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.