Simulation-based emergency department staffing and scheduling optimization considering part-time work shifts

Emergency department (ED) physicians have long been in short supply, which causes serious overcrowding and the excessive waiting of patients in many countries. ED managers are under great pressure to make staffing and scheduling decisions. To address this problem, this paper introduces part-time work shifts with fixed starting times and durations in peak hours to increase the flexibility and reduce patients’ waiting times. Then, a two-stage framework is proposed to optimize the weekly staffing and scheduling decisions with both fixed and part-time work shifts. Stage I is a weekly staffing problem to determine the number of physicians for both types of work shifts. The weekly staffing problem is decomposed and then solved using a simulation optimization method. Specifically, an adaptive partitioning empirical stochastic branch and bound (ESB&B-AP) algorithm is proposed by employing adaptive cut-generation methods in the process of feasible region partitioning, which significantly improves the searching efficiency of the algorithm. Stage II is a scheduling problem to determine the work schedules of physicians based on a predetermined set of work patterns. Numerical experiments validate the advantages of part-time work shifts, as well as the effectiveness of the two-stage optimization framework and the ESB&B-AP algorithm.