Dongyuan Zhan, Marshall School of Business, University of Southern California
06 8, 2012
【Title】Speed Quality Dilemma: Routing to Balance Waiting and Call-Backs in Large-Scale Call Centers with Heterogeneous Servers
【Location】Weilun 453，Tsinghua SEM
In a call center, there is usually a trade-off between two important metrics: service rate and service quality. We assume that the customers whose problems are not solved after the service would call back and rejoin the queue immediately. We measure the service rate by the number of customers leaving the system in unit time and measure the service quality by the number of call-backs in unit time. We study a model of a call center with one stream of customers and heterogeneous service pools with different service rates and resolution probabilities. The control is the routing policy which decides by which server pool an arrival should be served when servers from more than one pool are available. Routing to pools with higher effective service rate decreases the average waiting time; while routing to pools with higher resolution probabilities decreases the call-back rate. When these two metrics are not aligned among the server pools, there is a natural trade-off between minimizing the average waiting time and minimizing the callback rate. In the Halfin-Whitt heavy traffic regime, we find the diffusion approximation of the system and formulate a diffusion control problem (DCP). We solve the DCP and propose a threshold policy which is asymptotically optimal. The threshold policy is very intuitive in 2-pool system: when the number of the customers in the system is below a threshold, route to the server pool with higher resolution probability; when the number is above the threshold, route to the server pool with higher service rate. The structure of the threshold policies is of interest when there are more than 2 service pools in the system. We furthermore present simulation results to show the threshold policies outperform other commonly seen policies.
Dongyuan Zhan is a 2nd year Ph.D. student in Information and Operations Management Department at Marshall School of Business, University of Southern California. His research interests include Queueing Theory, Supply Chain Coordination and Information Sharing. M.S. in Operations Research, University of Southern California, 2010 M.S. in Control Science and Engineering, Tsinghua University, 2008 B.S. in Automation, Tsinghua University, 2006