Blood products, either whole blood or its components, are vital healthcare commodities for patients across all age groups, multiple diagnoses, and in a variety of settings. Meanwhile, blood shortages are common, and are projected to significantly increase in the near future in both developing and developed countries due to a limited supply of and increasing demand for blood, lack of resources, infrastructure. Unfortunately, today there remains a definable risk associated with the transfusion of blood and blood products. We explored, in depth, the resource allocation problem in reducing the risks of transfusion-transmitted infections (TTI). We developed models and algorithms to study the problem of selecting a set of blood screening tests for risk reduction, which we show to be very efficient in numerical studies with realistic-sized problems. This analysis also motivates the development of effective lower bounds with co-infection; our analysis indicates that these algorithms are very efficient and effective for the general problem. We also incorporate other objective functions and constraints (i.e., waste) into the analysis. Waste, defined as the fraction of disposed blood in the ``infection-free" blood, is incorporated into the risk-based model as a constraint. As an important extension, we compared our results of the blood screening problem in risk model with that of weighted risk objectives, which allows for different weights for each TTI. We further explored efficient algorithms to study this extension of the model and analyze how the test composition changes with the different objectives. Finally, in the context of blood screening, the last extension we investigated is to include a ``differential" testing policy, in which an optimal solution is allowed to contain multiple test sets, each applied to a fraction of the total blood units. In particular, the decision-maker faces the problem of selecting a collection of test sets as well as determining the proportion (or fraction) of blood units each test set will be administered to. We proposed the solution methodology and determined how the test sets under differential policy relate to those under the "same-for-all" policy; and how these changes impact the risk, and allow for better budget utilization. / Ph. D.

Blood products are essential components of any healthcare system, and their safety, in terms of being free of transfusion-transmittable infections, is crucial. While the Food and Drug Administration (FDA) in the United States requires all blood donations to be tested for a set of infections, it does not dictate which particular tests should be used by blood collection centers. Multiple FDA-licensed blood screening tests are available for each infection, but all screening tests are imperfectly reliable and have different costs. In addition, infection prevalence rates and several donor characteristics are uncertain, while surveillance methods are highly resource- and time-intensive. Therefore, only limited information is available to budget-constrained blood collection centers that need to devise a post-donation blood screening scheme so as to minimize the risk of an infectious donation being released into the blood supply. Our focus is on "robust" screening schemes under limited information. Toward this goal, we consider various objectives, and characterize structural properties of the optimal solutions under each objective. This allows us to gain insight and to develop efficient algorithms. Our research shows that using the proposed optimization-based approaches provides robust solutions with significantly lower expected infection risk compared to other testing schemes that satisfy the FDA requirements. Our findings have important public policy implications. / Ph. D.