A stochastic optimization model for shift scheduling in emergency departments

Abstract

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.

Methodological Approaches to Support Process Improvement in Emergency Departments: A Systematic Review

“…Interesting interventions employing this integration can be also evidenced in Bish et al [99], Ferrand et al [105], and Zeltyn et al [128]. Other papers integrating OR methods and simulation can be found in Ala and Chen [133], Diefenbach and Kozan [169], El-Rifai et al [170], Ghanes et al [107], Goienetxea Uriarte et al [108], Oueida et al [114], Sinreich et al [121], and Yousefi and Yousefi [134].…”

Assigning treatment rooms at the Emergency Department

“…[7][8][9]. These studies consider a multi-server queueing network in which customers can re-enter a queue, and the authors aim to determine appropriate staffing levels to achieve certain performance targets.…”

Scheduling Emergency Physicians Based on a Multiobjective Programming Approach: A Case Study of West China Hospital of Sichuan University

“…The decomposition strategy can handle up to 20 doctors, but the actual scheduling table is not shown. El-Rifai et al [22], based on the characteristics of emergency dynamic demand, set up a stochastic mixed integer programming model to achieve the best balance between the quality of service and the intensity of doctors' work. According to the fact that the patients' arrival rate is dynamic and random, Xie et al [23, 24] used the M/M/C queuing theory to estimate the patient's waiting time in the system of dynamic demand and then constructed the mixed integer programming model for EMR scheduling to obtain a flexible shifting scheme.…”