Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-27T14:16:17.863Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Armony, M., Shimkin, N. & Whitt, W. (2008). The impact of delay announcements in many-server queues with abandonment. Operations Research 56(9): 1–16.Google Scholar
2.Baron, O. & Milner, J. (2008). Staffing to maximize call centers with alternate service level agreements. http://www.rotman.utoronto.ca/~jmilner/papers/StaffingToMaximizeProfit.pdf.Google Scholar
3.Bassamboo, A., Zeevi, A. & Harrison, J.M. (2006). Design and control of a large call center: Asymptotic analysis of an LP-based method. Operations Research 54: 419–435.CrossRefGoogle Scholar
4.Bhandari, A., Harchol-Balter, M. & Scheller-Wolf, A. (2007). An exact and efficient algorithm for the contrained dynamic operator staffing problem for call centers. Management Science 54(2): 339–353.CrossRefGoogle Scholar
5.Borst, S., Mandelbaum, A. & Reiman, M.I. (2004). Dimensioning large call centers. Operations Research 51(1): 17–34.CrossRefGoogle Scholar
6.Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S. & Zhao, L. (2005). Statistical analysis of a telephone call center: A queueing-science perspective. Journal of the American Statistical Association 100: 36–50.CrossRefGoogle Scholar
7.Bryson, A. & Ho, Y. (1975). Applied optimal control. New York: Hemisphere.Google Scholar
8.Dixit, A.K. (1990). Optimization in economic theory. Oxford: Oxford University Press.CrossRefGoogle Scholar
9.Feldman, Z., Mandelbaum, A., Massey, W.A. & Whitt, W. (2008). Staffing of time-varying queues to achieve time-stable performance. Management Science 54(2): 324–338.CrossRefGoogle Scholar
10.Gans, N., Koole, G. & Mandelbaum, A. (2003). Telephone call centers: Tutorial, review and research prospects. Manufacturing Service Operations Management 5(2): 79–141.CrossRefGoogle Scholar
11.Garnett, O., Mandelbaum, A. & Reiman, M. (2002). Designing a call center with impatient customers. Manufacturing and Service Operations Management 4(3): 208–227.CrossRefGoogle Scholar
12.Green, L., Kolesar, P. & Whitt, W. (2007). Coping with time-varying demand when setting staffing requirement. Production and Operations Management 16(1): 13–39.CrossRefGoogle Scholar
13.Gregory, J. & Lin, C. (1992). Constrained optimization in the calculus of variations and optimal control theory. New York: Von Nostrand Reinhold.CrossRefGoogle Scholar
14.Gurvich, I. & Whitt, W. (2008). Service-level differentiation in many-server service systems: A solution based on fixed-queue-ratio routing. http://www.kellogg.northwestern.edu/faculty/gurvich/personal/FQR_Feasibility.pdf.Google Scholar
15.Hampshire, R.C. (2007). Dynamic queueing models for the operations management of communication services. Ph.D. dissertation, Princeton University, Princeton, NJ.Google Scholar
16.Hampshire, R.C. & Massey, W.A. (2005). Variational optimization for call center staffing (extended abstract). In Richard Tapia Celebration of Diversity in Computing, Proceedings of the 2005 Conference on Diversity in ComputingAlbuquerque, NM.Google Scholar
17.Hampshire, R.C., Massey, W.A., Mitra, D. & Wang, Q. (2003). Provisioning for bandwidth trading. Telecommunications network design and management (Boca Raton, FL, 2002), Operations Research/Computing Science Interfaces Series 23. Boston, MA: Kluwer, pp. 207–225.CrossRefGoogle Scholar
18.Harris, C.M., Hoffman, K.L. & Saunders, P.B. (1987). Modeling the IRS telephone taxpayer information system. Operations Research 35(4): 504–523.CrossRefGoogle Scholar
19.Jagerman, D.L. (1975). Nonstationary blocking in telephone traffic. Bell System Technical Journal 54(3): 625–661.CrossRefGoogle Scholar
20.Jennings, O.B., Mandelbaum, A., Massey, W.A. & Whitt, W. (1996). Server staffing to meet time-varying demand. Management Science 42(10): 1383–1394.CrossRefGoogle Scholar
21.Koole, G. & Mandelbaum, A. (2001). Queueing models of call centers: An introduction. Avaliable from http://www.cs.vu.nl/obp/callcenters or http://iew3.technion.ac.il/serveng.Google Scholar
22.Lanczos, C. (1970). The variational principles of mechanics, 4th ed.New York: Dover Publications.Google Scholar
23.Mandelbaum, A., Massey, W.A. & Reiman, M.I. (1998). Strong approximations for markovian service networks. Queueing Systems and Their Applications 30: 149–201.CrossRefGoogle Scholar
24.Massey, W.A. & Wallace, R.B. (to appear). An optimal design of the M/M/C/K queue for call centers.Google Scholar
25.Massey, W.A. & Whitt, W. (1994). An analysis of the modified offered load approximation for the nonstationary erlang loss model. The Annals of Applied Probability 4(4): 149–201.CrossRefGoogle Scholar
26.Wallace, R.B. (2003). Performance modeling of call centers with skill-based routing. Ph.D. dissertation, George Washington University, Washington, DC.Google Scholar
27.Whitaker, B.A. (1975). Analysis and optimal design of a multiserver, multiqueue system with finite waiting space in each queue. Bell System Technical Journal 54: 595–623.CrossRefGoogle Scholar
28.Zeltyn, S. & Mandelbaum, A. (2005). Call centers with impatient customers: Many-server asymptotics of the M/M/n+G queue. Queueing Systems 51 (3/4): 361–402.CrossRefGoogle Scholar
29.Zeltyn, S. & Mandelbaum, A. (2007). Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. Available from http://iew3.technion.ac.il/serveng/References/references.html.Google Scholar