Graphs are commonly used visualization tools in a variety of fields. Algorithms have been proposed that claim to improve the readability of graphs by reducing edge crossings, adjusting edge length, or some other means. However, little research has been done to determine which of these algorithms best suit human perception for particular graph properties. This thesis explores four different graph properties: average local clustering coefficient (ALCC), global clustering coefficient (GCC), number of triangles (NT), and diameter. For each of these properties, three different graph layouts are applied to represent three different approaches to graph visualization: multidimensional scaling (MDS), force directed (FD), and tsNET. In a series of studies conducted through the crowdsourcing platform Amazon Mechanical Turk, participants are tasked with discriminating between two graphs in order to determine their just noticeable differences (JNDs) for the four graph properties and three layout algorithm pairs. These results are analyzed using previously established methods presented by Rensink et al. and Kay and Heer.The average JNDs are analyzed using a linear model that determines whether the property-layout pair seems to follow Weber's Law, and the individual JNDs are run through a log-linear model to determine whether it is possible to model the individual variance of the participant's JNDs. The models are evaluated using the R2 score to determine if they adequately explain the data and compared using the Mann-Whitney pairwise U-test to determine whether the layout has a significant effect on the perception of the graph property. These tests indicate that the data collected in the studies can not always be modelled well with either the linear model or log-linear model, which suggests that some properties may not follow Weber's Law. Additionally, the layout algorithm is not found to have a significant impact on the perception of some of these properties.

This dissertation addresses access management problems that occur in both emergency and outpatient clinics with the objective of allocating the available resources to improve performance measures by considering the trade-offs. Two main settings are considered for estimating patient willingness-to-wait (WtW) behavior for outpatient appointments with statistical analyses of data: allocation of the limited booking horizon to patients of different priorities by using time windows in an outpatient setting considering patient behavior, and allocation of hospital beds to admitted Emergency Department (ED) patients. For each chapter, a different approach based on the problem context is developed and the performance is analyzed by implementing analytical and simulation models. Real hospital data is used in the analyses to provide evidence that the methodologies introduced are beneficial in addressing real life problems, and real improvements can be achievable by using the policies that are suggested.

This dissertation starts with studying an outpatient clinic context to develop an effective resource allocation mechanism that can improve patient access to clinic appointments. I first start with identifying patient behavior in terms of willingness-to-wait to an outpatient appointment. Two statistical models are developed to estimate patient WtW distribution by using data on booked appointments and appointment requests. Several analyses are conducted on simulated data to observe effectiveness and accuracy of the estimations.

Then, this dissertation introduces a time windows based policy that utilizes patient behavior to improve access by using appointment delay as a lever. The policy improves patient access by allocating the available capacity to the patients from different priorities by dividing the booking horizon into time intervals that can be used by each priority group which strategically delay lower priority patients.

Finally, the patient routing between ED and inpatient units to improve the patient access to hospital beds is studied. The strategy that captures the trade-off between patient safety and quality of care is characterized as a threshold type. Through the simulation experiments developed by real data collected from a hospital, the achievable improvement of implementing such a strategy that considers the safety-quality of care trade-off is illustrated.

Breeding seeds to include desirable traits (increased yield, drought/temperature resistance, etc.) is a growing and important method of establishing food security. However, besides breeder intuition, few decision-making tools exist that can provide the breeders with credible evidence to make decisions on which seeds to progress to further stages of development. This thesis attempts to create a chance-constrained knapsack optimization model, which the breeder can use to make better decisions about seed progression and help reduce the levels of risk in their selections. The model’s objective is to select seed varieties out of a larger pool of varieties and maximize the average yield of the “knapsack” based on meeting some risk criteria. Two models are created for different cases. First is the risk reduction model which seeks to reduce the risk of getting a bad yield but still maximize the total yield. The second model considers the possibility of adverse environmental effects and seeks to mitigate the negative effects it could have on the total yield. In practice, breeders can use these models to better quantify uncertainty in selecting seed varieties

The shift in focus of manufacturing systems to high-mix and low-volume production poses a challenge to both efficient scheduling of manufacturing operations and effective assessment of production capacity. This thesis considers the problem of scheduling a set of jobs that require machine and worker resources to complete their manufacturing operations. Although planners in manufacturing contexts typically focus solely on machines, schedules that only consider machining requirements may be problematic during implementation because machines need skilled workers and cannot run unsupervised. The model used in this research will be beneficial to these environments as planners would be able to determine more realistic assignments and operation sequences to minimize the total time required to complete all jobs. This thesis presents a mathematical formulation for concurrent scheduling of machines and workers that can optimally schedule a set of jobs while accounting for changeover times between operations. The mathematical formulation is based on disjunctive constraints that capture the conflict between operations when trying to schedule them to be performed by the same machine or worker. An additional formulation extends the previous one to consider how cross-training may impact the production capacity and, for a given budget, provide training recommendations for specific workers and operations to reduce the makespan. If training a worker is advantageous to increase production capacity, the model recommends the best time window to complete it such that overlaps with work assignments are avoided. It is assumed that workers can perform tasks involving the recently acquired skills as soon as training is complete. As an alternative to the mixed-integer programming formulations, this thesis provides a math-heuristic approach that fixes the order of some operations based on Largest Processing Time (LPT) and Shortest Processing Time (SPT) procedures, while allowing the exact formulation to find the optimal schedule for the remaining operations. Computational experiments include the use of the solution for the no-training problem as a starting feasible solution to the training problem. Although the models provided are general, the manufacturing of Printed Circuit Boards are used as a case study.

Researchers and practitioners have widely studied road network traffic data in different areas such as urban planning, traffic prediction and spatial-temporal databases. For instance, researchers use such data to evaluate the impact of road network changes. Unfortunately, collecting large-scale high-quality urban traffic data requires tremendous efforts because participating vehicles must install Global Positioning System(GPS) receivers and administrators must continuously monitor these devices. There have been some urban traffic simulators trying to generate such data with different features. However, they suffer from two critical issues (1) Scalability: most of them only offer single-machine solution which is not adequate to produce large-scale data. Some simulators can generate traffic in parallel but do not well balance the load among machines in a cluster. (2) Granularity: many simulators do not consider microscopic traffic situations including traffic lights, lane changing, car following. This paper proposed GeoSparkSim, a scalable traffic simulator which extends Apache Spark to generate large-scale road network traffic datasets with microscopic traffic simulation. The proposed system seamlessly integrates with a Spark-based spatial data management system, GeoSpark, to deliver a holistic approach that allows data scientists to simulate, analyze and visualize large-scale urban traffic data. To implement microscopic traffic models, GeoSparkSim employs a simulation-aware vehicle partitioning method to partition vehicles among different machines such that each machine has a balanced workload. The experimental analysis shows that GeoSparkSim can simulate the movements of 200 thousand cars over an extensive road network (250 thousand road junctions and 300 thousand road segments).

I study the problem of locating Relay nodes (RN) to improve the connectivity of a set

of already deployed sensor nodes (SN) in a Wireless Sensor Network (WSN). This is

known as the Relay Node Placement Problem (RNPP). In this problem, one or more

nodes called Base Stations (BS) serve as the collection point of all the information

captured by SNs. SNs have limited transmission range and hence signals are transmitted

from the SNs to the BS through multi-hop routing. As a result, the WSN

is said to be connected if there exists a path for from each SN to the BS through

which signals can be hopped. The communication range of each node is modeled

with a disk of known radius such that two nodes are said to communicate if their

communication disks overlap. The goal is to locate a given number of RNs anywhere

in the continuous space of the WSN to maximize the number of SNs connected (i.e.,

maximize the network connectivity). To solve this problem, I propose an integer

programming based approach that iteratively approximates the Euclidean distance

needed to enforce sensor communication. This is achieved through a cutting-plane

approach with a polynomial-time separation algorithm that identies distance violations.

I illustrate the use of my algorithm on large-scale instances of up to 75 nodes

which can be solved in less than 60 minutes. The proposed method shows solutions

times many times faster than an alternative nonlinear formulation.

When looking at drawings of graphs, questions about graph density, community structures, local clustering and other graph properties may be of critical importance for analysis. While graph layout algorithms have focused on minimizing edge crossing, symmetry, and other such layout properties, there is not much known about how these algorithms relate to a user’s ability to perceive graph properties for a given graph layout. This study applies previously established methodologies for perceptual analysis to identify which graph drawing layout will help the user best perceive a particular graph property. A large scale (n = 588) crowdsourced experiment is conducted to investigate whether the perception of two graph properties (graph density and average local clustering coefficient) can be modeled using Weber’s law. Three graph layout algorithms from three representative classes (Force Directed - FD, Circular, and Multi-Dimensional Scaling - MDS) are studied, and the results of this experiment establish the precision of judgment for these graph layouts and properties. The findings demonstrate that the perception of graph density can be modeled with Weber’s law. Furthermore, the perception of the average clustering coefficient can be modeled as an inverse of Weber’s law, and the MDS layout showed a significantly different precision of judgment than the FD layout.

Coastal areas are susceptible to man-made disasters, such as oil spills, which not

only have a dreadful impact on the lives of coastal communities and businesses but also

have lasting and hazardous consequences. The United States coastal areas, especially

the Gulf of Mexico, have witnessed devastating oil spills of varied sizes and durations

that resulted in major economic and ecological losses. These disasters affected the oil,

housing, forestry, tourism, and fishing industries with overall costs exceeding billions

of dollars (Baade et al. (2007); Smith et al. (2011)). Extensive research has been

done with respect to oil spill simulation techniques, spatial optimization models, and

innovative strategies to deal with spill response and planning efforts. However, most

of the research done in those areas is done independently of each other, leaving a

conceptual void between them.

In the following work, this thesis presents a Spatial Decision Support System

(SDSS), which efficiently integrates the independent facets of spill modeling techniques

and spatial optimization to enable officials to investigate and explore the various

options to clean up an offshore oil spill to make a more informed decision. This

thesis utilizes Blowout and Spill Occurrence Model (BLOSOM) developed by Sim

et al. (2015) to simulate hypothetical oil spill scenarios, followed by the Oil Spill

Cleanup and Operational Model (OSCOM) developed by Grubesic et al. (2017) to

spatially optimize the response efforts. The results of this combination are visualized

in the SDSS, featuring geographical maps, so the boat ramps from which the response

should be launched can be easily identified along with the amount of oil that hits the

shore thereby visualizing the intensity of the impact of the spill in the coastal areas

for various cleanup targets.

Project portfolio selection (PPS) is a significant problem faced by most organizations. How to best select the many innovative ideas that a company has developed to deploy in a proper and sustained manner with a balanced allocation of its resources over multiple time periods is one of vital importance to a company's goals. This dissertation details the steps involved in deploying a more intuitive portfolio selection framework that facilitates bringing analysts and management to a consensus on ongoing company efforts and buy into final decisions. A binary integer programming selection model that constructs an efficient frontier allows the evaluation of portfolios on many different criteria and allows decision makers (DM) to bring their experience and insight to the table when making a decision is discussed. A binary fractional integer program provides additional choices by optimizing portfolios on cost-benefit ratios over multiple time periods is also presented. By combining this framework with an `elimination by aspects' model of decision making, DMs evaluate portfolios on various objectives and ensure the selection of a portfolio most in line with their goals. By presenting a modeling framework to easily model a large number of project inter-dependencies and an evolutionary algorithm that is intelligently guided in the search for attractive portfolios by a beam search heuristic, practitioners are given a ready recipe to solve big problem instances to generate attractive project portfolios for their organizations. Finally, this dissertation attempts to address the problem of risk and uncertainty in project portfolio selection. After exploring the selection of portfolios based on trade-offs between a primary benefit and a primary cost, the third important dimension of uncertainty of outcome and the risk a decision maker is willing to take on in their quest to select the best portfolio for their organization is examined.

Commuting is a significant cost in time and in travel expenses for working individuals and a major contributor to emissions in the United States. This project focuses on increasing the efficiency of an intersection through the use of "light metering." Light metering involves a series of lights leading up to an intersection forcing cars to stop further away from the final intersection in smaller queues instead of congregating in a large queue before the final intersection. The simulation software package AnyLogic was used to model a simple two-lane intersection with and without light metering. It was found that light metering almost eliminates start-up delay by preventing a long queue to form in front of the modeled intersection. Shorter queue lengths and reduction in the start-up delays prevents cycle failure and significantly reduces the overall delay for the intersection. However, frequent deceleration and acceleration for a few of the cars occurs before each light meter. This solution significantly reduces the traffic density before the intersection and the overall delay but does not appear to be a better emission alternative due to an increase in acceleration. Further research would need to quantify the difference in emissions for this model compared to a standard intersection.