Optimal Staffing Policies to Stabilize Performance at Target Levels in Service Networks with Time-Varying Arrivals

本研究的重点是开发、实施和评估新的有效政策，以在大规模多服务器排队网络中设置适当的人员配备水平，这些网络配备了现实世界服务系统中典型的复杂特征。首先，服务系统的到达率通常会随着时间的推移而显著变化，而标准排队模型并没有考虑到这一点。其次，等待客户的放弃，相当于病人离开而没有得到护理提供者的照顾，或者呼叫中心的呼叫者挂断电话，可以显著改变系统性能。此外，经验数据表明，服务时间和放弃时间都不呈指数分布。最后，服务系统往往表现出复杂的网络结构，例如：(a)已接受服务但仍需要更多服务的顾客重新试用；(b)在多个设施之间流动，如在医院的不同部门之间流动。尽管有大量的排队理论文献，但这些特征的模型复杂性使得精确分析远远超出了现有方法的范围。针对这些挑战，本研究将开发具有上述所有现实特征的大规模排队网络的最优人员配置策略，旨在揭示基本原理，推进运筹学方法，设计有效的控制策略以更好地管理服务系统，并寻求有效的近似，将大规模转化为优势而不是劣势。如果成功，这项研究的结果将为更好地设计和管理服务系统提供新的工具，特别强调医疗保健系统。为了控制成本，许多医院严重人手不足；当资源（如护士和床位）不可避免地有限时，低效的人员配置策略可能导致过度痛苦、低质量的护理、最终治疗结果的退化以及死亡率的显著增加。本文的研究旨在帮助系统管理者做出正确的运营决策；它将有助于回答以下问题：医院应该如何在接下来的一周内安排医生和护士，以使治疗前的延误最多不超过一个小时？有多少病人需要等待超过4个小时？这项研究也适用于许多其他应用，例如，客户联络中心；向低收入租户提供公寓的公共住房当局；处理网页请求的web服务器农场；金融后台处理贷款。教育推广将是这个项目的关键组成部分，因为研究者对本科和研究生阶段的工程教育都有着深刻的承诺。通过一系列的暑期讲习班和夏令营，研究者一直积极向K-12学生介绍运筹学技术（特别强调排队论）。这个项目的结果将被整合到研究者新的本科和研究生课程中。

This research is focused on the development, implementation, and evaluation of new and effective policies to set appropriate staffing levels in large-scale multiserver queuing networks that are equipped with complex features typically found in real-world service systems. First, arrival rates in service systems typically vary significantly over time, which is not accounted for by standard queuing models. Second, abandonment by waiting customers, which corresponds to patients leaving without being seen by a care provider, or to callers hanging up in a call center, can significantly alter system performance. In addition, empirical data show that neither service time nor abandonment time is exponentially distributed. Finally, service systems often exhibit complicated network structures, such as the following: (a) retrials by customers who have received service but still need more service; and (b) flows among multiple facilities, as occurring among different units in a hospital. Despite the immense queuing-theory literature, the model complexity of these features makes exact analysis far beyond the scope of existing methodologies. In response to these challenges, this research will develop optimal staffing strategies for large-scale queuing networks with all the above realistic features, aiming at uncovering fundamental principles, advancing operations research methodologies, devising effective control policies for better managing service systems, and seeking effective approximations that turn the large scale into an advantage instead of a disadvantage.If successful, the results of this research will provide new tools to better design and manage service systems, with special emphasis on healthcare systems. To contain costs, many hospitals are significantly understaffed; when resources (such as nurses and beds) are inevitably limited, inefficient staffing strategies can cause excessive suffering, low quality care, degradation of the ultimate treatment outcomes, and significant increases in mortality. The proposed research intends to help system managers make the right operational decisions; it will help answer questions such as: How should a hospital staff the doctors and nurses over the course of the next week so that the delays before treatments are at most one hour? What percentage of patients will have to wait more than four hours? This research is also relevant for many other applications, for example, customer contact centers; public housing authorities providing apartments to low-income tenants; web-server farms processing requests for web pages; and financial back offices processing loans. Education outreach will be a key component of this project, because the investigator shares a deep commitment to engineering education at both the undergraduate and graduate levels. The investigator has been active in introducing operations research techniques (with a special emphasis on queuing theory) to K-12 students through a series of summer workshops and camps. The results of this project will be integrated into the investigator's new undergraduate and graduate courses.