Intention aware routing system is a route-planning algorithm for electric vehicles that minimizes overall travel time by taking into consideration congestion at charging stations. This thesis extends this algorithm to allow choices to be made based on prices at charging stations. The goal of this thesis is to find a way to minimize maximum congestion while maximizing overall profit across the stations. To achieve this an optimal price has to be calculated. To this end, a formula is devised and applied to several graphs.

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.

Velotech Solutions (VTS) is a company specialised in detecting damages in public spaces, such as road damages, non-working light posts or crooked traffic signs. This detection happens by bike or by car, and covers every street in the city or neighbourhood. The routes for navigation are currently created by hand. In this thesis, a proposal is given for the first step of automating this process meeting the requests of Velotech Solutions. A mathematical model is formulated for creating the routes. Firstly, the basic model is formulated to minimize the total distance of all routes that are created. Secondly, minimization of self crossings in every route is added. This is the main request, to prevent routes from becoming too complicated for the navigation devices and cyclists. Thirdly, two solution methods are presented. In the first one, all routes are created at once. In the second one, routes are created one-by-one. The methods are applied to the neighbourhoods Parkwijk and Boeier. From the results, the conclusion is drawn that the first solution method gives the most logical routes. However, the second method, is able to handle larger sets of data, since the solution space is smaller when creating only one route at the time. Lastly, recommendations for further research are given. These include research on the input parameters, the behaviour of the second method on larger datasets and using heurisitcs to solve this problem instead of exact solution methods.

Facility location problems are an important set of problems within the field of optimisation. These problems consider which facilities to open out of a set of possible facilities and how to assign users to the open facilities. Most of the facility location problems studied have a linear objective. In this thesis, we consider a facility location problem with a quadratic objective, the Balanced Facility Location Problem (BFLP). This problem, and facility location problems in general, quickly becomes difficult to solve for standard MIP solvers as the input size increases. The difficulty of this problem is further supported by it being a NP-hard problem.

Hence, we develop three heuristics for the BFLP: two greedy heuristics and one local search heuristic. These heuristics are adapted from heuristics used for the standard Capacitated Facility Location Problem (CFLP).

The idea behind the first greedy heuristic is to close one facility at a time, starting with all facilities being open, until we have as many facilities open as the budget constraint of the BFLP dictates. At each step, the best facility to close is closed. Apart from adapting this heuristic to accommodate the slightly different constraints of the BFLP, we also make some further adjustments in order to reduce the running time.

The second heuristic that we adapt is a heuristic that instead of closing facilities one at a time, opens facilities one by one, until we reach the budget of open facilities that the BFLP allows. These simple heuristics perform very well in practice on both small and large instances of the BFLP.

Lastly, we discuss a local search heuristic, which attempts to improve a solution to the BFLP by opening one facility and closing another facility at each iteration. The local search only improves marginally upon the results of the greedy algorithms.

For use within the heuristics for the BFLP, we require fast heuristics to solve a subproblem of the BFLP, the problem of assigning users to facilities where the set of open facilities is fixed. Hence, we develop three heuristics for this subproblem and also adapt a previously developed heuristic to be optimised for its use within the BFLP heuristics.

Our heuristics achieve results that are similar or better than what a MIP solver achieves and find a good solution in significantly less time. Especially when the MIP solver struggles, due to the size or limited capacity of the BFLP instance, our heuristics are able to outperform the MIP solver.

Surgical scheduling is a complex task that requires consideration of various factors, including the probability of overtime. In this study, we address the research problem of surgery scheduling while accounting for the likelihood of exceeding scheduled operating room (OR) time. To tackle this problem, we employ integer linear programming (ILP) models to determine the optimal number of surgeries per group, with the objective of maximizing OR utilization while incorporating the probability of overtime as a constraint.

To capture the probabilistic nature of surgery durations, we investigate suitable probability distributions. Existing literature suggests that surgery durations follow a lognormal distribution. However, since the sum of lognormally distributed random variables lacks a closed form solution, we initially assume a normal distribution for analytical convenience. Subsequently, we approximate the lognormal distribution using the Fenton-Wilkinson method to account for its realistic behavior. To incorporate the
lognormalistic behavior and solve the ILP models efficiently, we employ a column based approach. This approach enables us to handle the complexities introduced by the lognormal distribution. Our study utilizes data provided by a hospital in the Netherlands, including information on surgeries, specialties, groups, and the master surgery schedule (MSS). Given the consideration of both normal and lognormal distributions for surgery durations, we assess the goodness of fit using appropriate statistical
tests.

Our results reveal that using averages or expected values yields the highest OR utilizations. However, there is a discussion regarding the validity of this method, as it does not explicitly incorporate the probabilistic overtime constraints. Nevertheless, we observe that all methods include cases which
surpass the predetermined overtime threshold, suggesting that utilizing averages or expected values can be a valid alternative. However, utilizing averages or expected values gives rise to high percentage
of cases surpassing our overtime threshold. So, we suggest to use a method which explicitly uses the probabilistic nature of the surgery durations.

During the examination of our methods, we had to take a minimum number of mandatory scheduled surgeries for each group into account. This means that another dataset, with different mandatory numbers, might lead to different results. Additionally, we noticed that our overtime definition might not be the most optimal, as we still have cases that surpass our overtime threshold. In future research, it would be valuable to include financial and staff factors, which can further enhance the scheduling process.

Overall, this study contributes to the field of surgery scheduling by addressing the probability of overtime and presenting insights into the trade-offs between OR utilization and the inclusion of probabilistic
constraints. Further research can build upon these findings to refine the scheduling approaches and incorporate additional factors for a more comprehensive solution.

The real-life Vehicle Routing Problem (VRP) is the problem in which a set of vehicles needs to perform a set of tasks such that we have a shortest total driving distance. Such problems can be solved using construction algorithms. Finding the best-performing construction algorithm is time-consuming because these algorithms consist of many different elements, which differ between algorithms. In this thesis, a Neural Network (NN) model is built that predicts the best-performing algorithm from a pre-determined set of algorithms for a specific input case. These predictions are based on problem features extracted from real-life data. For our first NN model, we evaluate the best settings with a grid search, which leads to a model with a mean-squared error of 0.147 and an accuracy of $58.6\%$. We try to improve this original model by data balancing and varying the input features. First, we balance the data using downsampling and oversampling performed by an Integer Linear Program (ILP), which does not lead to a better-performing NN. Secondly, we add more input features to the model, which leads to a slight improvement because the model has more information about the problem at hand. After, we perform an elaborate feature analysis using permutation feature importance, SHAP, and Greenwell numbers. Based on this analysis, we reduce the number of input features to only 12. This reduction leads to the best-performing model with a mean-squared error loss of 0.125 and an accuracy of 61.7\%. To investigate whether our prediction model indeed improves the routes using the predicted algorithm, we look at the distribution of predictions. For each company, we replace the algorithm in use with the algorithm most often predicted by our model. This replacement indeed improves the results for most of the considered companies.

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 global push for renewable energy faces challenges due to the unpredictable and inconsistent nature of wind and solar sources. These inherent characteristics of renewable energy sources add volatility to the electricity markets. In response, electrical energy storage (EES) emerges as a solution for maintaining grid flexibility, stability, and reliability. Therefore, it is important to understand the potential interdependence of the wholesale electricity markets and the EESs.
This thesis focuses on short-term EES scheduling, comparing pumped hydropower storage (PHS), compressed air energy storage (CAES), and battery energy storage systems (BESS). This thesis aims to optimize EES scheduling, which includes charging and discharging actions, in the intraday electricity market, considering market price uncertainties. Storage decisions are optimized for one day (24 hours) from the perspective of the storage owner, and its objective is to maximize its profit through market operations. The research introduces a two-stage stochastic programming approach with a rolling horizon method (SORH) to adapt to changing conditions of the intraday market throughout the day.
The results of SORH, its deterministic counterpart (DORH), and simple deterministic optimization (DO) are compared by implementing a case study organized in four typical days based on trading data from the German electricity market. SORH consistently outperforms DORH and DO and is a suitable optimization strategy. SORH reaches on average 72 percentage of the theoretical optimum, where all prices are known in advance. Moreover, SORH offers opportunities for speculative trading using the storage as an option rather than only physically operating the storage. For a practical application of the model, future research could explore methods to match the current day with representative typical days to construct relevant price scenarios.

In this thesis, a simulated annealing algorithm is implemented to optimize the efficiency of a tandem solar cell. The efficiency of a tandem solar cell is approximated by the current of the tandem solar cell. This current is determined by the simulation program GenPro4. Firstly, the general concepts of simulated annealing is described. After understanding these concepts, a simulated annealing algorithm is implemented for our specific problem. This algorithm includes the handling of discrete variables which describe the structure of the solar cell. The results contain multiple variants of the newly implemented simulated annealing algorithm, which differ in the used temperature schedule. Finally, a conclusion is made that a temperature schedule with a slower convergence gives the best results. However, one should consider a slightly faster convergence whenever there is a need to reduce the computational time. Moreover, one should write their own implementation of a simulated annealing algorithm when dealing with discrete variables, thus not use the provided function of MATLAB.

This study researches how station-based bike-sharing can be implemented in strategic transport models. Implementing station-based bike-sharing is a challenging topic, as it requires to combine two modelling techniques. The first is modelling transport tours to make sure that a person who rents a bike returns the bike to the same station. The second challenge is to model multimodality, because shared-bike are always used in combination with other modes. The most prevalent approach on the market to combine the topics is the two-step mode-choice approach. However, the two-step mode choice approach has three important limitations to model SB-bike-sharing. Therefore a new approach is proposed in this study; “The tour-based mode-chain and station choice approach”. Based on a small-scale theoretical case-study the new method gives promising results regarding modelling the combination of tour-based-mode-choice and multimodality.

Tandem solar cells are a new type of solar cells that are currently being developed. Soms proporties of these solar cells are variable. In this scription, it is studied how genetic algoritms can be applied to optimize these tandem solar cells. Genetic algoritms are algorithms that find a good solution using the principles of evolution theory. It is studied what the influences are of several choices. In this way, this scription gives which genetic algorithms should be applied in several situations. Hereby, it provides insight in how genetic algorithms can be applied to optimize genetic algorithms.

The introduction of Robotic & Autonomous Systems (RAS) in modern combat seems inevitable, with clear advantages like reduced risk and extensification of personnel. To scope this research, persistent reconnaissance with heterogeneous Unmanned Aerial Vehicles (UAVs) is selected, being one of the more prominent applications. Despite continuous efforts developing advanced hardware and algorithms, real-world implementations are still lacking. The root cause seems to be that state-of-the-art algorithms deal insufficiently with the high dynamics and uncertainty in a military environment. Currently, the military uses intent-based Command & Control (C2) to deal with precisely these challenges, as they are inherently tied to combat. Therefore, a conversion of the communicative principles of C2 towards a mathematical approach applicable to RAS seems promising, of which intent-based coordination is the result. To be able to deal with the high dynamics and uncertainty, three requirements are formulated. First, flexibility is needed to revise the solution locally. Secondly, robustness against unreliable communications is necessary, and thirdly, scalability is required to ensure the performance can also be maintained for larger Areas of Interest (AOIs) and larger teams of UAVs. The Single-Agent Reconnaissance Problem (SARP) and Multi-Agent Reconnaissance Problem (MARP) are formulated as a compact combination between the visitation frequency and coverage level approach for persistent reconnaissance. Based on advancements made on teamwork and organizations for Multi-Robot Systems (MRSs), a coordinative method is formulated. This coordinative method partitions an AOI for the MARP into smaller disjoint subsets, such that separate SARPs can be solved independently by each UAV. The key contribution of this research is that this coordinative method functions based on intent, enabling the required flexibility, robustness, and scalability. It does so by constructing a hierarchy of supervisors that perform distributed cooperation on overlapping subsets. This distributed problem is solved using the novel Complex Concurrent Bounding (CCB), which is an adjusted version of Concurrent Forward-Bounding (ConcFB) for Distributed Constraint Optimization Problems (DCOPs) with complex local problems. Additionally, a lower bound is generated to benchmark the obtained solutions, based on the pricing step of branch & price, by applying column generation to a reformulated version of the MARP. Intent-based coordination shows flexibility against perturbations of the AOI. Especially when changes are spread out, it is not necessary to revise the solution as a whole immediately. Furthermore, if the cooperation is preemptively terminated due to failing communication, robustness is observed against the resulting suboptimal subsets. Especially for higher levels in the hierarchy, the suboptimal solutions can partially be corrected by lower levels. Lastly, the method shows a sublinear growth in computation time for increasingly larger problem instances. As such, intent-based coordination provides an exciting approach to maintain the performance of RAS even in more challenging environments.

With the increasing number of electric vehicles on the road, the routing problem has become more complex. As charging electric vehicles takes longer than fueling non-electric vehicles, congestion can occur at charging stations. This might lead to the shortest route not being the fastest route, due to long waiting times at the stations. By communicating the intentions of each vehicle, the vehicles can spread out over multiple stations. This thesis investigates the eect of such a routing system on the profitability of charging stations. In particular, the influence of a charging station's location on its profitability has been researched. In order to do this, a pricing model has been developed to extend the routing model. It has become clear that due to the intention-aware routing, the number of visits at stations is harder to predict, and there is not always a clear pattern to be found between the location and the number of visits. This research does, however, propose an optimisation model, which can decide where to build a new charging station, such that the number of visits will be the highest.

This thesis aimed to aid ErasmusMC in the workforce planning process of deciding how to implement training among the nursing personnel in order to build a more flexible workforce, so the hospital can be prepared for fluctuating and unexpected demand, while minimizing the costs of doing so.

To accomplish this, a mathematical model was developed taking into account the structure of the nursing personnel within the hospital, and the structure of how training among nurses is implemented. Since the planning was aimed to be done on a daily basis, the contractual obligations between nurses and the hospital had to be respected as well.

The resulted model was tested using real data provided by Erasmus MC, and with the mathematical optimization solver Gurobi. Consequently, a Genetic Algorithm (GA) approach was proposed; this heuristic accomplished to outperform Gurobi when applied to the biggest two instances considered in this project.