Alternative mathematical formulation and hybrid meta-heuristics for patient scheduling problem in health care clinics

The proper management of patients’ waiting time requires the use of reasonable decision logic and tool. Simulation and optimization techniques can support management decisions to reduce the risk of the decision process by evaluating and analyzing various patient flow control strategies. The purpose of this study is to propose mathematical models and algorithmic frameworks to minimize the waiting time of patients and to determine the timing of the services of an emergency center. The patient scheduling problem is formulated as integer programming models, and the large instances of the problem are solved by Tabu search method and L-shaped algorithm. This cross-sectional descriptive study is conducted on 150 patients referred to the emergency department of a government hospital, and the required data are collected through a questionnaire. A discrete-event simulation model is also designed using the Arena software. According to the results of this paper, to reduce the waiting time of patients, execution of the triage process of patients in the emergency department, the use of an emergency medicine specialist for medical diagnosis and ordering the diagnostic procedures in the early stages of the process—as well as a specialist laboratory for emergency patients—are suggested to accelerate the hospital process. In the secondary work, we extended a first come first serve algorithm using a fairness ratio. The extended system prioritized the entry patients and separated non-urgent from others in terms of frequency. The result of the numerical experiments shows that the implementation of the system in five scenarios results in 11% decrement in operation time.