Healthcare operations have enjoyed reduced costs, improved patient safety, and

innovation in healthcare policy over a huge variety of applications by tackling prob-

lems via the creation and optimization of descriptive mathematical models to guide

decision-making. Despite these accomplishments, models are stylized representations

of real-world applications, reliant on accurate estimations from historical data to jus-

tify their underlying assumptions. To protect against unreliable estimations which

can adversely affect the decisions generated from applications dependent on fully-

realized models, techniques that are robust against misspecications are utilized while

still making use of incoming data for learning. Hence, new robust techniques are ap-

plied that (1) allow for the decision-maker to express a spectrum of pessimism against

model uncertainties while (2) still utilizing incoming data for learning. Two main ap-

plications are investigated with respect to these goals, the first being a percentile

optimization technique with respect to a multi-class queueing system for application

in hospital Emergency Departments. The second studies the use of robust forecasting

techniques in improving developing countries’ vaccine supply chains via (1) an inno-

vative outside of cold chain policy and (2) a district-managed approach to inventory

control. Both of these research application areas utilize data-driven approaches that

feature learning and pessimism-controlled robustness.

In healthcare facilities, health information systems (HISs) are used to serve different purposes. The radiology department adopts multiple HISs in managing their operations and patient care. In general, the HISs that touch radiology fall into two categories: tracking HISs and archive HISs. Electronic Health Records (EHR) is a typical tracking HIS, which tracks the care each patient receives at multiple encounters and facilities. Archive HISs are typically specialized databases to store large-size data collected as part of the patient care. A typical example of an archive HIS is the Picture Archive and Communication System (PACS), which provides economical storage and convenient access to diagnostic images from multiple modalities. How to integrate such HISs and best utilize their data remains a challenging problem due to the disparity of HISs as well as high-dimensionality and heterogeneity of the data. My PhD dissertation research includes three inter-connected and integrated topics and focuses on designing integrated HISs and further developing statistical models and machine learning algorithms for process and patient care improvement.

Topic 1: Design of super-HIS and tracking of quality of care (QoC). My research developed an information technology that integrates multiple HISs in radiology, and proposed QoC metrics defined upon the data that measure various dimensions of care. The DDD assisted the clinical practices and enabled an effective intervention for reducing lengthy radiologist turnaround times for patients.

Topic 2: Monitoring and change detection of QoC data streams for process improvement. With the super-HIS in place, high-dimensional data streams of QoC metrics are generated. I developed a statistical model for monitoring high- dimensional data streams that integrated Singular Vector Decomposition (SVD) and process control. The algorithm was applied to QoC metrics data, and additionally extended to another application of monitoring traffic data in communication networks.

Topic 3: Deep transfer learning of archive HIS data for computer-aided diagnosis (CAD). The novelty of the CAD system is the development of a deep transfer learning algorithm that combines the ideas of transfer learning and multi- modality image integration under the deep learning framework. Our system achieved high accuracy in breast cancer diagnosis compared with conventional machine learning algorithms.

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.

One of the greatest 21st century challenges is meeting the needs of a growing world population expected to increase 35% by 2050 given projected trends in diets, consumption and income. This in turn requires a 70-100% improvement on current production capability, even as the world is undergoing systemic climate pattern changes. This growth not only translates to higher demand for staple products, such as rice, wheat, and beans, but also creates demand for high-value products such as fresh fruits and vegetables (FVs), fueled by better economic conditions and a more health conscious consumer. In this case, it would seem that these trends would present opportunities for the economic development of environmentally well-suited regions to produce high-value products. Interestingly, many regions with production potential still exhibit a considerable gap between their current and ‘true’ maximum capability, especially in places where poverty is more common. Paradoxically, often high-value, horticultural products could be produced in these regions, if relatively small capital investments are made and proper marketing and distribution channels are created. The hypothesis is that small farmers within local agricultural systems are well positioned to take advantage of existing sustainable and profitable opportunities, specifically in high-value agricultural production. Unearthing these opportunities can entice investments in small farming development and help them enter the horticultural industry, thus expand the volume, variety and/or quality of products available for global consumption. In this dissertation, the objective is three-fold: (1) to demonstrate the hidden production potential that exist within local agricultural communities, (2) highlight the importance of supply chain modeling tools in the strategic design of local agricultural systems, and (3) demonstrate the application of optimization and machine learning techniques to strategize the implementation of protective agricultural technologies.

As part of this dissertation, a yield approximation method is developed and integrated with a mixed-integer program to estimate a region’s potential to produce non-perennial, vegetable items. This integration offers practical approximations that help decision-makers identify technologies needed to protect agricultural production, alter harvesting patterns to better match market behavior, and provide an analytical framework through which external investment entities can assess different production options.

This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs.

In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects.

Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship.

The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.

The following is a case study composed of three workflow investigations at the open source software development (OSSD) based Apache Software Foundation (Apache). I start with an examination of the workload inequality within the Apache, particularly with regard to requirements writing. I established that the stronger a participant's experience indicators are, the more likely they are to propose a requirement that is not a defect and the more likely the requirement is eventually implemented. Requirements at Apache are divided into work tickets (tickets). In our second investigation, I reported many insights into the distribution patterns of these tickets. The participants that create the tickets often had the best track records for determining who should participate in that ticket. Tickets that were at one point volunteered for (self-assigned) had a lower incident of neglect but in some cases were also associated with severe delay. When a participant claims a ticket but postpones the work involved, these tickets exist without a solution for five to ten times as long, depending on the circumstances. I make recommendations that may reduce the incidence of tickets that are claimed but not implemented in a timely manner. After giving an in-depth explanation of how I obtained this data set through web crawlers, I describe the pattern mining platform I developed to make my data mining efforts highly scalable and repeatable. Lastly, I used process mining techniques to show that workflow patterns vary greatly within teams at Apache. I investigated a variety of process choices and how they might be influencing the outcomes of OSSD projects. I report a moderately negative association between how often a team updates the specifics of a requirement and how often requirements are completed. I also verified that the prevalence of volunteerism indicators is positively associated with work completion but what was surprising is that this correlation is stronger if I exclude the very large projects. I suggest the largest projects at Apache may benefit from some level of traditional delegation in addition to the phenomenon of volunteerism that OSSD is normally associated with.

Distributed Renewable energy generators are now contributing a significant amount of energy into the energy grid. Consequently, reliability adequacy of such energy generators will depend on making accurate forecasts of energy produced by them. Power outputs of Solar PV systems depend on the stochastic variation of environmental factors (solar irradiance, ambient temperature & wind speed) and random mechanical failures/repairs. Monte Carlo Simulation which is typically used to model such problems becomes too computationally intensive leading to simplifying state-space assumptions. Multi-state models for power system reliability offer a higher flexibility in providing a description of system state evolution and an accurate representation of probability. In this study, Universal Generating Functions (UGF) were used to solve such combinatorial problems. 8 grid connected Solar PV systems were analyzed with a combined capacity of about 5MW located in a hot-dry climate (Arizona) and accuracy of 98% was achieved when validated with real-time data. An analytics framework is provided to grid operators and utilities to effectively forecast energy produced by distributed energy assets and in turn, develop strategies for effective Demand Response in times of increased share of renewable distributed energy assets in the grid. Second part of this thesis extends the environmental modelling approach to develop an aging test to be run in conjunction with an accelerated test of Solar PV modules. Accelerated Lifetime Testing procedures in the industry are used to determine the dominant failure modes which the product undergoes in the field, as well as predict the lifetime of the product. UV stressor is one of the ten stressors which a PV module undergoes in the field. UV exposure causes browning of modules leading to drop in Short Circuit Current. This thesis presents an environmental modelling approach for the hot-dry climate and extends it to develop an aging test methodology. This along with the accelerated tests would help achieve the goal of correlating field failures with accelerated tests and obtain acceleration factor. This knowledge would help predict PV module degradation in the field within 30% of the actual value and help in knowing the PV module lifetime accurately.

Resource allocation in cloud computing determines the allocation of computer and network resources of service providers to service requests of cloud users for meeting the cloud users' service requirements. The efficient and effective resource allocation determines the success of cloud computing. However, it is challenging to satisfy objectives of all service providers and all cloud users in an unpredictable environment with dynamic workload, large shared resources and complex policies to manage them.

Many studies propose to use centralized algorithms for achieving optimal solutions for resource allocation. However, the centralized algorithms may encounter the scalability problem to handle a large number of service requests in a realistically satisfactory time. Hence, this dissertation presents two studies. One study develops and tests heuristics of centralized resource allocation to produce near-optimal solutions in a scalable manner. Another study looks into decentralized methods of performing resource allocation.

The first part of this dissertation defines the resource allocation problem as a centralized optimization problem in Mixed Integer Programming (MIP) and obtains the optimal solutions for various resource-service problem scenarios. Based on the analysis of the optimal solutions, various heuristics are designed for efficient resource allocation. Extended experiments are conducted with larger numbers of user requests and service providers for performance evaluation of the resource allocation heuristics. Experimental results of the resource allocation heuristics show the comparable performance of the heuristics to the optimal solutions from solving the optimization problem. Moreover, the resource allocation heuristics demonstrate better computational efficiency and thus scalability than solving the optimization problem.

The second part of this dissertation looks into elements of service provider-user coordination first in the formulation of the centralized resource allocation problem in MIP and then in the formulation of the optimization problem in a decentralized manner for various problem cases. By examining differences between the centralized, optimal solutions and the decentralized solutions for those problem cases, the analysis of how the decentralized service provider-user coordination breaks down the optimal solutions is performed. Based on the analysis, strategies of decentralized service provider-user coordination are developed.