Abstract: Outpatient services are a vital interface between hospitals and patients, serving as the frontline of hospital operations. The quality of these services significantly influences patients’ perceptions, evaluations and choices of hospitals. Currently, outpatient services in China face considerable challenges, including high patient demand and the persistent issue of “three kinds of long wait and one short visit.” Addressing these challenges and improving the quality of outpatient services are an urgent societal concern. This study focuses on the patient admission decision-making process in complex outpatient departments.
Complex outpatient services are characterized by extended treatment durations, multiple visits and numerous treatment activities. In these departments, patients undergo long-term treatment cycles, with varying combinations of medical service needs across different treatment stages. A key challenge for such outpatient services lies in balancing long-term patient demand with the department’s service capacity. This imbalance often results in excessive overtime or an inability to meet all patient needs. To mitigate this, outpatient managers commonly regulate the number of patients entering the system. Given that admitted patients require continuous care, managers may sometimes need to decline new patients and suggest referrals. Thus, the key management problem for complex outpatient services is how to design a reasonable admission strategy that maximizes the number of patients served while ensuring high-quality care and smooth hospital operations. Another challenge lies in the need for managers to frequently adjust admission decisions based on daily applications and the status of existing patients. As a result, this is an online scheduling problem with distinct multi-stage and dynamic characteristics.
Taking obstetric outpatient services as an example, this study develops an infinite-horizon discounted Markov Decision Process (MDP) model to address these challenges. The model accounts for several real-world uncertainties, including variability in patients’ gestational weeks at the time of application, individual preferences for specific doctors and unpredictable dropout behavior. Additionally, it captures the diverse medical service needs of heterogeneous patients at different stages of treatment and considers the varying costs associated with service provision. The objective is to optimize long-term mutual benefits for both hospitals and patients.
To tackle the “curse of dimensionality” posed by the model’s expansive state and decision space, the study proposes a solution approach based on Approximate Dynamic Programming (ADP). This approach employs basis functions to linearly approximate the value function and utilizes a dual-column generation algorithm to efficiently derive near-optimal strategies. The proposed MDP model and its solution method effectively encapsulate the complex management characteristics of outpatient services. The numerical experiments reveal significant improvements, with the model and algorithm enhancing performance by approximately 41% compared to the current practices in tertiary hospitals and by around 14% relative to heuristic threshold strategies.
The proposed complex outpatient admission model is readily applicable to the daily management of obstetric outpatient services and can be adopted with minor modifications for other complex outpatient departments with similar characteristics. Future research could explore more dynamic elements, such as demand fluctuations and seasonal effects, which may further complicate the admission decision-making process.

Key words: complex outpatient departments, admission policy, Markov decision process

摘要： 复杂门诊具有长周期、多重入、多项目的特点,其接收策略的好坏直接影响了门诊运营效率和患者服务质量。本文针对复杂门诊的患者接收问题,综合考虑多重不确定性,以最大化长期总效益为目标函数,提出一种基于无限时域折扣MDP模型的动态策略优化方法。针对模型中状态和决策空间巨大而造成的“维数灾”,设计提出基于近似动态规划的求解方法,并使用列生成方法解决了算法效率问题。本文提出的MDP模型及其求解方法(ALP-CG算法)可以精准刻画复杂门诊的管理特点,对比实验表明该模型及算法的优化效果显著,与某三甲医院实际运营情况相比,总效益提升41%,同时相较于阈值策略提升14%。

关键词: 复杂门诊, 接收策略, 马尔可夫决策过程