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A stochastic optimization model for shift scheduling in emergency departments.

Omar El-Rifai1, Thierry Garaix, Vincent Augusto

  • 1ROGI - LIMOS UMR CNRS 6158, Center for Biomedical and Healthcare Engineering, Ecole Nationale Superieure des Mines de Saint Etienne, Saint Etienne, France.

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Optimizing emergency department (ED) staffing schedules can reduce patient wait times. This study developed a model to balance staff workload and improve patient care by minimizing delays in EDs.

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Area of Science:

  • Operations Research
  • Healthcare Management
  • Emergency Medicine

Background:

  • Excessive patient waiting times in Emergency Departments (EDs) are a significant concern, impacting patient health and satisfaction.
  • ED service capacity is constrained by human resources and bed availability, leading to demand exceeding service capacity.
  • Effective personnel scheduling is crucial for balancing service quality and staff working conditions in EDs.

Purpose of the Study:

  • To optimize personnel scheduling in Emergency Departments (EDs) to minimize total expected patient waiting times.
  • To balance the competing demands of service quality and employee working conditions through efficient shift distribution.
  • To address the complexities of a multi-stage re-entrant service process within the ED patient flow.

Main Methods:

  • Development of a stochastic mixed-integer programming model to approximate patient waiting times.
  • Utilization of a Sample Average Approximation (SAA) approach to solve the proposed optimization model.
  • Evaluation of personnel schedules using a discrete-event simulation model with data from a French hospital.

Main Results:

  • The study successfully formulated and solved an optimization model for ED personnel scheduling.
  • Simulation results demonstrated the effectiveness of the proposed scheduling strategies in reducing patient waiting times.
  • Numerical experiments provided insights into comparing different personnel scheduling approaches in a real-world ED setting.

Conclusions:

  • Optimized personnel scheduling significantly reduces patient waiting times in Emergency Departments.
  • The developed stochastic programming and simulation approach offers a valuable tool for ED resource management.
  • Balancing staff scheduling with patient flow is key to improving ED operational efficiency and patient outcomes.