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

  • Ali Ala
  • Feng ChenEmail author
Original Article


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.


Patient scheduling Prioritize optimization Waiting time Heuristic algorithms 



The author gratefully acknowledges that the funding is supported by Medicine and Engineering Interdisciplinary Research Fund of (YG2013ZD05). The authors also thank the anonymous reviewer and editor for their insightful comments that have helped in boosting this paper significantly.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial Engineering and ManagementShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Sino-Us Global Logistics Institute, Antai College of Economy and ManagementShanghai Jiao Tong UniversityShanghaiChina

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