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.

摘要

医院急诊科 (ED) 经常出现人满为患、等待时间过长和延误的情况。主要原因是患者到达急诊室的随机且随时间强烈变化的需求以及急诊室的临时过载。在与大型 ED 合作的推动下，我们调查了 ED 中的医生调度问题，以解决每周计划范围内的随机和随时间变化的需求。医患服务系统被建模为一个随时间变化的临时超载排队系统，不会被遗弃。我们采用连续时间马尔可夫链和统一方法来分析评估患者的等待时间。基于递增的凸阶属性，患者等待时间被证明在系统状态下是凸的。基于这种凸性，建立了一种近似技术，将医生调度问题建模为一个混合整数程序，以决定医生的开始和结束工作时间。我们还获得了这个调度问题的最优解的严格下界。设计了一种基于局部搜索的算法来解决这个调度问题。我们的方法改进了通过文献方法获得的医生排班，显着改善了实际的医院排班，同时减少了医生的工作时间和病人的等待时间。