Patients visiting a hospital for elective surgery often have multiple consultations with a surgeon before undergoing surgery. Hospitals discern between different types of consultations, and make a schedule allocating timeslots of outpatient department sessions to these different consultation types several weeks in advance. Changing the proportion of consultation types affects the patient waiting lists for both consultations and surgery. However, the precise consequences of such interventions are uncertain, as not all patients follow the same treatment pathway. Furthermore, as these planning decisions are made far in advance, they are based on an uncertain prediction of future waiting lists. The goal is to use these interventions to control waiting lists, in order to reduce waiting times for patients and ensure that all available time capacity in the outpatient department and operating room is used. This problem is referred to as the timeslot allocation problem. In this thesis, we study the performance of various solution methods in achieving this goal.

The problem is modelled as a Markov decision process (MDP). As the state space is very large, the problem does not admit an exact solution. Therefore, least-squares policy iteration is used to find an approximate solution. We also formulate an (integer) linear program which is used to solve a deterministic variant of the MDP, and investigate some simple decision rules.

This thesis features a case study at the Sint Maartenskliniek, a hospital focusing on orthopaedic care in Nijmegen, the Netherlands. Data from the hospital is used to make a simulation with which solution methods can be tested and compared. We find that all methods improve on the static roster method used by the hospital, with the linear program leading to the best results. Furthermore, planning less far ahead allows for a better prediction of the state for which to plan, and so also leads to better performance. In the case of SMK, we recommend fixing 60\% of the timeslots using a static roster method 12 weeks in advance, and using the integer linear program to schedule the remaining 40\% of appointments 6 weeks in advance.

Over the past three decades, the singular value decomposition has been increasingly used for various big data applications. As it allows for rank reduction of the input data matrix, it is not only able to compress the information contained, but can even reveal underlying patterns in the data through feature identification. This thesis explores algorithms for large-scale SVD calculation, and uses these to demonstrate how the SVD can be applied to a variety of fields, including information retrieval, recommender systems and image processing.

The algorithms discussed are Golub-Kahan-Lanczos bidiagonalization, randomized SVD and block power SVD. Each algorithm is implemented in Matlab and both error and time taken by each algorithm are compared. We find that the block power SVD is very effective, especially when only the truncated SVD is required. Due to its simplicity, speed and relatively small error for low-rank matrix approximation, it is an ideal method for the applications discussed in this thesis.

We show how the SVD can be used for information retrieval, through Latent Semantic Indexing. The method is tested on the Time collection and we find that the SVD removes much of the noise present in the data and solves the issues of synonymy and polysemy. Then, SVD-based algorithms for recommender systems are presented. We implement a basic SVD algorithm called Average Rating Filling, and a (biased) stochastic gradient descent algorithm, which was developed for the Netflix recommender-system prize. These are tested on the Movielens 100k dataset, resulting in the best performance by biased stochastic gradient descent. Finally, the SVD is used for image compression and we find that, while not very useful for face recognition, the SVD could provide a time- and space-efficient method for searching through an image database for similar images.