A stochastic optimization model for shift scheduling in emergency departments

Omar El-Rifai (1) , Thierry Garaix (2, 1) , Vincent Augusto (2) , Xiaolan Xie (3)

1 CIS-ENSMSE - Centre Ingénierie et Santé
2 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
3 DIELM - Department of Industrial Engineering and Logistics Management

Excessive waiting time in Emergency Departments (ED) can be both a cause of frustration and more importantly, a health concern for patients. Waiting time arises when the demand for work goes beyond the facility's service capacity. ED service capacity mainly depends on human resources and on beds available for patients. In this paper, we focus on human resources organization in an ED and seek to best balance between service quality and working conditions. More specifically, we address the personnel scheduling problem in order to optimize the shift distribution among employees and minimize the total expected patients' waiting time. The problem is also characterized by a multi-stage re-entrant service process. With an appropriate approximation of patients' waiting times, we first propose a stochastic mixed-integer programming model that is solved by a sample average approximation (SAA) approach. The resulting personnel schedules are then evaluated using a discrete-event simulation model. Numerical experiments are then performed with data from a French hospital to compare different personnel scheduling strategies.

Domaines: Recherche opérationnelle [math.OC]

Omar El-Rifai, Thierry Garaix, Vincent Augusto, Xiaolan Xie. A stochastic optimization model for shift scheduling in emergency departments. Health Care Management Science, 2015, 18 (3), pp.289 - 302. ⟨10.1007/s10729-014-9300-4⟩. ⟨hal-01905878⟩