Test Allocation and Pool Composition in Heterogenous Populations Under Strict Capacity Constraints
研究在检测能力严格受限时，如何分配检测资源以及是否采用混合检测（池检测）策略，发现优先检测感染概率低的患者可能更优，且最优策略可能同时包含对低风险人群的池检测和对高风险人群的单独检测。
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. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation [Grant 1634822]. S. Ziya was supported by the National Science Foundation [Award CMMI1635574]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0149 .