Medical Physics is recognized for the first time in the Healthcare System of the Grand Duchy of Luxembourg through the ordinance of 16 March 2001. This ordinance regulates the measures of quality assurance towards the radiation protection of patients, as well as the responsibilities and tasks of the Medical Physics Experts. The ordinance does not specify the number of qualified personnel required to perform all the quality controls demanded for the hospitals. In this work calculations were carried out, resulting in personnel requirements of 19 persons, 7 of whom as Medical Physics Experts. Also, a concept is presented proposing an optimum distribution of the personnel in order to ensure the practical implementation of the European Directive 97/43 EURATOM.