively combine the respective strengths of different delivery methods. For example, in 2023 REWE Group launched the "Liefer Michel" experiment, which combined drones and cargo bikes to deliver groceries to more remote areas (see https://www.rewe-group.com/de/presse-und-medien/newsroom/pressemitteilungen/in-michelstadt-der-bringer/). Merck tested the use of drones to transport medical samples between two nearby sites (https://www.merckgroup.com/de/research/science-space/envisioning-tomorrow/smarter-connected-world/wingcopter-hot-topic.html). The innovative combination of different modes of transport makes it possible to reduce traffic-related obstacles such as congestion or to bypass natural barriers by including airspace in the delivery process. These combinations contribute to greater flexibility and automation in the logistics process, which is particularly important for last-mile transport. Work in this area aims to develop appropriate quantitative models that allow the efficient integration and coordination of these different transport modes to optimise delivery processes.

Many practical problems can be represented by mixed integer linear models, since some variables in reality can only assume integer values, e.g. number of packets to be sent, number of machines to be used, etc. In contrast to linear optimization, the solvability of mixed integer problems is made more difficult by the additional limitation of the decision variables. Exact methods, such as the branch-and-bound method, usually require too much computation to solve problems with a large number of integer variables and/or constraints. For this reason, heuristics are often used to provide a good (but not necessarily optimal) solution within a reasonable time. The aim of the work is to identify the advantages and disadvantages of heuristic and exact solution methods and to implement suitable solution methods for a selected problem in Python or MATLAB. (Note: Basic knowledge of programming is helpful)

Reliable delivery commitments are a critical component of customer-centric supply chains. Available-to-Promise (ATP) methodologies support decision-making by integrating available inventory, planned production, and existing commitments. The objective is to enhance customer satisfaction and resource utilization through realistic delivery promises. Linear and mixed-integer linear programming (MILP) models are applied to determine feasible delivery dates based on constraints such as capacity, inventory levels, and current order backlogs. Additionally, multi-criteria decision-making approaches are incorporated to balance competing objectives, including cost efficiency, delivery reliability, and order prioritization.

In contrast to ATP, Capable-to-Promise (CTP) further accounts for the availability of production capacity and components. Its purpose is to identify and prioritize fulfillable orders based on a realistic assessment of resource availability. To model these decisions, mixed-integer linear programming (MILP) is employed. These models capture complex interdependencies such as capacity limitations, bill of materials (BOM) structures, production lead times, and material compatibility constraints. The resulting optimization models enable the efficient allocation of scarce production resources across single or multi-site manufacturing networks. Moreover, decision rules are derived to guide order acceptance strategies that reflect customer-specific requirements, delivery deadlines, and order profitability. The approach supports both operational decision-making and strategic planning in environments with high variability and limited resources.

In the context of production planning, machine scheduling addresses the central question of which job should be processed on which machine and at what time in order to achieve key operational goals such as minimized throughput time, on-time delivery, or maximized resource utilization. The objective is to use available machine capacities efficiently while optimizing performance indicators like delivery reliability and equipment usage. Machine scheduling becomes particularly challenging when multiple jobs with varying processing times, priorities, and dependencies must be allocated across a limited set of machines. In complex manufacturing environments, such as mechanical engineering, semiconductor production, or assembly planning, precise control over machine allocation is critical for operational efficiency and profitability. To solve such problems, companies apply mathematical optimization models, such as integer programming, as well as heuristic and metaheuristic methods like genetic algorithms or simulated annealing. These approaches often need to account for additional constraints such as maintenance intervals, or shift schedules. When applied effectively, machine scheduling helps companies increase delivery performance, reduce costs, and avoid bottlenecks by managing production processes in a dynamic, data-driven way.

In workforce-intensive sectors such as aviation, rail transport, or healthcare, crew scheduling addresses the central question of which staff member should work where, when, and on which task in order to meet operational requirements while complying with legal, contractual, and organizational constraints. The goal is to efficiently allocate personnel, optimize shift plans, and ensure both cost control and employee satisfaction. Crew scheduling is particularly challenging due to the complex interplay of constraints: working time regulations, rest periods, qualifications, personal preferences, and availability must all be balanced with operational goals such as continuity of service, minimal transition times, and maximum flexibility. Especially in dynamic environments, like airlines, hospitals, or rail operators, robust and adaptive workforce planning is key to operational success. Solutions often rely on mathematical optimization models (e.g., mixed-integer programming), heuristics, and AI-based techniques capable of processing large data sets and generating actionable schedules. When applied effectively, crew scheduling increases operational resilience, improves cost efficiency, and enables more flexible and equitable workforce deployment, making it a strategic asset in people-driven industries.