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Disaster management generally includes the post-disaster stage, which consists of the actions taken in response to the disaster damages. These actions include the employment of emergency plans and assigned resources to (i) rescue affected people immediately, (ii) deliver personnel, medical care and equipment to the disaster area, and (iii) aid to prevent the infrastructural and environmental losses. In the response phase, humanitarian logistics directly influence the efficiency of the relief operation. Ambulances routing problem is defined as employing the optimisation tools to manage the flow of ambulances for finding the best ambulance tours to transport the injured to hospitals. Researchers pointed out the importance of equity and fairness in humanitarian relief services: managing the operations of ambulances in the immediate aftermath of a disaster must be done impartially and efficiently to rescue affected people with different priority in accordance with the restrictions. Our research aim is to find the best ambulance tours to transport the patients during a disaster in relief operations while considering fairness and equity to deliver services to patients in balance. The problem is formulated as a new variant of the team orienteering problem with hierarchical objectives to address also the efficiency issue. Due to the limitation of solving the proposed model using a general-purpose solver, we propose a new hybrid algorithm based on a machine learning and neighbourhood search. Based on a new set of realistic benchmark instances, our quantitative analysis proves that our algorithm is capable to largely reduce the solution running time especially when the complexity of the problem increases. Further, a comparison between the fair solution and the system optimum solution is also provided.

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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 https://doi.org/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.

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