Developing an optimal appointment scheduling for systems with rigid standby time under pre-determined quality of service

A critical step in patient care path is diagnosis. The demand for advanced imaging tests, such as computerized axial tomography, magnetic resonance imaging and positron emission tomography (PET), increased dramatically in the past 15 years. Since imaging equipment remains relatively expensive, in order to fit the demand, the imaging resources must be managed effectively while ensuring required quality of service. In PET, a radiopharmaceutical (radioactive substance) is injected to patients prior to their scans. The time between substance injection and scan (standby or uptake time) is rigid. This constraint makes the patient appointment scheduling more challenging, because if at the end of the expected uptake time the scanner is not available, the quality of the scan is jeopardized (due to short half-life duration of the substance). The availability of the scanner is a consequence of prior scans’ appointments and durations. The aim of this work is to develop an approach for appointment scheduling in a system with one scanner, given a sequence of patients and rigid uptake time, in order to minimize the length of day while satisfying a minimal pre-determined quality of service. In order to solve this stochastic problem, we formulate its equivalent deterministic problem, based on simulated data, as a mixed-integer linear programming. To overcome the dimensionality limitations, we develop a simulation-based sequential algorithm that solves the problem in a reasonable time. We found that a fixed slot per scan policy, as a benchmark, is inferior to our method, especially in achieving stable and fair quality of service for patients.