Collaborative Research: Staffing and Routing in Service Systems with Uncertain Arrival Rates: An Integrated Stochastic Programming and Asymptotic Analysis Approach

该奖项的研究目标是为管理人员提供合理，实用的工具，以有效地平衡成本和质量时，在一般服务系统的人员配置和路由决策。具体来说，我们认为服务系统有多个客户和服务器类型，客户到达量和服务器可用性的不确定性。一个关键的复杂性是，这些系统具有多个尺度的不确定性：服务和到达时间的运营不确定性，以及客户量和服务器可用性的高阶不确定性。我们将研究这个问题使用的方法，集成渐近分析，有效地解决了操作的不确定性，和随机规划，有效地解决高阶不确定性。 具体来说，我们将探讨使用影子政策的实时客户路由决策，并使用渐近分析，以证明其质量的大容量系统。 这一分析的结果将被纳入一个随机整数规划方法，确定人员配备水平和服务器时间表。 扩展的方法，以找到良好的时间表为中型和小型服务系统也将studied.Our研究将提供复杂的服务系统的管理人员与客户的实时分配到服务器和服务器调度方法，提供解决方案，是强大的客户量和服务器可用性的不确定性的实用政策。 这些方法直接适用于呼叫中心系统，通过更好地匹配服务器的要求，有可能降低成本，同时提供更高质量的服务。 如果成功的话，我们的方法扩展到中小型系统也将帮助医疗保健系统的管理者计划医生，护士和其他医疗保健提供者的时间表，面对一个非常不确定和异质性的病人群体。 PI还将合作将彼此学科的选择性组成部分纳入他们教授的课程，从而增加学生学习的处理不确定性的工具范围。

The research objective of this award is to provide managers with sound, practical tools to efficiently balance cost and quality when making staffing and routing decisions in general service systems. Specifically, we consider service systems having multiple customer and server types, and uncertainties in customer arrival volume and server availability. A key complication is that these systems possess uncertainties at multiple scales: operational uncertainty in the service and arrival times, and higher-order uncertainty in the customer volumes and server availability. We will study this problem using an approach that integrates asymptotic analysis, which effectively addresses operational uncertainties, and stochastic programming, which effectively addresses high-order uncertainties. Specifically, we will explore the use of shadow policies for real-time customer routing decisions and use asymptotic analysis to demonstrate their quality for high-volume systems. The results of this analysis will be integrated into a stochastic integer programming approach that determines staffing levels and server schedules. Extensions of the methodology to find good schedules for medium and small-scale service systems will also be studied.Our research will provide managers of complex service systems with practical policies for real-time assignment of customers to servers and methods for server scheduling that provide solutions that are robust to uncertainties in customer volume and server availability. These methods are directly applicable to call center systems and, by better matching servers to requirements, have the potential to reduce costs while providing higher quality service. If successful, the extensions of our methods to small and medium-scale systems will also help managers of health-care systems plan schedules of physicians, nurses, and other health-care providers in the face of a very uncertain and heterogeneous patient population. The PI's will also collaborate to include selective components of each other's discipline into the courses they teach, thereby increasing the range of tools for dealing with uncertainty that their students learn.