Background: In treatment planning for intensity-modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed-integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose-volume constraints. In this study, we incorporated dose-volume constraints in an MIP model to generate treatment plans for IMPT. Methods: We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method while the other plan was derived with our MIP model with dose-volume constraints. We then compared these two plans by dose-volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose-volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection. Results: The MIP model with dose-volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial-and-error process. Some notable reduction in the mean doses of OARs is observed. Conclusions: The treatment plans from our MIP model with dose-volume constraints can meetall dose-volume constraints for OARs and targets without any tedious trial-and-error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.

This thesis proposes and verifies a number of optimization models for re-designing a master surgery schedule with minimized peak inpatient load at the ward. All models include limitations on Operating Rooms and surgeons availability. Surgeons` preference is included with regards to a consistent weekly schedule over a cycle. The uncertain in patients` length of stay was incorporated using discrete probability distributions unique to each surgeon. Furthermore, robust optimization was utilized to protect against the uncertainty in the number of inpatients a surgeon may send to the ward per block. Different scenarios were developed that explore the impact of varying the availability of operating rooms on each day of the week. The models were solved using Cplex and were verified by an Arena simulation model.

Almost every medium and large company has to deal with an optimal placing of administrative workers. This thesis focuses on solving a problem of dislocation of employees of the Ministry of Finance of the Czech Republic (MFCR) and it proposes a possible solution of the current situation. The basis for finding the optimal solutions are integer programming tasks. The structure of the MFCR and the description of the current/future state of dislocations has been defined in cooperation with the MFCR. Therefore, the solution fully meets the MFCR specifications. The thesis also outlines another optional solution for dislocations within MFCR. Finally, there are summarized other aspects of optimal dislocation of employees that can further improve the solution given in this thesis, especially in terms of efficiency, satisfaction and health of the employees.

The goal of this project is to implement and verify an optimization model for finding a min-cost selection of switches and train paths at railway stations. The selected train paths must satisfy traffic requirements that commonly apply to regular railway traffic. The requirements include different combinations of simultaneous and overtaking train movements. The model does not rely on timetables but does instead utilize different path sets that are produced via algorithms based on a network representation of the station layout. The model has been verified on a small test station and also on the real station layout at Katrineholm. These tests show that the model can solve the problem for mid size stations with through traffic. In addition, we have performed a literature study regarding maintenance problems for switches and crossings. We have also looked at articles regarding the scheduling and routing of trains through railway stations. Finally we present some possible ways to further improve the model for more realistic experiments.

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The goal of this dissertation is to study optimization models that integrate location, production, inventory and transportation decisions for industrial products and apply the knowledge gained to develop supply chains for agricultural products (biomass). We estimate unit cost for the whole biomass-to-biofuels’ supply chain which is the per gallon cost for biofuels up till it reaches the markets. The unit cost estimated is the summation of location, production, inventory holding, and transportation costs. In this dissertation, we focus on building mathematical models for designing and managing the biomass-to-biofuels’ supply chains. The computational complexity of the developed models makes it advisable to use heuristic solution procedures. We develop a Lagrangean decomposition heuristic. In our heuristic, we divide the problem into two sub-problems, sub-problem 1 is a transportation problem and sub-problem 2 is a combination of a capacitated facility location and production planning problem. Subproblem 2 is further divided by commodities. The algorithm is tested for a number of different scenarios. We also develop a decision support system (DSS) for the biomass-to-biofuels’ supply chain. In our DSS, the main problem is divided into four easy-to-solve supply chain problems. These problems were determined based on our knowledge of supply chain and discussions with the experts from the biomass and biofuels’ sector. The DSS is coded using visual basic applications (VBA) for Excel and has a simple user interface which assists the user in running different types of supply chain problems and provides results in form of reports which are easy to understand.

A recent trend among sports fans along both sides of the letterman jacket is that of Daily Fantasy Sports (DFS). The DFS industry has been under legal scrutiny recently, due to the view that daily sports data is too random to make its prediction skillful. Therefore, a common view is that it constitutes online gambling. This thesis proves that DFS, as it pertains to Baseball, is significantly more predictable than random chance, and thus does not constitute gambling. We propose a system which generates daily lists of lineups for Fanduel Daily Fantasy Baseball contests. The system consists of two components: one for predicting player scores for every player on a given day, and one for generating lists of the best combinations of players (lineups) using the predicted player scores. The player score prediction component makes use of deep neural network models, including a Long Short-Term Memory recurrent neural network, to model daily player performance over the 2016 and 2017 MLB seasons. Our results indicate this to be a useful prediction tool, even when not paired with the lineup generation component of our system. We build off of previous work to develop two models for lineup generation, one completely novel, dependent on a set of player predictions. Our evaluations show that these lineup generation models paired with player predictions are significantly better than random, and analysis shows insights into key aspects of the lineup generation process.

Addressing fairness among users and risk mitigation in the context of resource allocation in transportation systems under uncertainties poses a crucial challenge yet to be satisfactorily resolved. This dissertation attempts to address this challenge, focusing on achieving a balance between system-wide efficiency and individual fairness in stochastic transportation resource allocation problems. To study complicated fair and risk-averse resource allocation problems - from public transit to urban air mobility and multi-stage infrastructure maintenance - we develop three models: DrFRAM, FairUAM, and FCMDP. Each of these models, despite being proven NP-hard even in a simplistic case, inspires us to develop efficient solution algorithms. We derive mixed-integer linear programming (MILP) formulations for these models, leveraging the unique properties of each model and linearizing non-linear terms. Additionally, we strengthen these models with valid inequalities. To efficiently solve these models, we design exact algorithms and approximation algorithms capable of obtaining near-optimal solutions. We numerically validate the effectiveness of our proposed models and demonstrate their capability to be applied to real-world case studies to adeptly address the uncertainties and risks arising from transportation systems. This dissertation provides a foundational platform for future inquiries of risk-averse resource allocation strategies under uncertainties for more efficient, equitable, and resilient decision-making. Our adaptable framework can address a variety of transportation-related challenges and can be extended beyond the transportation domain to tackle resource allocation problems in a broader setting. / Doctor of Philosophy / In transportation systems, decision-makers constantly strive to devise the optimal plan for the most beneficial outcomes when facing future uncertainties. When optimizing overall efficiency, individual fairness has often been overlooked. Besides, the uncertainties in the transportation systems raise serious questions about the adaptability of the allocation plan. In response to these issues, we introduce the concept of fair and risk-averse resource allocation under uncertainties in this dissertation. Our goal is to formulate the optimal allocation plan that is both fair and risk-averse amid uncertainties. To tackle the complexities of fair and risk-averse resource allocation problems, we propose innovative methods and practical algorithms, including creating novel formulations as well as deriving super-fast algorithms. These solution approaches are designed to accommodate the fairness, uncertainties, and risks typically in transportation systems. Beyond theoretical results, we apply our frameworks and algorithms to real-world case studies, thus demonstrating our approaches' adaptability to various transportation systems and ability to achieve various optimization goals. Ultimately, this dissertation aims to contribute to fairer, more efficient, and more robust transportation systems. We believe our research findings can help decision-makers with well-informed choices about resource allocation in transportation systems, which, in turn, lead to the development of more equitable and reliable systems, benefiting all the stakeholders.

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