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Inspired by the testing and vaccination center location during COVID-19 pandemic, we discuss models for covering stationary and mobile customers in an urban region. In the first part of the talk, we focus on stationary customers and introduce the 'location-or-routing problem', in which open facilities cover the customers in their neighborhood and the uncovered customers are served by capacitated vehicles dispatched from open facilities. In this setting, a customer can be covered either by location or by routing, hence the problem name. We develop a branch-and-price algorithm, investigate the impacts of facility coverage range on the total cost and find a linear relationship between the two factors. We discuss the reasons behind this observation using arguments from asymptotic analysis. In the second part of the talk, we focus on mobile customers and drive-in facilities. We present the maximum availability service facility location problem, for which we develop an accelerated Benders decomposition algorithm. Experimental study marks the importance of mobile facilities in rapidly changing environments such as confinements. In conclusion, these generalized models have the potential to improve the availability of the service facilities for the general public and improve the system performance.