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On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design

Stern School of Business, New York University, 44 West 4th Street, Suite 8-66, New York, New York 10012
Columbia Business School, 409 Uris Hall, 3022 Broadway, New York, New York 10027
marmony{at}stern.nyu.edu
c.maglaras{at}columbia.edu

Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for real-time telephone service, and another for a postponed call-back service offered with a guarantee on the maximum delay until a reply is received. Customers are sensitive to both real-time and call-back delay and their behavior is captured through a probabilistic choice model. The dynamics of the system are modeled as an M/M/N multiclass system. We rigorously justify that as the number of agents increases, the system's load approaches its maximum processing capacity. Based on this observation, we perform an asymptotic analysis in the many-server, heavy traffic regime to find an asymptotically optimal routing rule, characterize the unique equilibrium regime of the system, approximate the system performance, and finally, propose a staffing rule that picks the minimum number of agents that satisfies a set of operational constraints on the performance of the system.

Subject classifications: service networks; call centers; heavy traffic; service level guarantees; choice models; Nash equilibrium; Halfin-Whitt regime.
History: Received September 2001; revision received May 2002; accepted May 2003.