Early diagnosis and treatment of newborns with Human Immunodeficiency Virus (HIV) can substantially reduce mortality rates. Polymerase chain reduction technology is desirable for diagnosing HIV-exposed infants and for monitoring the disease progression in older patients. In low- and middle-income countries (LMICs), processing both types of tests requires the use of scarce resources. In this article, we present a supply chain network model for referring/assigning HIV test samples from clinics to labs. These assignments aim to minimize the expected infant mortality from AIDS due to delays in the return of test results. Using queuing theory, we present an analytical framework to evaluate the distribution of the sample waiting times at the testing labs and incorporate it into a mathematical model. The suggested framework takes into consideration the non-stationarity in the availability of reagents and technical staff. Hence, our model provides a method to find an assignment strategy that involves an indirect prioritization of samples that are more likely than others to be positive. We also develop a heuristic to simplify the implementation of an assignment strategy and provide general managerial insights for operating sample referral networks in LMICs with limited resources. Using a case study from Tanzania, we show that the potential improvement is substantial, especially when some labs are utilized almost to their full capacity. Our results apply to other settings in which expensive equipment with volatile availability is used to perform crucial operations, for example, the recent COVID-19 pandemic.
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