This research addresses the operational challenges faced by the Sophia Children’s Hospital through a comprehensive analysis of its current state, literature review, and mathematical modeling. A model is created that produces a master surgery schedule, allowing for the allocation of patients to specific specialties, operating rooms, and days. Our aim is to maximize the utilization of the OR while also striving for a leveled bed occupancy and a balanced relative OR assignment for the specialties.

To address the uncertainty of future patient characteristics, we consider the surgery durations and the downstream to the nursing wards in a probabilistic manner. For the latter, we follow the approach of Schneider et al. (2020). For the first aspect, we devised a column generation based approach in which, assuming that individual surgery durations follow a log-normal distribution, we employ the
Fenton-Wilkinson method to estimate the distribution of the total sum of individual surgery durations. When this distribution is known, it becomes feasible to identify pairs of specialties with corresponding surgery counts that can be scheduled within our overtime restriction. The resulting model that includes this incorporation is referred to as the Log-normal Column model.

For our research, we use historical data provided by the Sophia Children’s Hospital. The data included properties about the patients’ surgeries and bed assignments. Due to the presence of errors in the data, we conducted preprocessing before utilizing it as input in our modeling. Additionally, we conducted goodness of fit tests to assess whether adopting the log-normal distribution for surgery duration was genuinely superior to the normal distribution. Our analysis revealed that, for the majority of instances, the log-normal distribution outperformed the normal distribution. This was the case for individual surgeries, as well as the Fenton-Wilkinson approximation for the duration of multiple surgeries.

We compared the performance of our Log-normal Column model to two other models which assume normality for the surgery durations. One is, similar to the Log-normal Column model, created with the column generation based approach, while the other is the model described by Schneider et al. (2020). The two column generation based approach models performed significantly better than the model proposed by Schneider et al. (2020). Furthermore, we compared our Log-normal Column model to the real-life situation with the help of a simulation.

Principal Component Analysis (PCA) is a mathematical instrument beneficial for its dimension reduction whilst keeping the most important data. Due to its advantages, PCA is chosen to handle a substantial amount of data. In this thesis two questions are answered: what variables influence a pupil's attainment test score using linear regression and whether PCA provides better linear regression models? The data used in this thesis is provided by DUO, the Dutch Executive Agency for Education. The data contains information about pupils who completed the attainment test in 2008-2013. This thesis starts with a brief description of the data set used for the research and some background information about PCA. Before linear regression can be used, the data is preprocessed. Creating a linear model with all variables resulted in the largest absolute coefficients for teachers' secondary school recommendations. When PCA is applied, it gives great insight into which variables are (likely) dependent on each other: dependent not only in the sense of linear dependency but also the influences on each other in general. Furthermore, PCA also indicates which variables are most likely to have a significant impact. When the data set is free of linearly dependent variables, PCA may give worse fitted models. However, the models are better than models with randomly chosen variables.