During the COVID-19 pandemic, many elective surgeries had to be rescheduled as resources suchas beds and ventilators were reallocated, causing significant delays in patient care. To avoid such disruptions in the future effective resource management and planning approaches for elective surgery are essential. Optimisation is a commonly used method to enhance elective operating theatre scheduling, it is a technique used for mathematical modeling. It can integrate various criteria to maximise benefits and minimise costs within specified constraints. However, optimisation alone often falls short in addressing the complexities and required flexibility of operating theatre scheduling. This is where simulation can build upon these limitations. Simulation techniques can model system behaviour by replicating real-world processes, introduce uncertainty, and evaluate responses to different policies, helping to identify bottlenecks and improve system efficiency. Sequencing optimisation and simulation can test theoretically sound solutions under real-world uncertainties and complexities. This leads to the following research question:

“How can Discrete Event Simulation evaluate optimisation-generated Master Surgery Schedules for operating theatres?”

The research question focuses on a Master Surgery Schedule, which coordinates different surgical specialities, sharing OTs and pre- and post-surgery resources. While this approach increases resource utilisation, it also adds complexity by needing to accommodate the varying requirements of each speciality. The research aims to evaluate different Master Surgery Schedule using Discrete Event Simulation to contribute to the optimisation model.

Overall, the use of the Discrete Event Simulation model provided detailed insights into the
performance of various schedules. Testing these schedules under different types of uncertainty
demonstrated their robustness, as the behaviour remained consistent across scenarios. By
comparing the schedules side by side, the simulation model effectively evaluated their
effectiveness, ensuring the intended purposes were served and identifying areas for improvement.

The research specifically considers Discrete Event Simulation as this method can queue patients for different resources and have them move throughout the system based on decision rules. It is also a standard applied method for modelling healthcare systems. Both Discrete Event Simulation and optimisation are standard methods for improving OT scheduling. Even sequencing the methods has been proven to contribute to OT scheduling. However, applying this approach to a Master Surgery Schedule is new and introduces additional complexity related to the shared OTs and pre- and postsurgery resources.

To explore this research question, a case study was conducted at Sophia Children’s Hospital in
Rotterdam. Previous research developed the Master Surgery Schedule using an optimization
model, resulting in four different schedules. These schedules either balanced ward leveling and operating theatre utilization equally or prioritized ward leveling. They also varied in computational requirements, as the model updated the bed availability either every 15 minutes or every hour. This research categorizes 18 different surgical departments into 50 groups based on their surgery duration and length of stay, assigning time slots to these groups in the schedules.

This research uses these groupings to fit different distributions for the input variables of length of stay and surgery duration. Five different types of distributions were tested for each group, and the best-fitting distribution was assigned. Additionally, previous research provides a schedule for ward capacity and establishes decision rules for patient management. In collaboration with the hospital, the probability of Intensive Care assignment and the various decision rules were validated.

The sensitivity analysis revealed a slight overestimation of surgery duration compared to the test data, but this did not significantly impact outcomes. The model is more vulnerable to ward capacity and length of stay, which were then selected for scenario analysis. The schedule prioritising ward levelling and checking availability every 15 minutes outperformed others, effectively addressing ward unavailability, the primary bottleneck. However, increasing capacity improves the number of successful surgeries but also leads to more cancellations due to operating theatre unavailability and increased overtime occurrences. This highlighted a trade-off between operating theatre utilisation and other Key Performance Indicators.

The sensitivity analysis revealed a slight overestimation of surgery duration compared to the test data, but this did not significantly impact the overall outcomes. The model was found to be more sensitive to ward capacity and length of stay, which were then selected for scenario analysis. Among the different schedules, the one prioritizing ward leveling and checking bed availability every 15 minutes outperformed the others, effectively addressing ward unavailability, which was identified as the primary bottleneck. However, while increasing ward capacity improved the number of successful surgeries, it also resulted in more cancellations due to operating theatre unavailability and increased overtime occurrences. This finding highlighted a trade-off between operating theatre utilization and other Key Performance Indicators.

In line with the literature, the research reveals that striving for increased operating theatre
utilisation puts excessive pressure on other resources. Ward unavailability is identified as the main reason for surgery cancellations, indicating that wards require even greater focus. An increase in ward capacity had the best outcomes during the scenario analysis, showing that this is the biggest bottleneck in the system.

The simulation model identified new parameters for the optimisation model and highlighted
weaknesses in the system to be improved upon. Future research should explore ward capacity in greater detail and develop better methods for sharing resources across different operating theatres and wards to reduce the differences in utilisation. Additionally, further research could investigate other causes of surgery cancellations and refine the definitions of surgery groups

In the past few years, rapid strides have been made in the modelling of complex systems due to the advent of machine learning (ML) technologies. In particular, the transformer neural network (TNN) has gained a lot of attention due to its powerful “sequence-to-sequence” modelling for several tasks in science and engineering. Predictive ML models are trained to learn the relationship between a set of input and output data so that new input data can be mapped to their expected output values. This gives us the ability to understand the key factors impacting a system and to make predictions about its future behaviours. This research investigates how to use TNNs for decision making by optimising the output of a TNN. To this end, a non-convex mixed-integer non-liner programming (MINLP) formulation for a trained TNN is proposed. The proposed formulation facilitates solving problems with TNNs embedded
to global optimality. The effectiveness of the formulation is tested on three case studies consisting of an optimal trajectory problem, a verification problem, and a reactor optimization case study. Results show that optimisation over small TNNs can be achieved in under 3 minutes. However the tractability of the formulation quickly vanishes for larger models, highlighting the need for further research to refine the proposed formulation.

In the near future, next-generation telescopes will be able to observe Earth-like exoplanets illuminated by their parent stars for long periods of time. As the distance between exoplanet and observer is enormous, exoplanets will only make up a pixel on our image. However, the observed intensity of this pixel will fluctuate over time as the exoplanet rotates about its axis and orbits around its parent star. These fluctuations in the reflected light contain information about the planet’s surface. Previous researchers have developed a retrieval method known as spin-orbit tomography which uses these intensity fluctuations to construct a surface map of the exoplanet assuming fully diffuse reflection as a model for the reflection of starlight. In this thesis, we aim to build on this method by introducing two new reflection models, namely Fresnel and Lommel-Seeliger reflection, and by using this composite reflection model for the starlight we attempt to reconstruct the surfaces of exoplanets based on their observed light curve. We will derive an analytical expression for the observed intensity of the light reflected off an exoplanet. Next, we will simulate intensity observations along the orbit of an exoplanet with a pseudo-randomly generated surface containing terrain types found on Earth.
As we assign a measure of reflectance for each reflection model, we will construct three distinct reflectance maps for one planet, nd simulate the observed light curve by linearly transforming these maps. Afterward, we attempt to retrieve the reflectance maps from the observed signal by inverting the transformation.
We show that the retrieval of all three maps is successful if the light curve is observed without noise, even when the number of samples is low. If artificial shot noise is imposed on our signal, we are still able to retrieve glossy reflectance maps for Lambertian and Lommel-Seeliger reflection by truncating the transformation matrix. Lastly, we show that even if the original light signal originates from an exoplanet that only reflects according to the Lambertian model, then the composite reflection model still retrieves the Lambertian map accurately. On the other hand, if the original light curve is simulated by the composite reflection model, then the Lambertian method does not retrieve an accurate surface map.

Demand for online grocer Picnic has increased exponentially over the past years, and their truck transport operation must scale with it. Given the resource constraints at all warehouses, as well as other specific restrictions, this poses a Multi Depot Pickup and Delivery Problem with Resource Constraints, for which no good solutions are found to date. The goal of this thesis is to develop an algorithm that provides good solutions to this problem within 30 minutes.

This thesis presents three solution methods to solve this problem. The first is an Adaptive Large Neighbourhood Search (ALNS) algorithm closely related to earlier research. We propose a mechanism with only linear time additional complexity to impose the resource constraint. We also demonstrate ways to take additional constraints into account, such as minimum route duration and driver switches. For the second method, dubbed ALNS+LS, we extend the ALNS with local search heuristics to enhance its performance. As a third method, we propose a matheuristic novel to this specific problem class. This consists of the ALNS+LS algorithm applied to the problem without resource constraints in the first phase, and imposing the constraints using a Constraint Programming model in the second phase. We show that the ALNS+LS outperforms the other two algorithms on a real-life-inspired benchmark set, and that the matheuristic comes close to the ALNS+LS for small instances. We finally show that the full problem is best solved by decomposing it into four parts and solving these separately.

The growing demand for cardiovascular treatments and the need to control the ever rising health care expenditures require efficient use of expensive resources, such as cardiac catheterization laboratories (cath labs). These in cardiac catheterization specialized operating rooms are labor and capital-intensive. Therefore, a high utilization is desired, although overtime should be prevented. However, this is complex in practice, because uncertainty in procedure duration and the number of patients makes it difficult to predict shift duration. At the moment, scheduling is mainly done by hand and the result strongly depends on the scheduler’s experience. Furthermore, little research is done on cath lab scheduling. Hence, this study aims to further define the cath lab scheduling process, identify the areas of improvement, and explore the usefulness of Monte Carlo simulation to support human schedulers. Schedulers of two Dutch hospitals, the Reinier de Graaf Gasthuis and the HagaZiekenhuis, are interviewed to map the scheduling process and identify the main difficulties. According to the schedulers, the main area of improvement is the estimation of procedure and shift duration, which currently is based on experience and rules of thumb. Based on the process in the HagaZiekenhuis, a Monte Carlo simulation is developed that computes the shift duration, utilization, and number of deferrals based on the blueprint schedule, the distributions of procedure duration and the emergency arrival rate. A first attempt to validate the model is done with input data from the VUmc as reported in another paper, as no historical data of the HagaZiekenhuis was available. The number of simulations required for convergence of the model was found to be at least 300. Next, the utilization, overtime, and undertime of the simulation were compared with these metrics from the VUmc. They were found to be close, even though the scheduling decisions are based on another hospital. To examine the sensitivity of the model, several scenarios are tested, namely, no emergency arrivals, a double amount of emergency arrivals, both halving and doubling the standard deviation of input distributions, adding extra patients to the inpatient waiting list to increase the demand, changing the threshold when patients are deferred and changing the type of input distribution from lognormal to normal. The effect of these scenarios is mainly as expected. Less variation in the output can be obtained by reducing the variance of the input distributions. Additionally, the type of input distribution seems to have limited effect on the output distribution. Furthermore, the effect of changing the deferral threshold, which is stochastic according to the interviews, seems limited. Moreover, no inexplicable behaviour was discovered by inspecting the realizations of the blue print schedule. Lastly, the data of the VUmc was applied to the blueprint of the HagaZiekenhuis, but inspection of the blueprint schedule revealed that the procedure duration in the VUmc data is longer than in the HagaZiekenhuis. This demonstrates that one cannot use the data and blueprint of different hospitals. An attempt was done to correct for this by scaling the distributions such that the mean corresponds to the scheduled duration. This led to more realistic results for some procedure types, although the standard procedure duration appears to not match the average duration for other types. The first results are promising, hence, a more in-depth validation of the model is recommended. The most promising application of this simulation seems the estimation of shift duration given a specific set of patients, integrated in the scheduling software.

The Multi-Agent Path Finding (MAPF) problem is the problem of planning paths for multiple agents without any collisions. There are also many variants such as the waypoint variant, where each agent also has a set of waypoints it must visit before reaching its goal. The colored variant, in which the agents are grouped into teams and each team has a set of targets that need to be reached. And the colored MAPFW variant is a combination of the two. This paper presents an SAT-solver for the sum-of-costs objective for these variants based on the sum-of-costs SAT solver for MAPF. It also introduces a MaxSAT solver for the makespan objective while also minimizing the sum-of-costs, where instead of having a cardinality constraint on the cost it is minimized. Experimental evaluation showed that these methods perform well on different graph types compared to existing algorithms and that MaxSAT solves more instances than SAT but is only optimal in 90\% of the instances.

Enterprise Modelling (EM) is the process of producing models, which in turn can be used to support understanding, analysis, (re)design, reasoning, control and learning about various aspects of an enterprise. Various EM techniques and languages exist, and are often supported by computational tools, in particular simulation. The goal of this thesis is to study the effects and advantages of applying constraint programming (CP) to EM. To the best of my knowledge, no previous study has explicitly combined EM and CP. On the topic of applying CP to EM, this thesis explains where it can be applied, as well as its requirements and advantages. Furthermore, it explains a possible approach where a neural network, trained on a simulation model that represents an enterprise model, is embedded into a constraint program. This approach is supported with experiments, that show typical business objectives can be embedded in a constraint program and find solutions to it in a multi-objective context. The main conclusion is that due to CP being a declarative programming technique, business constraints and goals can be effectively modelled into a constraint program, making the approach understandable and intuitive for business analysts to use. This thesis argues alternative approaches to apply CP to EM can also be realised. Some of these, as well as improvements over the proposed method, are also discussed.

The Port of Antwerp is the second-largest container port in Europe. The rising demand for container transport requires significant investments in infrastructure projects. Macomi helps the Port of Antwerp to determine the effect of different projects on the throughput of the port using simulation. In this thesis, the aim is to create algorithms for the introduced online variant of the lock scheduling problem which are applicable for a real-time simulation. In addition, an algorithmic approach to recover the existing schedule when a vessel is delayed is required. To achieve these goals, three online lock scheduling algorithms are introduced and tested on realistic problem instances. Their run-time is negligible compared to exact methods and the resulting lock schedules are competitive. Assuming a constant lockage duration during scheduling allows the number of interactions to be reduced significantly with a small decrease in lock schedule quality. The online lock scheduling algorithms could also be applied to the problem of disruption management. The results are comparable to the high-performing adaptive large neighbourhood search meta-heuristic.

In this thesis we build a goal based planning framework that takes into account goal priorities. Goal based planning is a type of personal wealth planning, with a focus on the feasibility of an investor's goals. Currently, to take goal priorities into account a dynamic asset allocation is created. We focus on incorporating goal priorities by ensuring goal cash flows reflect investors' preferences, no matter the asset allocation. No money should be spent on less important goals if it jeopardises achieving more important goals. With such a goal cash flow strategy, an investor gains valuable insight into the feasibility of her goals. We build such a framework in two ways. First, we use utility theory. With utility theory, we can quantify an investor's satisfaction with the goal cash flows. For that purpose, we create a total utility function that takes into account goal priorities. Then, we optimise over the goal cash flows such that it results in the highest expected total utility. Second, we use conditional expectations. With conditional expectations, we determine the relationship between earlier wealth and future goal achievability. Therefore, we create a framework with a spending rule based on the conditional expectation. We implement conditional goal cash flows. With conditional cash flows, we create a goal based planning framework that takes into account goal priorities for multi-goal investors.

To reduce the CO2 emissions of the maritime industry, several alternative fuels are being researched to possibly achieve this goal. The absence of an infrastructure for alternative fuels in the current port environment is one of the barriers towards implementation of these high potential fuels. The goal of this thesis project was to create an optimization model which can provide more insight into the initial sizing, phased growth and corresponding cost of an infrastructure needed for maritime transport using different forms of alternative fuels. The corresponding main research question is: "How do the port refueling infrastructures of sodium borohydrate, liquid hydrogen and gaseous hydrogen compare to each other with respect to costs and supply chain set-up in terms of where, when, and at what sizes to build up the production, storage, distribution and refueling facilities?" To answer this research question a single-objective multi-period mathematical optimisation model (Mixed Integer Programming) has been created for the port refueling environment. The most important model innovations are the inclusion of a maritime refueling convention and the possibility to model less conventional alternative fuels such as sodium borohydrate (NaBH4). Furthermore, input for the model has been gathered from several sources. Next, some parameters of the model have been varied to research their effect on the total alternative fuel infrastructure. As a result it has been found that the gaseous hydrogen infrastructure is the cheapest with respect to facility capital costs and facility operating costs, but was the most expensive when looking at transportation of the fuel within the port. The liquefied hydrogen was the cheapest with respect to fuel transportation, but scored average on facility capital cost. Furthermore it is the most expensive infrastructure with respect to facility operating cost. The NaBH4-infrastructure is the most expensive infrastructure when looking at the facility capital cost, but scores average on facility operating cost and transportation cost. Overall the gaseous hydrogen infrastructure was the cheapest infrastructure, followed by liquefied hydrogen. The NaBH4-infrastructure turned out to be the most expensive with the current input. The input parameters for NaBH4 are still very uncertain at this stage as the production of this fuel on a large scale is still at a low Technology Readiness Level and there is still unfamiliarity with large scale storage and transport of the substance. A reduction in the corresponding cost parameters would lead to the NaBH4-infrastructure becoming more competitive with a liquefied hydrogen infrastructure. The input used in the model should thus be further researched to reduce the corresponding uncertainties. While the current model focuses on optimising the infrastructure from a cost perspective, it must be taken into account that other factors also influence the favouring of certain alternative fuels, such as safety, policy, public acceptance and the preference for certain fuels from the perspective of the maritime users. In future research the expansion of the model towards a multi-objective model should be evaluated.

The Train Unit Shunting Problem (TUSP) is a well studied problem within the NS (Dutch Railways). TUSP is a problem where trains have to be routed on a shunting yard such that maintenance tasks can be performed and no collisions occur. Furthermore, incoming trains have to be matched to outgoing trains, since trains of the same type can be used interchangeably. Currently, the NS uses a local-search approach to solve TUSP; however, this approach is sometimes unable to find a simple detour route when the initial route of the train is blocked by another train. This research models the TUSP as a Multi-Agent Pathfinding (MAPF) problem to solve the routing issue. We solve this model of the TUSP using Conflict-Bases Search (CBS). To achieve this, CBS is altered to work with multiple trains on the same node, to work with directed edges, and to only allow wait-moves on certain nodes. In this work, we propose two ways of routing multiple trains on the same node; CBSL, where trains are given an exact location on the track; and CBSQ, where the order in which trains enter a track is recorded with a queue. Of these two methods, the queue model was deemed best. Finally, we propose a heuristic to prefer solutions where trains are more spread out on the shunting yard. This heuristic greatly improves the runtime at a loss of optimality.

An electric-recharging planning algorithm was developed in this study to accompany a dispatching algorithm that assigns real-time trip requests to vehicles of a shared taxi fleet owned by an operator. The algorithm decides on when, where, and how much each vehicle should charge, in real-time. It will also relocate idle vehicles if needed. The approach, to designing the algorithm, was to allow maximum flexibility for the dispatcher, not forcing charging on vehicles ahead of time, and restricting their chance of picking up a customer meanwhile, having limited empty routing cost (going to charger and back, and relocating trips), of course while providing enough charge for the expected level of demand to be met. Three sequential mixed linear integer programming (MLIP) optimizations were designed to achieve a pro-active charging planner, that can use aggregated prediction data, run in manageable time, and remain scalable with respect to the fleet-size.

Humanitarian organisations have a goal to help people in need by providing help in all kinds of ways.
Supplies and humanitarian workers have to be transported to every place where support is required. Even remote locations, where transport over conventional roads might be impossible, have to be accessible. Aviation is the solution for these areas. UNHAS (United Nations Humanitarian Air Service) provides passenger and cargo transport for the humanitarian community. A logistic problem arises when passengers have to be transported to multiple destinations with multiple aircraft. The goal of the research is to improve the routing and scheduling operations of humanitarian air services by means of a scheduling model. By implementing the Humanitarian Flight Optimization Model, the efficiency and effectiveness of the daily routing can be increased while giving an insight in what the impact of different routings can be on the total flight schedule.

This thesis investigates several kinds of models of describing multi-commodity dynamical flow. Three models have been developed for a spatial logistic network, on which packages are delivered by vehicles and another
model was developed to describe interactions between the customers, the stores and the deliverers, which does not explicitly take delivery time into account like before. The former three models consist of an agent-based model (ABM), and two different (differential) equation-based models (EBMs). One of the EBMs is built from the bottom up, and was created by averaging the randomness in the ABM. The other EBM was built top-down and involved optimizing a general model with respect to some parameters, such that its solution resembles the
ABM solution as closely as possible. These three models were tested and compared in the first half of the thesis.

In the second part of the thesis, the focus shifted to a generalized model (GM) approach of underlying interactions on multi-commodity dynamical
flow networks; especially the dynamics describing order placement,
scheduling and delivery. Such a network is cyclic and contains a feedback loop, where customers are less likely to order more products if they were recently delivered. This can range from someone not needing to purchase a
car if they just bought a brand new one to one not needing to order dinner when they just did so. Such networks are in general described by four kinds of elasticities in this thesis, namely the elasticities to stock, inventory level,
saturation, and co-production. These influence different parts in the network. For example, the negative elasticities to inventory level model that high inventory levels inhibit more inventory production, to prevent build-up,
and low inventory levels allow for larger inventory production, to prevent drainage. The other elasticities fulfil similar roles. This model was tested using a bifurcation analysis, a statistical ensemble method and by computing influences and sensitivities of parts and nodes in the network.

For airlines, crew costs make up the second largest expense, behind fuel costs. Because these costs are very high, there is a large potential gain in improving the crew efficiency within the bounds set by the law and collective labor agreements. This thesis investigates the dated crew pairing problem, and how the crew pairing problem can be integrated with aircraft routing and flight retiming in order to achieve more crew-efficient schedules for a low-cost airline operating a point-to-point network. Three different levels of problem integration, non-integrated, aircraft routing integrated, and aircraft routing integrated including retiming, are investigated on real point-to-point airline data, leading to five different models using either a generate-and-test or branch-and-price approach. It is shown that the currently presented models return pairings that reduce the number of duties up to 10% and increase the crew productivity up to 1.5%.

Wind turbine placement in a wind farm can be optimized to limit power losses due to wakes and improve the economic value of the plant. Seeing as wind farms are increasing in number and size, fast methods to generate good quality layouts can be beneficial for designers. Wind Farm Layout Optimization (WFLO) consists in finding a layout that maximizes the Annual Energy Production (AEP) of a wind farm. The procedure is driven by an algorithm that generates possible layouts and by a framework that evaluates their AEP. If the traditional method to assess AEP is adopted, layout optimization is computationally demanding due to the impact of each turbine's position on the productivity of the surrounding ones. Indeed, for any change in the layout, this inter-dependency forces designers to calculate wake effects and the wind resource-average energy production of the wind farm. This thesis proposes an approach to reduce the computational load of WFLO by pre-computing the power losses. Indeed, the approach avoids recalculating the expected power loss among turbines during the optimization procedure. This optimization strategy employs a novel approach, called Pre-Averaged Model (PAM), that expresses the expected power loss of a wake source at representative points around it. Firstly, the wind farm is discretized, and fictitious turbines are placed at each given spot. Secondly, PAM calculates the expected power loss caused by each fictitious turbine for the surrounding ones. Discontinuities introduced by wind resource discretization and top-hat wake deficit profiles affect PAM's accuracy substantially. Binning wind measurements in 72 wind directions solves the problem for typical engineering wake models. Then, a greedy algorithm uses the power losses of the fictitious turbines to build layouts constructively by adding an extra turbine per iteration. The effect of multiple wake sources on a wake target is modelled by linear superimposition of the pre-computed power losses. PAM is tested in combination with three greedy algorithms, namely, Basic Greedy (BG), Add-Remove-Move Greedy (ADREMOG), and ADREMOG II. This research demonstrates that the PAM and the superposition of the power losses can be reliably used for WFLO. Also, the joint use of PAM and greedy algorithms achieve an interesting trade-off between speed and quality of the layouts. Indeed, PAM is beneficial as it speeds up greedy algorithms. Furthermore, greedy algorithms allow generating better layouts at the cost of slowing down the algorithm. The balance between speed and quality can be regulated by using a finer discretization, testing different locations for the first turbine placement, or acting on the nature of the algorithm. In particular, the use of a re-location stage at each constructive iteration increases the quality of the layouts substantially but reduces the speed of execution. As a result, the proposed algorithms present different characteristics: the BG is the fastest but its median layout is the worst; ADREMOG produces the best layouts in the longest time; ADREMOG II is a compromise between the two former algorithms.