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A TIME-VARYING CALL CENTER DESIGN VIA LAGRANGIAN MECHANICS

Published online by Cambridge University Press:  16 February 2009

Robert C. Hampshire ,
Otis B. Jennings  and
William A. Massey
Robert C. Hampshire
Affiliation:
Heinz School of Public Policy and Management, Carnegie Mellon University, Pittsburgh, PA E-mail: hamp@andrew.cmu.edu
Otis B. Jennings
Affiliation:
Fuqua School of Business, Duke University, Durham, NC E-mail: otisj@duke.edu
William A. Massey
Affiliation:
Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ E-mail: wmassey@princeton.edu
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Abstract

We consider a multiserver delay queue with finite additional waiting spaces and time-varying arrival rates, where the customers waiting in the buffer may abandon. These are features that arise naturally from the study of service systems such as call centers. Moreover, we assume rewards for successful service completions and cost rates for service resources. Finally, we consider service-level agreements that constrain both the fractions of callers who abandon and the ones who are blocked.

Applying the theory of Lagrangian mechanics to the fluid limit of a related Markovian service network model, we obtain near-profit-optimal staffing and provisioning schedules. The nature of this solution consists of three modes of operation. A key step in deriving this solution is combining the modified offered load approximation for loss systems with our fluid model. We use them to estimate effectively both our service-level agreement metrics and the profit for the original queuing model. Second-order profit improvements are achieved through a modified offered load version of the conventional square root safety rule.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 2 , April 2009 , pp. 231 - 259
Copyright
Copyright © Cambridge University Press 2009

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