This thesis investigates optimization-based control allocation methods designed for fault-tolerant and scalable application in multi-stage rockets. It is particularly focused on rockets with Thrust Vector Control (TVC), aerodynamic fins and Reaction Control Systems (RCS). The aim is to minimize the error between control commands and actuator output, besides actuator effort. Both in nominal and faulty conditions. Three convex optimization formulations are proposed: an Angle-Deflection (AD) problem, a linearized problem and a Second-Order Cone Programming (SOCP) problem. The AD problem includes actuator deflections and the linearized and SOCP formulations jointly consider actuator deflections and engine throttling. This work allows integration of faulty scenarios by constraint tightening, allowing reconfiguration of control allocation without changing the problem structure. Simulation data is used to validate the effectiveness of the formulations in satisfying control commands and fault handling. The work contributes to fault-tolerant and scalable control allocation frameworks.

Efficient surgical scheduling is essential for maximizing patient outcomes and ensuring optimal use of hospital resources. This thesis proposes and evaluates optimization strategies that incorporate Maximum Waiting Times (MWTs) assigned by doctors—reflecting subjective urgency assessments—and medical urgency quantified objectively through Disability-Adjusted Life Years (DALYs), alongside operational constraints inherent in hospital scheduling. Using real-world surgical data from Erasmus MC, the study aims to identify approaches that effectively balance equity and efficiency in patient prioritization.

The scheduling problem is addressed through Integer Linear Programming (ILP). A core optimization model is developed to minimize the total DALY loss resulting from surgical delays while respecting MWTs. Two extensions of this model are introduced: one explicitly incorporating patient waiting time with a penalty on exceeding MWTs, and another designed to minimize the maximum DALY loss across patients to promote fairness. These three distinct models, each representing a different prioritization strategy, are empirically tested and compared. Additionally, a sensitivity analysis is conducted on the parameter gamma, which penalizes excess waiting time beyond the MWT, to assess how varying emphasis on excess waiting time impacts prioritization outcomes and overall scheduling effectiveness.

The results highlight key trade-offs between system-level efficiency and individual patient fairness, offering actionable insights for improving surgical scheduling practices. The findings support the integration of objective health-outcome metrics alongside clinical judgment into operational decision-making, contributing to a more equitable and effective allocation of surgical resources.

Overall, this study contributes to the field of surgical scheduling by incorporating the objective measure of Disability-Adjusted Life Years (DALYs) into prioritization decisions and promoting ethically grounded, outcome-oriented scheduling policies. The development of three distinct optimization models—balancing medical urgency, fairness, operational constraints, and MWTs—scheds light on the complex trade-offs between minimizing total DALY loss, considering waiting times and subjective urgency, and ensuring equitable patient outcomes.

Local search approaches are often used to find solutions for optimisation problems. However, these approaches easily get stuck in local optima, who are not yet globally optimal. More complex variants of those approaches cannot always escape those local optima easily. Thus, the need for another effective technique arises. This thesis proposes such a technique: potential KPIs. A potential KPI is an addition to the objective function such that the local search algorithm accepts solutions with `potential', i.e., solutions that are closer to the global optimum in some sense.
This thesis focuses on two optimisation problems, the bucketised planning problem (BPP) and the travelling salesman problem, to investigate the performance of potential KPIs. Various potential KPI functions and employment methods are tested to determine the efficacy of potential KPIs and to study their behaviour.
The findings of this thesis indicate that adding a potential KPI to the objective function can significantly improve a basic local search algorithm. The performance of the method with potential KPI is highly dependent on the chosen potential KPI function. Moreover, defining such a function is challenging since some knowledge about the local and global optima is needed. While a random function can already improve the algorithm a lot, using a well-constructed function performs even better as potential KPI.
Furthermore, the performance of the method is dependent on how the chosen function is employed. The method should always end with the local search with the original objective function, but whether to start with or without potential KPI is dependent on the function. Nevertheless, starting without potential KPI seems to be slightly better due to the lower runtime and ability to be always better than the basic local search. The weight of the potential KPI in comparison with the original objective should be high and instance-dependent. Additionally, the initial solution also influences the found solution of the method, as a better initial solution, such as a greedy solution, leaves less room for improvement for the basic local search. Thus, the technique of a potential KPI can significantly improve the basic local search, but its effectiveness is dependent on the method of employment and constructed function. Moreover, a potential KPI can only be used when enough information about the optimisation problem is known.

Scheduling surgeries in a hospital efficiently is a hard, but necessary task, because the Operating Rooms (ORs) contribute for about 40% of a hospitals total expenses. Therefore, we want to maximise the utilisation of the ORs. However, we want to prevent overtime, since there already is a lot of pressure on hospital employees. The overtime is not easily calculated, because of the stochastic nature of the surgery duration. In this thesis, we focus on maximising the utilisation of the ORs, without creating too much overtime. We model the scheduling of surgeries as integer linear programs (ILPs), which determine how many surgeries can be planned with the maximisation of the utilisation of the ORs as the objective. Different methods are used to include the overtime constraint and the resulting schedules are then compared and we take our conclusions. In our research, we use data provided by an academic hospital in the Netherlands, which provides spe-cialties, patient groups, a Master Surgery Schedule (MSS) and historical surgery durations. It also provides a minimum number of surgeries that have to be performed for each patient group. Preferably, we want to avoid overtime altogether. This however is not possible, due to the stochastic nature of the surgery duration. Instead we formulate an overtime constraint, by setting a probability that a surgery has to end within the opening hours. We call this, the overtime constraint. The premise of the first model is to create all possible combinations of surgeries which do not exceed the overtime constraint. In this model we create a variable which gives the distribution of the total surgery duration in a single OR on a single day. However, when adding multiple surgeries together we first need a distribution for the surgery duration. Unfortunately, we found that the surgery durations follow a log-normal distribution, which is supported by literature as well. The sum of log-normally distributed variables does not have a closed form, making it difficult to add the surgery durations together. To calculate the distribution of the total surgery duration, we use the Fenton-Wilkinson method. The second model discretises the opening hours of each OR into time blocks. We then define the probabil-ity that a surgery ends within a certain number of time blocks to incorporate the surgery duration. This way we can define a Mixed Integer Linear Program (MILP) without relying on any specific distribution. At first, we use historical data to create the probability that a surgery ends within a certain number of time blocks. However, to ensure we compare the different models fairly, we use the same log-normal distributions as the previous model and discretises them. We found that the Column Based Approach has a high utilisation and computes the columns and solves the ILP faster than the discrete model. Despite this, overtime can still occur with this approach. However, the number of times overtime occurs, remains well within acceptable limits. Additionally, the probability of no
overtime directly impacts utilisation, as intuitively expected...

Plastic waste transported to oceans through canals and rivers becomes increasingly challenging to retrieve and harmful to ecosystems. Catching systems designed by Noria Sustainable Innovators can be used to capture the plastics as close to their source as possible. Deciding the best locations to place these systems is a difficult task, which is why a model for location optimization of catching systems for plastic waste removal from waterways is designed in this thesis: the Plastic Waste Flow Capturing Location Model (PW-FCLM).

In this model, the plastic waste flow through a network of waterways is represented as a Markov chain, using environmental data as inputs to estimate the initial probabilities and transition probabilities of plastic waste in the network. The PW-FCLM extends an existing Markov Decision Process-based Flow Capturing Location Model by incorporating various types of catching systems, considering sensitive areas, and specifying orientations for the systems. The equivalence of the linearized version of the extended model is demonstrated, a proof of NP-hardness of the problem is given and a greedy heuristic is presented as an alternative solution method.

A sensitivity analysis on the different types of input parameters is performed, and the runtimes for different problem sizes and solution methods are tested for case studies of Delft and Groningen in the Netherlands. The model is most sensitive to changes in the distance between the nodes in the network and to the probability of getting stuck due to water vegetation. For budgets up to B=2 and problem sizes up to n=375 nodes, the exact optimal solution can be found efficiently without a commercial solver license. For larger problem sizes or a higher budget, the heuristic appears to be a more appropriate solution method.

For future research, it is recommended to further study the influence of the distance between the nodes on the optimal solution and to investigate the plastic flow representation in the Markov chain further. Exploring the model's application to larger areas, such as provinces or countries, would be beneficial. The real-life effectiveness of placing catching systems at the optimal locations suggested by the model, depends on the accuracy of the input parameters. In this thesis, the values of the input parameters are primarily based on estimations of experts. It would be beneficial for the user of the model to further validate the values of the input parameters through experiments.