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In the last two decades, the western world witnessed a continuous rise in the health expenditure. Meanwhile, complaints from patients on excessive waiting times are also increasing. In the past, many researchers have tried to devise appointment scheduling rules to provide trade-offs between maximizing patients’ satisfaction and minimizing the costs of the health providers. For instance, this challenge appears appointment scheduling problems (ASP). Commonly used methods in ASP include analytical methods, simulation studies, and combination of simulation with heuristic approaches. Analytical methods (e.g., queuing theory and mathematical programming) face challenges of fully capturing the complexities of systems and usually make strong assumptions for tractability of problems. These methods simplify the whole system to a single-stage unit and ignore the actual system factors such as the presence of multiple stages and/or resource constraints. Simulation studies, conversely, are able to model most complexities of the actual system, but they typically lack an optimization strategy to deliver optimal appointment schedules. Also, heuristic approaches normally are based on intuitive rules and do not perform well as standalone methods. In order to reach an optimal schedule while considering complexities in actual health care systems, this thesis proposes efficient and effective methods that yield (near) optimal appointment schedules by integrating mathematical programming, a tabu search optimization algorithm and discrete event simulation. The proposed methodologies address the challenges and complexities of scheduling in real world multistage healthcare units in the presence of stochastic service durations, a mix of patient types, patients with heterogeneous service sequence, and resource constraints. Moreover, the proposed methodology is capable of finding the optimum considering simultaneously multiple performance criteria. A Pareto front (a set of optimal solutions) for the performance criteria can be obtained using the proposed methods. Healthcare management can use the Pareto front to choose the appropriate policy based on different conditions and priorities. In addition, the proposed method has been applied to two case studies of Operating Rooms departments in two major Canadian hospitals. The comparison of actual schedules and the ones yielded by the proposed method indicates that proposed method can improve the appointment scheduling in realistic clinical settings.

Generation and transmission investment planning in deregulated markets faces new challenges particularly as deregulation has introduced more uncertainty to the planning problem. Tradi- tional planning techniques and processes cannot be applied to the deregulated planning problem as generation investments are profit driven and competitive. Transmission investments must facilitate generation access rather than servicing generation choices. The new investment plan- ning environment requires the development of new planning techniques and processes that can remain flexible as uncertainty within the system is revealed. The optimisation technique of Stochastic Dual Dynamic Programming (SDDP) has been success- fully used to optimise continuous stochastic dynamic planning problems such as hydrothermal scheduling. SDDP is extended in this thesis to optimise the stochastic, dynamic, mixed integer power system investment planning problem. The extensions to SDDP allow for optimisation of large integer variables that represent generation and transmission investment options while still utilising the computational benefits of SDDP. The thesis also details the development of a math- ematical representation of a general power system investment planning problem and applies it to a case study involving investment in New Zealand’s HVDC link. The HVDC link optimisation problem is successfully solved using the extended SDDP algorithm and the output data of the optimisation can be used to better understand risk associated with capital investment in power systems. The extended SDDP algorithm offers a new planning and optimisation technique for deregulated power systems that provides a flexible optimal solution and informs the planner about investment risk associated with uncertainty in the power system.

The genetic structure of an intra-host viral population has an effect on many clinically important phenotypic traits such as escape from vaccine induced immunity, virulence, and response to antiviral therapies. Next-generation sequencing provides read-coverage sufficient for genomic reconstruction of a heterogeneous, yet highly similar, viral population; and more specifically, for the detection of rare variants. Admittedly, while depth is less of an issue for modern sequencers, the short length of generated reads complicates viral population assembly. This task is worsened by the presence of both random and systematic sequencing errors in huge amounts of data. In this dissertation I present completed work for reconstructing a viral population given next-generation sequencing data. Several algorithms are described for solving this problem under the error-free amplicon (or sliding-window) model. In order for these methods to handle actual real-world data, an error-correction method is proposed. A formal derivation of its likelihood model along with optimization steps for an EM algorithm are presented. Although these methods perform well, they cannot take into account paired-end sequencing data. In order to address this, a new method is detailed that works under the error-free paired-end case along with maximum a-posteriori estimation of the model parameters.

In any supply chain, the location of facilities and the routing of material are important decisions that contribute a significant amount of costs, lowering a corporation's overall profits. These choices become more important when dealing with a global supply chain, whose players span multiple countries and continents. International factors, such as tax rates and transfer prices, must be carefully considered, while the advantages of timely delivery versus cost-effective transportation must be carefully weighed to ensure that customer demands are met at the best possible price. We examine an international supply chain with plants, distribution centers (DCs), and customers in the North American Free Trade Agreement (NAFTA) and the European Union (EU) regions. The company in question manufactures two sub-assemblies at its plant in Mexico, and then assembles them into a final product at DCs in North America and Europe. To better serve its European customers, the company wishes to locate a new plant in the EU, as well as determine the modes of transportation used to distribute products between nodes, while maximizing overall profit. The problem is formulated as a mixed integer linear program and is solved in two stages using a Strategic Model (SM) and an Operational Model (OM). In SM, each time period represents one month and we determine the optimal facility locations over a 12-month time horizon. With transportation lead times expressed in days, we can be certain that demand will be fulfilled within a single period, and for this reason, lead times are not considered in SM. At the operational level, however, each time period represents one day, and so lead times must be included as they will affect the choice of mode for a given route. The location results from SM are used as input for OM, which then gives the optimal modal and routing decisions for the network. A number of cases are tested to determine how the optimal network is affected by changes in fixed and variable costs of facilities, transfer prices charged by plants to DCs, and the differing tax rates of each country.

In the last two decades, the western world witnessed a continuous rise in the health expenditure. Meanwhile, complaints from patients on excessive waiting times are also increasing. In the past, many researchers have tried to devise appointment scheduling rules to provide trade-offs between maximizing patients’ satisfaction and minimizing the costs of the health providers. For instance, this challenge appears appointment scheduling problems (ASP). Commonly used methods in ASP include analytical methods, simulation studies, and combination of simulation with heuristic approaches. Analytical methods (e.g., queuing theory and mathematical programming) face challenges of fully capturing the complexities of systems and usually make strong assumptions for tractability of problems. These methods simplify the whole system to a single-stage unit and ignore the actual system factors such as the presence of multiple stages and/or resource constraints. Simulation studies, conversely, are able to model most complexities of the actual system, but they typically lack an optimization strategy to deliver optimal appointment schedules. Also, heuristic approaches normally are based on intuitive rules and do not perform well as standalone methods. In order to reach an optimal schedule while considering complexities in actual health care systems, this thesis proposes efficient and effective methods that yield (near) optimal appointment schedules by integrating mathematical programming, a tabu search optimization algorithm and discrete event simulation. The proposed methodologies address the challenges and complexities of scheduling in real world multistage healthcare units in the presence of stochastic service durations, a mix of patient types, patients with heterogeneous service sequence, and resource constraints. Moreover, the proposed methodology is capable of finding the optimum considering simultaneously multiple performance criteria. A Pareto front (a set of optimal solutions) for the performance criteria can be obtained using the proposed methods. Healthcare management can use the Pareto front to choose the appropriate policy based on different conditions and priorities. In addition, the proposed method has been applied to two case studies of Operating Rooms departments in two major Canadian hospitals. The comparison of actual schedules and the ones yielded by the proposed method indicates that proposed method can improve the appointment scheduling in realistic clinical settings.

As the "network of network", the Internet has been playing a central and crucial role in modern society, culture, knowledge, businesses and so on in a period of over two decades by supporting a wide variety of network technologies and applications. However, due to its popularity and multi-provider nature, the future development of the Internet is limited to simple incremental updates. To address this challenge, network virtualization has been propounded as a potential candidate to provide the essential basis for the future Internet architecture. Network virtualization is capable of providing an open and flexible networking environment in which service providers are allowed to dynamically compose multiple coexisting heterogeneous virtual networks on a shared substrate network. Such a flexible environment will foster the deployment of diversified services and applications. A major challenge in network virtualization area is the Virtual Network Embedding (VNE), which aims to statically or dynamically allocate virtual nodes and virtual links on substrate resources, physical nodes and paths. Making effective use of substrate resources requires high-efficient and survivable VNE techniques. The main contribution of this thesis is two high-performance p-Cycle-based survivable virtual network embedding approaches. These approaches take advantage of p-Cycle-based protection techniques that minimize the backup resources while providing a full VN protection scheme against link and node failures.

Chemical and biological contaminants can enter a drinking water distribution system through one of the many access points to the network and can spread quickly affecting a very large area. This is of great concern, and water utilities need to consider effective tools and mitigation strategies to improve water network security. This work presents two components that have been integrated into EPA’s Water Security Toolkit, an open-source software package that includes a set of tools to help water utilities protect the public against potential contamination events. The first component is a novel water quality modeling framework referred to as Merlion. The linear system describing contaminant spread through the network at the core of Merlion provides several advantages and potential uses that are aligned with current emerging water security applications. This computational framework is able to efficiently generate an explicit mathematical model that can be easily embedded into larger mathematical system. Merlion can also be used to efficiently simulate a large number of scenarios speeding up current water security tools by an order of magnitude. The last component is a pair of mixed-integer linear programming (MILP) formulations for efficient source inversion and optimal sampling. The contaminant source inversion problem involves determining the source of contamination given a small set of measurements. The source inversion formulation is able to handle discrete positive/negative measurements from manual grab samples taken at different sampling cycles. In addition, sensor/sample placement formulations are extended to determine the optimal locations for the next manual sampling cycle. This approach is enabled by a strategy that significantly reduces the size of the Merlion water quality model, giving rise to a much smaller MILP that is solvable in a real-time setting. The approach is demonstrated on a large-scale water network model with over 12,000 nodes while considering over 100 timesteps. The results show the approach is successful in finding the source of contamination remarkably quickly, requiring a small number of sampling cycles and a small number of sampling teams. These tools are being integrated and tested with a real-time response system.

A workforce plan states the number of workers required at any point in time. Efficient workforce plans can help companies achieve their organizational goals while keeping costs low. In ever increasing globalized work market, companies need a competitive edge over their competitors. A competitive edge can be achieved by lowering costs. Labour costs can be one of the significant costs faced by the companies. Efficient workforce plans can provide companies with a competitive edge by finding low cost options to meet customer demand. This thesis studies the problem of determining the required number of workers when there are two categories of workers. Workers belonging to the first category are trained to work on one type of task (called Specialized Workers); whereas, workers in the second category are trained to work in all the tasks (called Flexible Workers). This thesis makes the following three main contributions. First, it addresses this problem when the demand is deterministic and stochastic. Two different models for deterministic demand cases have been proposed. To study the effects of uncertain demand, techniques of Robust Optimization and Robust Mathemat- ical Programming were used. The thesis also investigates methods to solve large instances of this problem; some of the instances we considered have more than 600,000 variables and constraints. As most of the variables are integer, and objective function is nonlinear, a commercial solver was not able to solve the problem in one day. Initially, we tried to solve the problem by using Lagrangian relaxation and Outer approximation techniques but these approaches were not successful. Although effective in solving small problems, these tools were not able to generate a bound within run time limit for the large data set. A number of heuristics were proposed using projection techniques. Finally this thesis develops a genetic algorithm to solve large instances of this prob- lem. For the tested population, the genetic algorithm delivered results within 2-3% of optimal solution.

A t-design is a combinatorial structure consisting of a collection of blocks over a set of points satisfying certain properties. The existence of t-designs given a set of parameters can be reduced to finding nonnegative integer solutions to a given integer matrix equation. The matrix in this equation can be quite large, but by prescribing the automorphism group of the design, the matrix in the equation can be made more manageable so as to allow the equation to be solved via integer programming tools; this fact was developed by Kramer and Mesner. Algorithms to generate the matrix equation generally follow a simple template. In this thesis, a generic framework for generating the Kramer-Mesner matrix equation and solving it via integer programming is presented.