The daily swab test collection problem

Digital Contact Tracing (DCT) has been proved to be an effective tool to counteract the new SARS-CoV-2 or Covid-19. Despite this widespread effort to adopt the DCT, less attention has been paid to the organisation of the health logistics system that should support the tracing activities. Actually, the DCT poses a challenge to the logistics of the local health system in terms of number of daily tests to be collected and evaluated, especially when the spreading of the virus is soaring. In this paper we introduce a new optimisation problem called the Daily Swab Test Collection (DSTC) problem, that is the daily problem of collecting swab tests at home in such a way to guarantee a timely testing to people notified by the app to be in contact with a positive case. The problem is formulated as a variant of the team orienteering problem. The contributions of this paper are the following: (i) the new optimisation problem DSTC that complements and improves the DCT approach proposed by Ferretti et al. (Science 10.1126/science.abb6936, 2020), (ii) the DSCT formulation as a variant of the TOP and a literature review highlighting that this variant can have useful application in healthcare management, (iii) new realistic benchmark instances for the DSTC based on the city of Turin, (iv) two new efficient and effective hybrid algorithms capable to deal with realistic instances, (v) the managerial insights of our approach with a special regard on the fairness of the solutions. The main finding is that it possible to optimise the underlying logistics system in such a way to guarantee a timely testing to people recognised by the DCT.