Developing an Optimal Appointment Scheduling for Systems with non-Flexible Standby Time under pre-Determined Service Levels

One of the critical steps in patient care path is diagnosis. The demand for advance imaging tests, such as CT, MRI and 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. In most healthcare systems, where examination length is uncertain (stochastic), the goal of the appointment scheduling need to balance between resource utilization and patient waiting times.

In some imaging scans, such as PET, a radiopharmaceutical (radioactive substance) is injected to the patients in order to perform the diagnosis. In these systems, the time between the substance injection and the scan is non-flexible (for example, due to short half-life duration). This constraint makes the patient appointment scheduling more challenging, because, on the one hand, there is a predetermined time required between the injection of the radiopharmaceutical and the scan – the uptake time (time that it takes to the substance injected to be absorbed into the body), while on the other hand, if at the end of the expected uptake time the scanner is not available, the quality of the scan is jeopardized. Of course, the availability of the scanner is a consequence of appointments and durations of prior scans.

Therefore, the aim of this work is to develop a method for determining a patient appointment scheduling in a system with non-flexible uptake time in order to minimize the end of day and increase resource utilization while keeping minimal pre-determined service levels.

To this end, we consider the following setting: a given sequence of patients is to be scheduled on one scanner machine; the durations of scans are normally distributed with various expectations and variances; a minimal probability for each appointment to start on time is required (service level).

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 also develop a simulation-based sequential model. We found that a constant slot per scan, as a benchmark, is inferior to our method both in achieving stable service level and reducing the end of day.