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可靠、实用的工具，以便在一般服务系统中进行人员配置和路由决策时有效地平衡成本和质量。具体来说，我们考虑具有多种客户和服务器类型的服务系统，以及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在多个尺度上具有不确定性：服务和到达时间的操作不确定性，以及客户数量和服务器可用性的高阶不确定性。我们将使用一种集成渐近分析的方法来研究这个问题，渐近分析有效地解决了操作不确定性，随机规划有效地解决了高阶不确定性。具体来说，我们将探索影子策略在实时客户路由决策中的使用，并使用渐近分析来证明它们在大容量系统中的质量。这一分析的结果将纳入随机整数规划方法，以确定人员配备水平和服务器时间表。还将研究为中小型服务系统寻找良好时间表的方法的扩展。我们的研究将为复杂服务系统的管理者提供实用的策略，将客户实时分配到服务器上，并为服务器调度方法提供解决方案，以应对客户数量和服务器可用性的不确定性。这些方法直接适用于呼叫中心系统，并且通过更好地将服务器与需求匹配，有可能在提供更高质量服务的同时降低成本。如果成功，我们的方法扩展到中小型系统，也将帮助卫生保健系统的管理者在面对非常不确定和异质性的患者群体时，计划医生、护士和其他卫生保健提供者的时间表。PI还将合作，将彼此学科的选择性内容纳入他们所教授的课程中，从而增加学生所学到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.