The problem considered in this thesis is the box set optimization problem. In this problem the goal is to find the optimal dimensions of a number of shipping boxes which have to provide an optimal fit on a set of items. The application considered is e-commerce, and hence the number of items is relatively large compared to other applications found in literature. The literature describes multiple problem formulations where a small num- ber of optimal shipping boxes are selected from a large set containing candidate boxes. However, since the instances considered in e-commerce application are often too large to be solved in this way, we introduce a simulated annealing heuristic solution method. In this way we are able to generate box sets con- taining 10 to 20 boxes with centimeter accuracy for data sets containing up to XX single item orders. We pay special attention to an algorithm to very efficiently calculate the objective value associated to the fit of a selection of candidate boxes on a set of items. This is done by assigning items to shipping boxes using a pre-calculation table. Because the heuristic can process a larger set of candidate boxes than the exact solution method, ultimately results of the heuristic are better than those found by the exact solution method. Finally we generate multiple box sets based on the input data provided by the industry partner bol.com, and compare the results. We conclude that on almost all tested instances, the total amount of carton used can be reduced by more than XX in combination with a total send volume reduction of over XX in comparison with the box set that is currently used. Furthermore, we answer additional questions. We find that minimizing the total amount of carton used, instead of minimizing the total volume send, can lead to a result that is most desirable in practice. We discover that pack-line specific, warehouse specific or seasonal specific box sets provide none to only minor additional improvements.

In the current economy, there is an increasing focus on sustainability. Green transport solutions, like rail freight, are becoming more and more popular. We will look into the shunting operations at Kijfhoek shunting yard. This yard functions as the central hub for DB Cargo Nederland and connects the Port of Rotterdam with the hinterland. About 2000 cars are sorted at this yard each week. At the yard, there are 43 parallel classification tracks. Shunting problems come in many shapes and sizes but are generally hard to solve. To that end, we will use both exact algorithms and heuristics to solve the shunting problem at Kijfhoek within reasonable time. In practice, it is not known at the beginning of the planning horizon which cars will arrive. To that end, we will create general solutions which will be updated over time when new information becomes available. We test how well the solutions perform and/or can be reoptimized with the latest information using a simulator. We find that our solution approaches can generate solutions for instances with 28 classification tracks of similar quality as solutions found for the same instances with 43 classification tracks with complete information at the beginning of the planning horizon. Furthermore, with incomplete information, we find good solutions with 32 classification tracks.

This research is conducted in collaboration with the Sophia Children's Hospital (SCH). The hospital wants to provide their patients with more detailed information about when a patient is approximately scheduled to have a surgery. The first step is to create a model which optimises the operation room (OR) schedule and indicates when different kinds of surgeries are planned. This information, combined with the waiting list, provides insight in when a surgery of a specific patient is scheduled. In a hospital, different departments work together to treat the patient as good and efficient as possible. If a patient needs a surgery, not only an OR is needed, but also a bed at a ward which matches the patient's needs. The goal of this thesis is to use the different resources of the hospital as efficiently as possible. This is done by not only optimising the utilisation of the OR, but at the same time levelling the bed occupancy of the different wards. The levelling of the bed occupancy is done by minimising the maximum number of used beds at each ward. Because, if we minimise the maximum, we force that the patients are spread out more evenly over the day. For each specialty, the patients are divided into patient groups based on historical data using a constrained $k$-means clustering algorithm. For each patient group, information is gathered about the length of stay (LoS) and the surgery duration of patients in this patient group. Next to that, the number of patients in a patient group indicates how often a patient group needs to be scheduled at least. The probability distribution of the surgery duration is taken into account when deciding at which day, at what time, and in which OR a surgery is planned. A patient group can only be scheduled during OR shifts assigned to the corresponding specialty. At the same time, the levelling of the bed occupancy is taken into account. After some constraints are linearised, this model can be formulated as a mixed integer linear program (MILP). However, the model has a large number of variables. Therefore, column generation is used to split the model into smaller subproblems per specialty. Some of the pricing subproblems take a lot of time to optimise. For that reason, we set some time limits both on the runtime of the pricing subproblems and the runtime of the entire algorithm. Column generation does not guarantee an optimal solution of our MILP. However, the objective value of our MILP improves over time, when new columns are added to the set of available columns. This indicates that column generation can be used to optimise our model. In this thesis, several versions of the model are presented. For example, the schedule is different if the bed occupancy is calculated every hour or of every fifteen minutes. Next to that, the model can either be more focussed on maximising the OR utilisation or on levelling the bed occupancy.

The logistics industry is being modernized using information technology and robots. This change encompasses a new set of challenges in warehouses. Recently, some companies have started using robot fleets to sort products and parcels. This thesis studies those systems, and researches the combinatorial problems that arise within them. Three main optimization problems are identified: 1. Finding an optimal layout of the sorting system on the warehouse floor; 2. Allocating products or parcels to be sorted to robots; 3. Finding paths that all robots can follow concurrently, without colliding. These problems are considered one by one. The first problem is understood on an intuitive level, while the other two are considered more closely. For both problems, several algorithms are considered. Some utilize greedy heuristics while others model the problem at hand precisely using integer linear programming methods. The algorithm’s real world performance is then assessed using a simulation. Slow, ILP-based algorithms are found to produce optimal solutions for small instances. However, they don’t scale well, and are unable to solve large instances. Greedy approximation algorithms solve all problem instance sizes tested, but produce solutions of lower quality.

Phylogenetic trees are commonly utilised in evolutionary biology. These trees represent the evolution of a set of species. In case of gene transfer however, a phylogenetic tree is insufficient. In such cases, tree-based phylogenetic networks are more suitable as they can depict reticulate evolution. Nonetheless, tree-based phylogenetic networks have their limitations as they are unable to represent reticulate events occurring between different environments, families, or lineages of species. To address this, forest-based networks offer a solution. A forest-based network is a collection of leaf-disjoint phylogenetic trees with arcs added between different trees in case of reticulate evolution. In this thesis, an integer linear programme (ILP) is created to determine whether a binary phylogenetic network is forest-based. It is important to note that this thesis exclusively focuses on binary phylogenetic networks. This ILP model is expected to be valuable in the development of new models and algorithms for both binary and non-binary phylogenetic networks, thereby enhancing the understanding of reticulate evolution. Additionally, the ILP may lead to time-related challenges when processing bigger phylogenetic networks.

Phylogenetic networks represent the evolutionary history of organisms and the relationships among them. In the field of phylogenetics research has been done to reconstruct these networks. Several methods for reconstructing those networks have been developed over the years. One of them is the softwired parsimony score and another, a fairly new method, is the parental parsimony method. In theory this is a better and more accurate method, but before this thesis, it was not tested yet. In this thesis, we compare the softwired and the parental parsimony method in practice by implementing the methods and calculating their parsimony scores. The results will show that the parental parsimony is a better and more accurate method in practice as well.

Phylogenetic networks are used to represent evolutionary histories of a set of taxa. In this thesis, we look at a certain network class, called orchard networks. In the beginning of this thesis, definitions concerning phylogenetic networks and specifically orchard networks are introduced. The characterization of orchard networks involves time-labelling of the vertices. Then, an algorithm is given to see if a given network is orchard. The next section, explores a non-recursive labelling of a given network. There is not an explicit algorithm for the labelling. An algorithm for the labelling is given. The last chapter is about non-orchard networks. It contains multiple actions that can be performed on the non-orchard networks in order to transform the non-orchard networks into orchard networks.

In this thesis Bayesian Networks are used to predict European football matches between the years 2008 and 2016. The goal of this research is to see how the structures learned by different Bayesian Network learning algorithms influences the predictions. First the data is explored and modified to be used for Bayesian Networks and secondly the theory is explained using examples. Finally the theory is applied on the data and the structures are learned with the help of a bootstrap method and the predictions are validated using 5-fold cross validation. We can conclude that the networks learned by the algorithms and with the help of an expert give a good representation of the underlying relationships, but are not very good in prediction the end result.

The companies CQM and EVO-it work together to help many different companies with solving their vehicle routing problems. EVO-it provides the interface of the software that the companies can use for route planning and CQM provides the technology that is used to solve the route planning problems, which concerns a lot of mathematical programming. The difficulty of solving these problems is that real-life problems usually deal withmulti-attribute vehicle routing problems, which are problemswith multiple characteristics, such as time windows and vehicle restrictions. These characteristics influence the solving process and the quality of the solution of the method used to solve the problem. Since these attributes can vary a lot per company, it is a difficult task for CQM to provide the best solving method for all problem types. Even though CQM has provided a very complex method that can handle many problems, it is unclear how far from the optimum solution the provided solutions are. The goal of this project was to investigate the improvement possibilities of the current method used by CQM. In this thesis many different solving methods for the vehicle routing problem are evaluated and their qualities are discussed. Furthermore, information from the companies that are using the software of EVO-it is collected. With this information an overview of the problem types occurring at these companies is provided. Such an overview had not been made before and will be very useful for CQMand EVO-it to make more problem type specific improvements to the solving method. Furthermore, this thesis describes two exact methods for solving vehicle routing problems similar to the real-life problems occurring at the clients of EVO-it. One of these methods uses a three-index flow formulation and the other one uses a set partitioning formulation and is based on the method described by Baldacci andMingozzi. It is shown that this latter method can be used to solve instances with up to 40 orders. In addition, both methods can deal with several complicated attributes, including capacity constraints, distance constraints, different type of costs and heterogeneous vehicles. Moreover, it can even deal with instances where not all orders can or need to be scheduled. In such a case, the orders that are not scheduled will get a penalty. To the best of my knowledge, no previous exact method was able to deal with such instances.

Van Iersel, Moulton, and Murakami (2020) proved that a level-2 binary phylogenetic network can be uniquely reconstructed based on the matrix of mulitsets of the distances of the leaves. Using a handful of lemma’s each describing the steps of identifying cherries, uncontained leaves and blobs in the network, I created an algorithm for deconstruction the theoretical network corresponding to the matrix, and constructing the network based on the deconstruction steps. Unfortunately, this algorithm is not of polynomial time, as in the deconstruction programs are run that take time proportional to the sizes of the multisets of distances, which are upperbounded by 4n, where n is the number of leaves in the network. This algorithm is tested on more than 35000 networks with 10 to 24 leaves, and resulted in no errors.

In a semiconductor factory, integrated circuits (or chips) are constructed on top of slabs of silicon, called wafers. The construction of these wafers is complicated and many different processing steps are needed to gradually building the chip layer by layer. Of these steps, photolithography uses the most expensive equipment. Therefore, the photolithography equipment is often the bottleneck of the factory. Photolithography is used to transfer the geometric pattern of a chip on a wafer. First a light-sensitive photoresist is put on the wafer. ThenUV light is sent through a photomask on the photoresist. The exposed parts of the photoresist will chemically react, creating the pattern. After the exposure, chemical reactions and metal depositions make a layer of circuits on the wafer. In this thesis, we try to increase the production of the semiconductor factory by reducing the time needed for the photolithography. In the first part, we look at themachine level. The time to process a wafer on a lithography steppermachine is determined by different elements of the process (Chapter 2). It turns out that the blade movement required in the exposure step has a significant impact total time required to process a wafer. The blade movement in turn depends on the order in which the different images are processed. Hence we want to find an ordering of the images, such that the blade movement is minimized. This problem turns out to be equivalent to the a priori traveling salesmen problem in the scenario model. The practical problem instances found are solved a limited amount of time using an integer linear programming solver and the average blade movement is reduced by approximately 20%, which reduces the average exposure time 1.6%. @en