Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments

• Published in: European journal of operational research Vol. 219; no. 3; pp. 531 - 540
• Main Authors: Izady, Navid, Worthington, Dave
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.06.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: 98% Target; Applied sciences; Biological and medical sciences; Economy. Management; Emergency medical care; Exact sciences and technology; Firm modelling; Health and social institutions; Medical sciences; Operational research and scientific management; Operational research. Management science; Optimization algorithms; Public health. Hygiene; Public health. Hygiene-occupational medicine; Queuing theory; Queuing theory. Traffic theory; Simulation; Staffing emergency departments; Studies; Time-dependent queues; Workforce planning; United Kingdom > UK; Staffing emergency departments; 98% Target; Simulation; Time-dependent queues; Square root; Government; Iterative method; Staff management; Resource sharing; Queueing network; Waiting time; Recruitment; Time dependence; Network servers; Emergency department; Time queue; Time complexity
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.10.040

► We considered the staffing problem in English emergency departments. ► We combined queueing and simulation models to search for minimal staffing profiles. ► Applying the method to a generic ED shows that improvements can be made even without increase in total staff-hours. ► Improvements arise as the result of matching staffing levels closely with demand. An incentive scheme aimed at reducing patients’ waiting times in accident and emergency departments was introduced by the UK government in 2000. It requires 98% of patients to be discharged, transferred, or admitted to inpatient care within 4hours of arrival. Setting the minimal hour by hour medical staffing levels for achieving the government target, in the presence of complexities like time-varying demand, multiple types of patients, and resource sharing, is the subject of this paper. Building on extensive body of research on time dependent queues, we propose an iterative scheme which uses infinite server networks, the square root staffing law, and simulation to come up with a good solution. The implementation of this algorithm in a typical A&E department suggests that significant improvement on the target can be gained, even without increase in total staff hours.