A Mathematical Formulation for Reducing Overcrowding in Hospitals' Waiting Rooms

The COVID-19 pandemic has triggered several new measures in public and private companies to limit the spread of the virus. One of the most effective measures was shown to be social distancing, but such measure is not easy to implement for every entity, especially for hospitals. In this work, we study the case of an Italian hospital whose goal is to find the best layout of outpatient services to reduce overcrowding in the waiting rooms. We propose an Integer Linear Programming model to identify the weekly optimal layout and we test it on a set of real data from the year 2019. The results obtained by our model reduce the overcrowding by 80% on average with respect to the results obtained with the configuration used by the hospital, but such results can only be obtained if the layout is allowed to change every week. We then study the case in which we force the layout to be fixed for two or three consecutive weeks and outline that both the computational time and the solution quality worsen significantly.