Solving the Stochastic Dynamic Contagious Disease Testing Problem

PurposeIn early 2020, the coronavirus disease 2019 (COVID-19) pandemic reached global proportions within only a few weeks. A key strategy to contain and control pandemics is to isolate infected people, which requires making test results available quickly, in order to be effective. The contagious disease testing problem (CDTP) arises precisely in this context of testing potential cases (of infection). In this paper, we address the stochastic and dynamic version of the CDTP, where only some suspected cases are known in advance, while others arrive randomly throughout the course of the day. For each newly arriving suspected case, it must be decided whether to accept or reject it. The specimens of accepted suspected cases must be collected on the same day; either by assigning the case to a time slot in a test-center or by visiting the patient with a mobile test-team. Rejected suspected cases must be serviced on the next day. The task in this problem is to decide how many mobile test-teams to use, how many test-centers to open and where, which suspected cases to visit with a mobile test-team and which to assign to a test-center, and designing the vehicle routes for the mobile test-teams. The objective is to identify a dynamic assignment-and-routing policy that minimizes the number of open test-centers and used vehicles, services all early-known suspected cases, and maximizes the expected number of serviced late-known suspected cases.Design/methodology/approachWe introduce this new problem, which we call the stochastic dynamic contagious disease testing problem (SDCDTP), and formulate it as a Markov decision process. We propose a solution method based on value function approximation for solving the SDCDTP, and illustrate its performance with an extensive computational study.FindingsWe solve and analyze real-world-based problem instances from which we draw insights regarding the solution quality produced by our approach.Originality/valueWe find that a (significant) increase in the number of covered late-known suspected cases can be achieved by not minimizing the number of used vehicles and test-centers, albeit for the price of equally significant increases in the amount of used infrastructure.