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

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.