Department of Maternal and Child Health, UNC Gillings School of Global Public Health, 407A Rosenau Hall, CB# 7445, Chapel Hill, NC 27599 USA.
BMC Med Res Methodol. 2010 Jun 23;10:60. doi: 10.1186/1471-2288-10-60.
A recent joint report from the Institute of Medicine and the National Academy of Engineering, highlights the benefits of--indeed, the need for--mathematical analysis of healthcare delivery. Tools for such analysis have been developed over decades by researchers in Operations Research (OR). An OR perspective typically frames a complex problem in terms of its essential mathematical structure. This article illustrates the use and value of the tools of operations research in healthcare. It reviews one OR tool, queueing theory, and provides an illustration involving a hypothetical drug treatment facility.
Queueing Theory (QT) is the study of waiting lines. The theory is useful in that it provides solutions to problems of waiting and its relationship to key characteristics of healthcare systems. More generally, it illustrates the strengths of modeling in healthcare and service delivery.Queueing theory offers insights that initially may be hidden. For example, a queueing model allows one to incorporate randomness, which is inherent in the actual system, into the mathematical analysis. As a result of this randomness, these systems often perform much worse than one might have guessed based on deterministic conditions. Poor performance is reflected in longer lines, longer waits, and lower levels of server utilization.As an illustration, we specify a queueing model of a representative drug treatment facility. The analysis of this model provides mathematical expressions for some of the key performance measures, such as average waiting time for admission.
We calculate average occupancy in the facility and its relationship to system characteristics. For example, when the facility has 28 beds, the average wait for admission is 4 days. We also explore the relationship between arrival rate at the facility, the capacity of the facility, and waiting times.
One key aspect of the healthcare system is its complexity, and policy makers want to design and reform the system in a way that affects competing goals. OR methodologies, particularly queueing theory, can be very useful in gaining deeper understanding of this complexity and exploring the potential effects of proposed changes on the system without making any actual changes.
医学研究所和国家工程院的一份联合报告强调了——实际上，也需要——对医疗保健提供进行数学分析。几十年来，运筹学（OR）的研究人员已经开发出了用于此类分析的工具。从 OR 的角度来看，一个复杂问题通常是根据其基本的数学结构来构建的。本文说明了在医疗保健中使用和利用运筹学工具的方法。它回顾了一个 OR 工具，排队论，并提供了一个涉及假设药物治疗设施的例子。
排队论（QT）是对等待队列的研究。该理论之所以有用，是因为它为等待问题及其与医疗系统关键特征的关系提供了解决方案。更一般地说，它说明了建模在医疗保健和服务提供中的优势。排队论提供了最初可能隐藏的见解。例如，排队模型允许将系统中固有的随机性纳入数学分析。由于这种随机性，这些系统的性能往往比根据确定条件猜测的要差得多。较差的性能反映在更长的队列、更长的等待时间和更低的服务器利用率上。作为一个例子，我们指定了一个有代表性的药物治疗设施的排队模型。对该模型的分析提供了一些关键性能指标的数学表达式，例如入院平均等待时间。
我们计算了设施中的平均入住率及其与系统特征的关系。例如，当设施有 28 张床位时，平均入院等待时间为 4 天。我们还探讨了设施的到达率、设施的容量和等待时间之间的关系。
医疗保健系统的一个关键方面是其复杂性，政策制定者希望以影响竞争目标的方式设计和改革系统。OR 方法，特别是排队论，可以非常有助于更深入地了解这种复杂性，并在不进行任何实际更改的情况下探索拟议更改对系统的潜在影响。
