Imaging facilities are usually critical resources in the hospital.Managers are under high pressure to pursue the high utilization of these resources, which lead to long waiting time of patients.Long waiting may increase the patients' anxiety and the potential risk of aggravating patients' condition.By considering different waiting time target(WTT),this paper proposes a bi-level nested threshold.When non-emergency patients arrive, the nested threshold reserves a certain amount of capacity for the future-arrival emergency patients.When a patient cannot reserve the time slot within his/her WTT,the patient will leave the hospital which incurs a penalty for the hospital.The objective is to minimize the total penalty for losing the patients.By using the partial deriva-tives of objective function with respective to nested threshold as the descending direction,this paper uses simula-tion for estimating the partial derivatives and finds the good threshold by iteration.Compared with the traditional nested threshold policy in numerical experiments,the proposed bi-level nested threshold can greatly reduce the penalty for losing patients.%图像检查设备是医院的瓶颈资源.医院管理者通常追求瓶颈资源的高利用率,导致患者需长时间等待才能进行检查.长时间的等待加剧了患者的焦虑情绪,也会给患者造成病情加重等隐患.考虑患者具有不同的目标等待时间,本文针对医疗关键资源能力分派问题,提出了双层嵌套的阈值策略.非紧急患者预约时,双层嵌套阈值考虑为将来到达的紧急患者预留一定量的能力.如果患者在目标等待时间内预约不成功,则离开医院,并对医院造成患者流失惩罚.目标函数是使患者总流失惩罚最小.本文用目标函数对嵌套阈值的偏导数作为最速梯度法下降方向,基于样本路径对该偏导数进行估计,并通过不断迭代得到最优阈值.数值实验中,与医院应用的传统阈值策略比较,结果显示,本文所提嵌套阈值策略能够有效降低因超过目标等待时间而流失的患者给医院带来的损失.
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