He Qingyun, Shen Shuqun, Lv Zhiyu, Yang Shixin
School of Finance and Economics, Anhui Science and Technology University, Bengbu, 233000, China.
Dermatology Hospital, Southern Medical University, Guangzhou, 510515, China.
Sci Rep. 2025 May 23;15(1):18013. doi: 10.1038/s41598-025-01654-3.
Over the last decades, hospitals have faced shortages of medical personnel due to increasing demand. As one of the busiest divisions, the outpatient department plays a vital role in delivering public healthcare services, leading to a significant focus on physician work schedules. In this study, we develop a data-driven optimization framework for a mid-term period spanning several weeks within the outpatient department of a dermatology hospital. This framework integrates patient visit clustering and physician work scheduling sequentially, thereby ensuring its scalability for application in many other hospitals. We first employ a hybrid clustering model that classifies patient visits based on a joint distribution of physician-patient characteristics. This clustering model inherently captures patient preferences for physicians so that patient demand is stratified to each physician. Then, we propose a robust physician scheduling model based on a novel risk measure called Likelihood Robust Value at Risk (LRCVaR). In particular, the proposed LRCVaR considers the worst-case demand in an ambiguity set of possible distributions, leading to mitigated tail risks of service capacity shortages. Therefore, this scheduling model mitigates tail risks of service capacity shortages. A tractable reformulation of the proposed robust physician scheduling model is newly derived, and we show their equivalence using strong duality theory. An iterated algorithm for the reformulation is also delicately designed, and we demonstrate its applicability to off-the-shelf solvers. The case study demonstrates that our LRCVaR is less conservative while controlling for the risk level. Such a result indicates that our proposed approach can satisfy patient demand with a smaller number of physicians at the same level of risk. Dermatologists and venereologists serving as chief physicians in our studied hospital are more prone to reaching their service capacity limits. Thus, our framework outperforms existing robust approaches in reducing tail risks of capacity shortages and identifying the bottleneck of service provision.
在过去几十年里，由于需求不断增加，医院面临医务人员短缺的问题。作为最繁忙的科室之一，门诊部在提供公共医疗服务方面发挥着至关重要的作用，因此对医生工作安排给予了高度关注。在本研究中，我们为一家皮肤科医院门诊部的为期数周的中期时段开发了一个数据驱动的优化框架。该框架依次整合患者就诊聚类和医生工作安排，从而确保其在许多其他医院应用时的可扩展性。我们首先采用一种混合聚类模型，该模型基于医患特征的联合分布对患者就诊进行分类。这种聚类模型内在地捕捉了患者对医生的偏好，从而将患者需求分层到每位医生。然后，我们基于一种名为似然稳健风险价值（LRCVaR）的新型风险度量提出了一个稳健的医生排班模型。特别地，所提出的LRCVaR考虑了一组可能分布的模糊集中的最坏情况需求，从而减轻了服务能力短缺的尾部风险。因此，这个排班模型减轻了服务能力短缺的尾部风险。我们新推导了所提出的稳健医生排班模型的一个易于处理的重新表述，并使用强对偶理论证明了它们的等价性。还精心设计了该重新表述的迭代算法，并展示了其对现成求解器的适用性。案例研究表明，我们的LRCVaR在控制风险水平时不那么保守。这样的结果表明，我们提出的方法可以在相同风险水平下用更少的医生满足患者需求。在我们研究的医院中担任主任医师的皮肤科医生和性病科医生更容易达到其服务能力极限。因此，我们的框架在降低能力短缺的尾部风险和识别服务提供的瓶颈方面优于现有的稳健方法。
