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, we analyse the optimisation of an annualised hours problem. Annualised hours problems are a widely studied subjects, in which the working hours for a given number of employees per week are minimised. We approach this problem with a mixed integer linear program, where the objective function of this problem is divided into two parts; the first is to find the minimisation on the maximum over and under staffing per week, the second to find working hours for each employee as close as possible to their contract hours. Additionally, we have a number of restrictions on the duration of a shift and the minimum and maximum amount of shifts in a given period. The project is done in collaboration with the company ORTEC. ORTEC provided a random data generator, to test the model with different methods. The model is intended for application on a dataset of 100 employees and 52 weeks. However, we test the model on different data sets of 52 weeks with 50, 100, 150, 200, 250, 1000 employees and for 100 employees with 26, 52, 78 weeks. Besides analysing the model, we compare different algorithms. We use a Gurobi solver for an exact solution. Further, we consider Lagrangian relaxation, a heuristic method. In this method one of the constraints is put in the objective function. Besides this we consider a heuristic of hill climbing algorithm in combination with different local search algorithms. For the local search we use two neighbourhoods, one based on the employees, the other based on the weeks. We found that a Gurobi solver solves the model in reasonable computation time with an average of 6 seconds for a data set of 100 employees and 52 weeks. For Lagrangian relaxation, we found an even better computation time than with the Gurobi solver. However, this difference is hardly notable for a data set of 100 employees and 52 weeks and the effect of Lagrangian relaxation is more clear for bigger data sets. The hill climbing algorithm had a consistent and low computation time, but the objective function value differs considerably from the exact solution and resulted in most cases a difference of more than 10 percent.

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.

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.

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.

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.

Hospitals need to be staffed around the clock to ensure satisfactory care for all patients. To this end, a set of shifts is defined which are assigned to nurses in a work schedule. The nurse rerostering problem (NRRP) occurs when due to unforeseen circumstances some shifts become unassigned: one or more nurses are no longer able to work some of the shifts assigned to them. Changes must then be made to the existing schedule to ensure that the shift occupancy demand is once again satisfied. The number of changes should be minimized to disrupt nurses’ personal plans as little as possible. In this paper, a heuristic solution method (SSWAPS) is proposed for the NRRP. The heuristic systematically searches the solution space and estimates the solution quality using the assignment problem.

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.

In this thesis, we propose two mixed integer linear program formulations for an optimization problem that incorporates annualized hours: an exact one and an approximation. The objective of our model consists of three weighted parts: a part which minimizes the difference between working hours and contract hours for each employee per week, a part which minimizes over and under staffing, and a part which minimizes the difference between contract hours and working hours for each employee over the total planning period. Additionally, the working hours need to be distributed over shifts of a fixed shift duration. We also consider an extension where skills are introduced. In this case, employees can only work on a task for which they are qualified. To test the proposed formulations, a random data generator is provided by ORTEC. The model should be solvable for a data set up to 100 employees and 52 weeks (and 5 skills). We have tested it on several data sets of that size with varying weights in our objective function. We have compared the run time of our exact model with the run time of the approximate model for different weights. The approximate model gave a relatively quick approximation of the optimal solution when we do not consider skills, and when we do consider skills and vary the weight for the first part of the objective function. For varying the weight on the second part, we used a time limited version of our exact model to approximate the optimal solution. To be able to approximate the optimal solution when varying weight on the third part of the objective function, the approximate model is used with extra weight on the first part, instead of the third.

In this thesis, we investigate whether maximizing the coverage of taxis can be beneficial when the goal is to minimize the waiting times of the clients. When dispatching taxis, often only current requests are taken into account and not future ones. We examined how beneficial it can be to take coverage into account. For taxi companies it is important to keep their customers satisfied, by serving them as quickly as possible. Often companies assign the taxis to the nearest requests. We investigate whether there are better dispatch methods. We developed three dispatch policies which use ILP models, and discussed what the best option is. The first policy does not consider the coverage and minimizes the waiting times of the clients among the requests that are taking place at that moment. The second one aims to maintain a good coverage and short waiting times when assigning taxis to requests. The third one also aims to maintain a good coverage and short waiting times when assigning taxis to requests and also relocates taxis to gain a better covered area. Those policies can be a contribution for taxi companies because they help to serve clients more quickly. To determine what the best way is of dispatching taxis, we run a simulation on the different policies on a real-data map and compared the results. The literature over taxi dispatch mostly conducts research on a small area like a city or a village. In this thesis, taxis dispatch takes place on a larger area where taxis commute between cities.

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.

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.

In this thesis we investigate an extension of the famous Nurse Rostering Problem. The Nurse Rostering Problem is the problem of finding an optimal assignment of nurses to shifts given some constraints. We extend the problem by considering that the nurses different sets of skills by which they can only perform certain tasks. We want the working hours of the nurses to be as close as possible to their contract hours, and moreover, we want the amount of work done on a specific task to be as close as possible to the demand for that task. It is important that the user of the model has control over the execution time. We model this problem with an Integer Linear Program (ILP). The data we use to test the model is provided by ORTEC. ORTEC provided a random data generator which generates data such as contract hours and demands for certain skills, for a fictional company. The number of employees, skills and weeks can be determined by the user. We use small, medium and large data sets where large data sets consist of 100 employees, 52 weeks and 5 different skills. Our model is a linear approximation of a quadratic problem. It is based on minimizing the largest deviation in contract hours and demand. To get control over the computation time of the model, a timer is implemented. The desired maximum computation time can be set by the user and the model provides the best solution found within that time boundary. The initial model is tested with three different solvers: COIN-OR, CPLEX and Gurobi. The computation times and consistency of the solvers are compared. We found that CPLEX was in our case the best solver with an average computation time of 7.2 seconds for data sets of 100 employees, 5 skills, and 52 weeks. Next, we use an iterative procedure, which runs the model several times in order to obtain a more accurate solution. In this procedure, certain deviations, and their contributing variables, are fixed in every iteration while the model runs on the remaining non-fixed variables. An extension to this iterative procedure is also presented. In this extension, multiple deviations are fixed in every iteration to decrease the execution time. The fixed percentage of maximum deviations per iteration is tested on accuracy and computation time. We found that for small data sets it is best to use 1%, which results in one fixed deviation per iteration. For medium data sets, the best range is from 1% to 10%. Lastly for large data sets we recommend to use a range of 10% to 20%.

Plastic waste transported to oceans through canals and rivers becomes increasingly challenging to retrieve and harmful to ecosystems. Catching systems designed by Noria Sustainable Innovators can be used to capture the plastics as close to their source as possible. Deciding the best locations to place these systems is a difficult task, which is why a model for location optimization of catching systems for plastic waste removal from waterways is designed in this thesis: the Plastic Waste Flow Capturing Location Model (PW-FCLM). In this model, the plastic waste flow through a network of waterways is represented as a Markov chain, using environmental data as inputs to estimate the initial probabilities and transition probabilities of plastic waste in the network. The PW-FCLM extends an existing Markov Decision Process-based Flow Capturing Location Model by incorporating various types of catching systems, considering sensitive areas, and specifying orientations for the systems. The equivalence of the linearized version of the extended model is demonstrated, a proof of NP-hardness of the problem is given and a greedy heuristic is presented as an alternative solution method. A sensitivity analysis on the different types of input parameters is performed, and the runtimes for different problem sizes and solution methods are tested for case studies of Delft and Groningen in the Netherlands. The model is most sensitive to changes in the distance between the nodes in the network and to the probability of getting stuck due to water vegetation. For budgets up to B=2 and problem sizes up to n=375 nodes, the exact optimal solution can be found efficiently without a commercial solver license. For larger problem sizes or a higher budget, the heuristic appears to be a more appropriate solution method. For future research, it is recommended to further study the influence of the distance between the nodes on the optimal solution and to investigate the plastic flow representation in the Markov chain further. Exploring the model's application to larger areas, such as provinces or countries, would be beneficial. The real-life effectiveness of placing catching systems at the optimal locations suggested by the model, depends on the accuracy of the input parameters. In this thesis, the values of the input parameters are primarily based on estimations of experts. It would be beneficial for the user of the model to further validate the values of the input parameters through experiments.