Appointment scheduling for medical diagnostic centers considering time-sensitive pharmaceuticals: A dynamic robust optimization approach

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 case of a molecular imaging center that offers services for various diagnostic procedures for outpatient requests. Most procedures in molecular imaging involve several steps limited by strict time windows and require a time-sensitive chemical element, technetium-99m (99mTc) with a limited half-life, to produce the radiopharmaceuticals. We investigate the mathematical dynamics of 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 99mTc. We propose an uncertainty handling mechanism to reduce the uncertainty interval over time recursively. The proposed mechanism avoids over-conservatism and increases 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 with a decent degree of the constraint violation versus 30 outpatients with at most 50 percent according to the current practice.