Population growth is led to an increase in demand in the health sector. Health services need to be met at the maximum level in the face of increasing demand. The number of patients per each health personnel in Turkey is too much. Considering this situation, it is seen that ensuring patient satisfaction is directly proportional to the satisfaction of the personnel. For this reason, some studies such as the positioning of polyclinics and hospitals encountered in health services, capacity planning and demand estimations, as well as the studies about the creation of study schedules of health personnel are also gained importance. In this study, it is aimed to provide the personnel satisfaction as much as possible. The Law No. 3153 on Radiology, Radionomy and Electrical Therapy and Other Physiotherapy Institutions published by the Ministry of Health of the Republic of Turkey, dated 19/4/1937, as well as the requirements of the Annex-1 of 21/1/2010, is considered. The scheduling problem for eight radiology technicians working in a private hospital in Ankara is discussed. A mathematical model is proposed using the goal programming method in order to assign the technicians to the four shifts as equally as possible. According to the researches, this is the first study which has the feature of radiology technicians and by considering government and hospital conditions as well as with staff requests, by application area.