Growing attention is being paid to the problem of efficiently designing and operating reverse supply chain systems to handle the return flows of production wastes, packaging, and end-of-life products. Because uncertainty plays a significant role in all fields of decision-making, solution methodologies for determining the strategic infrastructure of reverse production systems under uncertainty are required. This dissertation presents innovative optimization algorithms for designing a robust network infrastructure when uncertainty affects the outcomes of the decisions. In our context, robustness is defined as minimizing the maximum regret under all realization of the uncertain parameters. These new algorithms can be effectively used in designing supply chain network infrastructure when the joint probability distributions of key parameters are unknown. These algorithms only require the information on potential ranges and possible discrete values of uncertain parameters, which often are available in practice. These algorithms extend the state of the art in robust optimization, both in the structure of the problems they address and the size of the formulations. An algorithm for dealing with the problem with correlated uncertain parameters is also presented. Case studies in reverse production system infrastructure design are presented. The approach is generalizable to the robust design of network supply chain systems with reverse production systems as one of their subsystems.

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.