School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China.
Department of Nuclear Medicine, Qilu Hospital of Shandong University, Jinan 250012, China.
Int J Environ Res Public Health. 2022 Oct 21;19(20):13685. doi: 10.3390/ijerph192013685.
This paper proposes an operating room (OR) scheduling model to assign a group of next-day patients to ORs while adhering to OR availability, priorities, and OR overtime constraints. Existing studies usually consider OR scheduling problems by ignoring the influence of uncertainties in surgery durations on the OR assignment. In this paper, we address this issue by formulating accurate patient waiting times as the cumulative sum of uncertain surgery durations from the robust discrete approach point of view. Specifically, by considering the patients' uncertain surgery duration, we formulate the robust OR scheduling model to minimize the sum of the fixed OR opening cost, the patient waiting penalty cost, and the OR overtime cost. Then, we adopt the box uncertainty set to specify the uncertain surgery duration, and a robustness coefficient is introduced to control the robustness of the model. This resulting robust model is essentially intractable in its original form because there are uncertain variables in both the objective function and constraint. To make this model solvable, we then transform it into a Mixed Integer Linear Programming (MILP) model by employing the robust discrete optimization theory and the strong dual theory. Moreover, to evaluate the reliability of the robust OR scheduling model under different robustness coefficients, we theoretically analyze the constraint violation probability associated with overtime constraints. Finally, an in-depth numerical analysis is conducted to verify the proposed model's effectiveness and to evaluate the robustness coefficient's impact on the model performance. Our analytical results indicate the following: (1) With the robustness coefficient, we obtain the tradeoff relationship between the total management cost and the constraint violation probability, i.e., a smaller robustness coefficient yields remarkably lower total management cost at the expense of a noticeably higher constraint violation probability and vice versa. (2) The obtained total management cost is sensitive to small robustness coefficient values, but it hardly changes as the robustness coefficient increases to a specific value. (3) The obtained total management cost becomes increasingly sensitive to the perturbation factor with the decrease in constraint violation probability.
本文提出了一种手术室（OR）调度模型，该模型将一组次日的患者分配到 OR 中，同时遵守 OR 的可用性、优先级和 OR 加班限制。现有研究通常通过忽略手术持续时间不确定性对 OR 分配的影响来考虑 OR 调度问题。在本文中，我们通过从鲁棒离散方法的角度将准确的患者等待时间表示为不确定手术持续时间的累积和来解决这个问题。具体来说，通过考虑患者不确定的手术持续时间，我们将鲁棒 OR 调度模型制定为最小化固定 OR 开启成本、患者等待惩罚成本和 OR 加班成本的总和。然后，我们采用盒式不确定性集来指定不确定的手术持续时间，并引入一个稳健系数来控制模型的稳健性。由于目标函数和约束中都存在不确定变量，因此这个原始的鲁棒模型本质上是难以解决的。为了使这个模型可解，我们然后通过采用鲁棒离散优化理论和强对偶理论将其转换为混合整数线性规划（MILP）模型。此外，为了评估不同稳健系数下鲁棒 OR 调度模型的可靠性，我们从理论上分析了与加班约束相关的约束违反概率。最后，进行了深入的数值分析，以验证所提出模型的有效性，并评估稳健系数对模型性能的影响。我们的分析结果表明：（1）通过使用稳健系数，我们获得了总管理成本和约束违反概率之间的权衡关系，即较小的稳健系数以显著较高的约束违反概率为代价产生显著较低的总管理成本，反之亦然。（2）所得到的总管理成本对小稳健系数值很敏感，但随着稳健系数增加到特定值，它几乎不变。（3）随着约束违反概率的降低，所得到的总管理成本对扰动因子变得越来越敏感。
