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

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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.