Designing a testing kit supply network for suspected COVID-19 cases under mixed uncertainty approach

Motivated by the COVID-19 (C-19) pandemic and the challenges it poses to global health and the medical communities, this research aims to investigate the factors affecting of reduction health inequalities related to the C-19 to tackle the increasing number of outbreaks and their social consequences in such a pandemic. Hence, we design a COVID-19 testing kit supply network (C-19TKSN) to allocate various C-19 test kits to the suspected C-19 cases depending on the time between the emergence of their first symptoms and the time they are tested. In particular, this model aims to minimize the total network cost and decrease false results C-19 test by considering the fundamental characteristics of a diagnostic C-19 test (i.e., specificity and sensitivity). In the sensitivity characteristic, a gamma formula is presented to estimate the error rate of false-negative results. The nature of the C-19TKSN problem is dynamic over time due to difficult predictions and changes in the number of C-19 patients. For this reason, we consider the potential demands relating to different regions of the suspected C-19 cases for various C-19 test kits and the rate of prevalence of C-19 as stochastic parameters. Accordingly, a multi-stage stochastic programming (MSSP) method with a combined scenario tree is proposed to deal with the stochastic data in a dynamic environment. Then, a fuzzy approach is employed based on $$ measure to cope with the epistemic uncertainty of input data. Eventually, the practicality and capability of the proposed model are shown in a real-life case in Iran. The results demonstrate that the performance of the MSSP model is significantly better in comparison with the two-stage stochastic programming (TSSP) model regarding the false results and the total cost of the network.