以三階段整數規劃模型求解麻醉護理人員排班問題

Abstract

在醫療技術不斷進步的同時，社會大眾對醫療系統的品質與數量需求也持續增加。不論是國外或是臺灣本地的醫療機構，都會面臨服務品質與服務成本之間的取捨，如何在盡力降低營運成本的同時，又能為病患帶來更好的醫療品質，成為各家醫院必須要思考的課題。在此挑戰之下，大部分醫院的護理人員排班問題卻依然是靠管理人員用人工的方式進行，人手排班不但費時，而且無法確保班表的品質，護理人員的上班狀況與醫療機構的服務品質及成本息息相關，如果能提升護理人員排班的效率，必然會對醫院營運有正面的影響。過往針對護理排班的相關研究不少，不過大多都是以病房護理師為研究對象，聚焦在麻醉護理師的則相對較少，而且很多時候會受限於問題的規模，當問題規模變大時就很難得到理想的結果。 本研究把麻醉護理人員的排班問題分解成三個部分，並建立一個三階段的護理人員排班模型。第一階段為決定最適班型組合，首先考量排班時的部分軟、硬限制，以一週為時間單位建構出一系列的可行週班型，並且以整數規劃模型求解符合需求限制的最適班型組合。第二階段為班型指派，把上一階段得到的班型組合指派給屬於不同組別的護理人員，此階段同樣是以整數規劃進行模型的建構。第三階段為排加班序，參考護理人員過去的歷史加班資料作為指標，搭配上一階段產出的班表，以公平性為原則決定在此班表下各班別護理人員的加班先後順序。本研究以臺北一大型醫學中心的麻醉部門作為排班模型建立的參考個案，並以個案提供的資料進行不同情境的分析，在模型的各階段都取得良好的結果，期望本研究能供未來護理人員排班問題的研究者與排班者作參考。

As medical technology advances, the public's demand for the quality and quantity of medical systems continues to increase. Many medical institutions, be they local or foreign, are facing a trade-off between service quality and service cost. Reducing operating costs and improving medical service quality at the same time is an important issue for healthcare industry. Since the working condition of nurses is closely related to the above two factors, improving the efficiency of nurse scheduling will inevitably have a positive impact on hospital operations. Unfortunately, the nurse rostering procedure in most hospitals still relies on the management personnel to perform it manually, which is not only time-consuming, but also cannot ensure the quality of the schedule. Although there were many studies on nurse scheduling, most of them focused on ward nurses, instead of the nurse anesthetists. Besides, it is difficult acquiring the desired result when the scale of the problem expands. This study decomposes the nurse anesthetists scheduling problem into three parts and establishes a three-stage nurse scheduling model. The first stage is to determine the optimal set of shift patterns. First, we consider several hard and soft constraints of the nurse scheduling problem, and construct a series of feasible weekly shift patterns. Then we apply a integer programming model to solve the optimal set of shift patterns that fulfill the workforce demand. The second stage is shift patterns allocation. The shift patterns obtained in the previous stage is allocated to different groups of nurses by a integer programming model. The third stage is to determine the overtime working schedule. By using the historical overtime working data as an indicator with the nursing schedule obtained in the previous stage, we proposed the queue of nurse working overtime based on the principle of fairness. This study uses the anesthesia department of a large hospital in Taipei as a reference case. Moreover, we use the information provided by the case to analyze different scenarios and achieve good results at all stages of the model. We believe that this research could be used as a reference for nurse scheduling researchers and schedulers.