Personnel and Patient Scheduling in the High Demanded Hospital Services: A Case Study in the Physiotherapy Service

High demand but limited staffs within some services of a hospital require a proper scheduling of staff and patients. In this study, a hierarchical mathematical model is proposed to generate weekly staff scheduling. Due to computational difficulty of this scheduling problem, the entire model is broken down into manageable three hierarchical stages: (1) selection of patients, (2) assignment of patients to the staff, (3) scheduling of patients throughout a day. The developed models were tested on the data collected in College of Medicine Research Hospital at Cukurova University using GAMS and MPL optimization packages . From the results of the case study, the presented hierarchical model provided a schedule that ensures to maximize the number of selected patients, to balance the workload of physiotherapist, and to minimize waiting time of patients in their treatment day.