Data-driven robust outpatient physician scheduling with medical visiting information

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.