Weekly scheduling of emergency department physicians to cope with time-varying demand

Abstract

Overcrowding, long waiting times and delays frequently occur in hospital Emergency Departments (EDs). The main causes are the stochastic and strongly time-varying demands of patient arrivals at an ED and the temporary overloading of EDs. Motivated by collaboration with large EDs, we investigate the physicians scheduling problem in the ED for a weekly planning horizon to address the stochastic and time-varying demands. The patient–physician service system is modeled as a time-varying and temporarily overloaded queueing system without abandonments. We employ a continuous-time Markov chain and uniformization method for the analytical evaluation of waiting times of patients. Based on an increasing convex order property, patient waiting times are proven to be convex in a system state. Based on this convexity, an approximation technique is established to model the physician scheduling problem as a mixed-integer program to decide the start and end working times of physicians. We also obtain a tight lower bound of the optimal solution to this scheduling problem. A local search-based algorithm is designed to solve this scheduling problem. Our method improves the physician schedule obtained via the approaches from the literature, significantly improves actual hospital scheduling, and simultaneously reduces physician working times and patient waiting times.

Keywords:

• Emergency department
• time-varying demand
• physician scheduling
• uniformization method

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (Grants 71972133, 71672112 and 71671111).

Notes on contributors

Ran Liu

Ran Liu is an associated professor in the Department of Industrial Engineering and Management, Shanghai Jiao Tong University, Shanghai, China. His research interests include combinational optimization, stochastic optimization, and the applications to healthcare and manufacturing operations management. He earned a PhD in industrial engineering from Shanghai Jiao Tong University, Shanghai, China, and a BEng in industrial engineering from Northwestern Polytechnical University, Xi’an, China.

Xiaolan Xie

Xiaolan Xie is a professor of industrial engineering and the head of the Department of Healthcare Engineering of the Center for Biomedical and Healthcare Engineering, Ecole Nationale Superieure des Mines, Saint Etienne, France. He has also been a chair professor at Shanghai Jiao Tong University, a research director at the Institute National de Recherche en Informatique et en Automatique (INRIA), and a full professor at Ecole Nationale d’Ingenieurs de Metz. His research interests include modeling, performance evaluation, optimization, and data analytics of healthcare and manufacturing systems. He is the author/coauthor of 300+ publications including 120+ journal articles and six books. He is a fellow of IEEE. He received his PhD from the University of Nancy I, Nancy, France, in 1989, and the Habilitation à Diriger des Recherches degree from the University of Metz, France, in 1995.