Call Center Co-Sourcing: A Joint Pricing and Staffing Framework
Jeffrey P. Kharoufeh, Ph.D.
Associate Professor
Department of Industrial Engineering
University of Pittsburgh
Abstract
Increasingly, service organizations are electing to co-source some of their customer support functions,
especially those handled by call centers. That is, rather than servicing requests exclusively with in-house
agents, a portion of service capacity can be delegated to an outside service provider (or contractor) to
reduce costs. Indeed, the business of co-sourcing customer service centers has rapidly grown into a
multinational, multibillion dollar industry. However, organizations must weigh the economic benefits of
co-sourcing against the perceived (or real) costs of surrendering control of their primary source of direct
customer support. Specifically, they must decide how much of the operation should be co-sourced, and
how much should be kept in-house, when faced with uncertain and dynamic demand.
In this talk, I will present a joint queueing- and game-theoretic framework for analyzing the behavior of
an external contractor who serves multiple, independent call centers. The contractor seeks to set per
unit agent holding and activation prices so as to maximize expected revenues over a finite contract
period. The call centers, faced with stochastic arrivals, forecasting uncertainty and quality-of-service
(QoS) requirements, respond to the contractor’s pricing strategy by setting staffing levels. Before the
contract period begins, the call centers decide how many in-house agents to staff and how many cosourced agents to place on hold for each period. Subsequently, they reactively activate agents during
each period in order to satisfy their QoS constraints. This problem is formulated as a Stackelberg game
in which the contractor plays the part of the leader, and the multiple, independent call centers
represent the follower. It is shown that the bi-level program can be reformulated so that the optimal
holding and activation prices are obtained by solving a quadratically constrained linear program. The
call centers’ optimal staffing decisions are shown to be highly tractable under an expected delay
constraint. Computational results illustrate the usefulness of the model, even in the absence of perfect,
symmetric information.
Biography
Jeffrey P. Kharoufeh is an Associate Professor in the Department of Industrial Engineering at the
University of Pittsburgh. His methodological areas of expertise are applied probability and stochastic
modeling with applications in queueing theory, reliability theory, maintenance optimization and
renewable energy systems. His research has been funded by the National Science Foundation, the Air
Force Office of Scientific Research, the National Reconnaissance Office, the Department of Veterans
Affairs and other federal agencies. Dr. Kharoufeh earned a Ph.D. in Industrial Engineering and
Operations Research at the Pennsylvania State University where he was an inaugural Weiss Graduate
Fellow. He currently serves as Area Editor of Operations Research Letters and Associate Editor of
Operations Research (Stochastic Models). He is a Senior Member of IIE and a professional member of
the INFORMS Applied Probability Society.