This paper aims to reduce the length of stay (LOS) in Emergency Departments (EDs) by designing a systematic response policy for various specialists depending on the demands of their consultation. We model the specialist consultation (SC) demands via non-homogeneous Poisson process of a daily cycle; and then based on the martingale representation theorem, we figure out the optimal SC start times for a Fixed Time (FT) policy, in order to minimize the average per-person wait time. We further compare FT policy with several alternative policies for specialists' response to consultation requests, and propose a guideline of different SC policies depending on demand volume and the duration of SCs. Moreover, using the framework of a tandem queueing network, we recommend a patient scheduling rule to incorporate with the existing triage, so that the patients requiring SC following FT can be ensured ready for SC by the specialist' arrival. The feasibility of this patient scheduling and optimal timing policies are guaranteed by an accurate prediction of ED patients' likelihood of requiring SC with their clinical information available in our empirical study. Finally, we validate our analytical results through numerical experiments and a comprehensive simulation model using ED visit record data from two Montreal hospitals of varied scales. The simulation shows that our proposed optimal times in a FT policy can reduce the wait time for specialists by 13%, and the patient scheduling together with optimal time results in a 20% decrease in total wait time.
Emily (Cheng) Zhu, Ph.D., M.Sc., is Research Associate at McGill University, Canada, and Postdoctoral Fellow at McMaster University, Canada. Her research focuses on improving the effectiveness of healthcare and enhancing efficiency in healthcare and other service systems. She contributes to strategic and operational policy making in healthcare and public health as well as clinical decision-making, by applying interdisciplinary approaches, including mathematical modelling, statistical tools, operations management and economics theory. Closely collaborating with physicians, health administrative, and researchers, she is working on several projects related to maternity care, autism, oncology, alternate-level-of-care and shared transport. Currently she is holding a Postdoctoral Fellowship from the McMaster Institute Research for Aging, and Canada’s Mitacs Accelerate Fellowship. Her doctoral dissertation was partially funded by Fonds de recherche du Québec - Société et culture. Her teaching experience includes instructing undergraduate and graduate level business and management courses, such as operations management, operations research and statistics. Additionally, she has been supervising undergraduate and graduate students’ research projects. Dr. Emily Zhu received her PhD in Operations Management from McGill University, Canada; she has an MSc in Mathematical and Computational Finance from University of Oxford, UK, and a BSc degree in Computational Mathematics from Nanjing University, China. She has passed all three levels of the Chartered Financial Analyst (CFA) program. Her previous industry experience involves quantitative financial analysis with Électricité de France (EDF) group in Europe and Desjardins Group in Canada. She was selected to attend the 2017 Saint Gallen Symposium as a Leader of Tomorrow, and is currently leading a diverse team to promote personalized healthcare, particularly preventive care and education for chronic diseases, in local communities.