A multi-objective optimization scheduling problem for a Destination Medical Center

This research addresses the issue of scheduling medical treatments for patients who are coming from out-of-town for follow-up appointments in a Destination Medical Center (DMC). Scheduling all patient appointments (itineraries) in a relatively short period of time (minimum waiting time) for such patients is studied. In practice, patient waiting time is comprised of three segments: indirect-waiting time (time duration between patient call and the start day of the treatment process), inter-waiting time (waiting time between multiple appointments in a single day), and itinerary duration (in days). Compact scheduling allows patients to finish their medical treatment in fewer days. This will result in reducing patients' lodging expenses and increasing patients' satisfaction.;A multi-objective compact scheduling (MOCS) model is proposed to minimize the inter-waiting time between the medical treatment procedures while maximizing the number of scheduled patients in the time horizon. Binary integer programming (BIP) mathematical modeling is proposed with a large number of binary variables to address this scheduling problem. Additionally, the proposed model incorporates various constraints that identify the availability of resources and providers in the time horizon. A bi-level programming is used to approximate the two objectives in the model. Various analyses are performed to approximate the weight coefficient in the objective function. Three optimization search algorithms are proposed and implemented to find the Pareto optimal in the discreet search space. Tabu search, Variable Neighborhood Search (VNS), and Binary Search (BS) were tested for three performance measures: computational complexity (CPU time), the average number of scheduled patients, and time to third next available appointment (3NA).;Case studies are also used to test the models robustness by changing the setup variables. A one-way ANOVA analysis shows that there is no significant difference between the three algorithms in terms of the average number of scheduled patients. BS was the worst search algorithm in with respect to 3NA, where it shows a longer waiting time than the other two search algorithms. Experimental results show high model robustness in terms of changing the experimental setting. Overall, the multi-objective compact scheduling model generates adequate solutions to the problem under study.