Robust location for quarantine facilities under decentralized room assignment: A bi-level mixed-integer programming approach

Centralized quarantine has been proven an effective counter-pandemic measure. However, the design of quarantine facility location and allocation remains challenging because it should strike a balance among costs, cross-infection risk and public acceptance. In this study, we consider the quarantine facility location problem where different arrival nodes (e.g., airports, railway stations, etc.) are allocated with different groups of designated quarantine hotels (DQHs) to reduce the cross-infection risk while public acceptance is maintained by allowing inbound travelers to choose any available rooms in the DQHs. Under some mild assumptions on travelers’ room choice behavior, we first mathematically derive a novel equilibrium condition to model all possible outcomes of the decentralized room assignment. Due to the non-uniqueness of the equilibrium, we then develop a robust quarantine facility location model which optimizes the worst-case scenario. The model appears as a bi-level mixed-integer program (BMIP), in which the government decides the DQH location and allocation in the upper level to minimize the total cost, while inbound travelers in the lower level make their room choices to maximize the government’s objective. To solve the proposed BMIP on large-scale problems, we design an iterated local search (ILS) algorithm. Numerical results show that the ILS algorithm outperforms the state-of-the-art BMIP solver and a column-and-row-generation-based exact algorithm given a 2-hour running time limit. Finally, we conduct a case study based on the data published by the Hong Kong government. The result suggests that the proposed model can significantly decrease the cost variation due to decentralized room assignment.