This study applies the Physical Optimum (PhO) as a reference value to rate the efficiency of two technical options for the oxygen supply of a hospital. The systematic comparison of the alternative processes using the PhO as a benchmark for the minimum input (exergy in this case) required to run a process with a certain benefit allows to determine the potential for optimization of each technology. Differences are analyzed by visualizing the losses of each individual production step in a process as well as by the resulting overall energy demand, including the primary energy. Possible alternatives are purchasing liquid oxygen from a cryogenic process or the production by means of Pressure Swing Adsorption (PSA) on site. The cryogenic production shows a lower exergy demand even though it also has a higher potential for optimization. Yet, the total losses, significantly impacted by the unavoidable transportation, sum up, resulting in the conclusion that the PSA is the preferable option overall, considering energy aspects. Finally, additional criteria such as economic, legal, and structural consequences of the respective choices are briefly outlined.