Optimal Establishments of Massive Testing Programs to Combat COVID-19: A Perspective of Parallel-Machine Scheduling-Location (ScheLoc) Problem

Abstract

Massive testing to identify COVID-19-infected people is crucial in combating COVID-19. However, from the perspective of facility location problems, many current massive testing programs are not properly set, leading to unreasonable travelling distances, long makespan, unbalanced workload, and long queues. This article proposes a decision framework for developing massive testing programs. Specifically, a biobjective parallel-testing-site Scheduling-location (ScheLoc) model is formulated, simultaneously minimizing the makespan and total travelling distance. The former can help reduce the time length of potential virus spread, and the latter can help alleviate the risk of virus spread and traveler inconvenience. To solve the proposed biobjective ScheLoc problem, in addition to the standard <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\epsilon }$</tex-math></inline-formula> -constraint method, we further develop two novel strategies. The first one iteratively solves simpler approximate MIP models (IMIP). The second innovatively extends the classical logic-based Benders decomposition approach to solve biobjective problems (B-LBBD). A Hong Kong-based case study shows that the proposed decision framework can significantly reduce the makespan and travelling distance (with a mean of 13 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and 5.1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , respectively) and enhance workload balancing. Besides, the developed solution methods, especially the B-LBBD, outperform the adapted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\epsilon }$</tex-math></inline-formula> -constraint method in various aspects.