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【主题】Speed Quality Dilemma: Routing to Balance Waiting and Call-Backs in Large-Scale Call Centers with Heterogeneous Servers
【演讲者】Dongyuan Zhan, Marshall School of Business, University of Southern California.
【合作作者】Amy R. Ward, Associate Professor, Marshall School of Business, University of Southern California.
【时间】15:00-16:30pm, 2011-12-29, Thursday
【地点】管理学院 801
【内容摘要】 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.
【主讲人简介】 Dongyuan Zhan studies 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
【中文简介】CallCenter研究，研究如何平衡速度和质量这两个重要指标。对于质量我们用客户因之前电话中没有解决的问题打回电话的数量来衡量。我们假定有几个服务速度和质量各异的客服代表组，我们的问题是当一个新来的客户面对多个不同的可以提供服务的客服代表，应该把他route到哪个，以最小化平均等待时间和单位时间打回的电话数的加权和？我们的研究发现：对于2个客服组的情形，当系统比较拥挤时，应该把客户交给速度快的客服代表；当系统比较空闲时，应该把客户交给质量好的客服代表。我们给出找到阈值的办法。对于2个以上的客服组的情形，最优策略会包含多个阈值。这个发现给Call Center的管理人员提供了设计route规则的参考依据，不同的管理者对速度和质量有不同的权重，按照我们给出的方法可以找到不同的阈值
【演讲者】Dongyuan Zhan, Marshall School of Business, University of Southern California.
【合作作者】Amy R. Ward, Associate Professor, Marshall School of Business, University of Southern California.
【时间】15:00-16:30pm, 2011-12-29, Thursday
【地点】管理学院 801
【内容摘要】 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.
【主讲人简介】 Dongyuan Zhan studies 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
【中文简介】CallCenter研究，研究如何平衡速度和质量这两个重要指标。对于质量我们用客户因之前电话中没有解决的问题打回电话的数量来衡量。我们假定有几个服务速度和质量各异的客服代表组，我们的问题是当一个新来的客户面对多个不同的可以提供服务的客服代表，应该把他route到哪个，以最小化平均等待时间和单位时间打回的电话数的加权和？我们的研究发现：对于2个客服组的情形，当系统比较拥挤时，应该把客户交给速度快的客服代表；当系统比较空闲时，应该把客户交给质量好的客服代表。我们给出找到阈值的办法。对于2个以上的客服组的情形，最优策略会包含多个阈值。这个发现给Call Center的管理人员提供了设计route规则的参考依据，不同的管理者对速度和质量有不同的权重，按照我们给出的方法可以找到不同的阈值
