This paper studies optimal criteria for the appointment scheduling of outpatients in a medical imaging center. The main goal of this study is to coordinate the assignments of radiopharmaceuticals and the scheduling of outpatients on imaging scanners. We study a special case of a molecular imaging center that offers services for various diagnostic procedures for outpatient requests. Most procedures in molecular imaging require a time-sensitive chemical element, technetium-99m (\texttt{99mTc}) with a limited half-life, and involve several steps that are constrained by strict time windows. The most important component of the radiopharmaceuticals produced in a molecular imaging center is \texttt{99mTc}. We investigate the mathematical dynamics of \texttt{99mTc} dosages to construct optimal schedules for preparing the radiopharmaceuticals. We develop a rigorous mixed-integer programming model to coordinate the assignment of the radiopharmaceuticals and the scheduling of outpatients on the scanners. The objective is to minimize the total deviation from the scheduled scanning times. We also develop a novel, less conservative robust optimization approach to capture the uncertainty raised by the availability of \texttt{99mTc}. We propose an uncertainty handling mechanism to recursively reduce the uncertainty interval over time. The proposed mechanism avoids over-conservatism and increase the reliability of mathematical robust models. We evaluate the proposed models by multiple criteria. The final results suggest that the robust model is able to schedule up to 40 outpatients with at most 20 percent of deviation from the scheduled scan times versus 30 outpatients with at most 50 percent according to the current practice. The other criteria, such as the degree of the constraint violation, suggest that the proposed model is practical and consistent with the clinical requirements.