Healthcare service centers must be sited in strategic locations that meet the immediate needs of patients. The current situation due to the COVID-19 pandemic makes this problem particularly relevant. Assume that each center corresponds to an assigned place for vaccination and that each center uses one or more vaccine brands/laboratories. Then, each patient could choose a center instead of another, because she/he may prefer the vaccine from a more reliable laboratory. This defines an order of preference that might depend on each patient who may not want to be vaccinated in a center where there are only her/his non-preferred vaccine brands. In countries where the vaccination process is considered successful, the order assigned by each patient to the vaccination centers is defined by incentives that local governments give to their population. These same incentives for foreign citizens are seen as a strategic decision to generate income from tourism. The simple plant/center location problem (SPLP) is a combinatorial approach that has been extensively studied. However, a less-known natural extension of it with order (SPLPO) has not been explored in the same depth. In this case, the size of the instances that can be solved is limited. The SPLPO considers an order of preference that patients have over a set of facilities to meet their demands. This order adds a new set of constraints in its formulation that increases the complexity of the problem to obtain an optimal solution. In this paper, we propose a new two-stage stochastic formulation for the SPLPO (2S-SPLPO) that mimics the mentioned pandemic situation, where the order of preference is treated as a random vector. We carry out computational experiments on simulated 2S-SPLPO instances to evaluate the performance of the new proposal. We apply an algorithm based on Lagrangian relaxation that has been shown to be efficient for large instances of the SPLPO. A potential application of this new algorithm to COVID-19 vaccination is discussed and explored based on sensor-related data. Two further algorithms are proposed to store the patient’s records in a data warehouse and generate 2S-SPLPO instances using sensors.