Test Allocation and Pool Composition in Heterogenous Populations Under Strict Capacity Constraints

Problem definition : Motivated by the persistent lack of testing capacity in the first year of the COVID-19 pandemic, we study the question “who should be tested?” when there are general costs and rewards, testing capacity is strictly limited, tests have errors, and patients differ in their prior probability of being infected. We specifically study how the answer to that question changes when pooled testing, a method of grouping samples to conserve tests, is an option. Methodology/results : We use a two-stage stochastic optimization model with recourse, incorporating costs and rewards for different test outcomes, under a conservative capacity constraint that reflects severe shortages of tests or high uncertainty about future test availability. This setting reflects the situation decision makers faced at the beginning of the COVID-19 pandemic in March 2020. Although health officials might intuitively prioritize testing patients who are highly likely to be infected, we find that it may be better to focus on patients who are less likely to be infected, particularly when the test has low sensitivity (i.e., the false-negative rate is substantial). Moreover, it may be optimal to test two groups of individuals: those who are very unlikely to be infected (in pools) and those who are very likely to be infected (individually). Managerial implications : We develop a heuristic policy supported by the analysis, which indicates when pooling should be used and which type of samples should be tested. In some settings, the decision may be characterized simply by understanding the costs and rewards involved. In more complex testing settings, the characteristics of the test and the size of the pool affect the desirability of pooling: Lower specificity, higher sensitivity, and larger pool sizes all result in testing environments that are more favorable to pooling. Managers and policymakers should understand how characteristics of the test and the setting impact whether it is optimal to test patients who are deemed likely to test positive or those who are likely to test negative. Incorporating pooling as a test strategy may change which patients should be prioritized for a test. Our results can inform both public health policy and healthcare operations management in settings where testing capacity is strictly limited.