Hostname: page-component-6766d58669-vgfm9 Total loading time: 0 Render date: 2026-05-20T17:52:02.188Z Has data issue: false hasContentIssue false
  • English
  • Français

FORECAST ERRORS IN SERVICE SYSTEMS

Published online by Cambridge University Press:  16 February 2009

Samuel G. Steckley ,
Shane G. Henderson  and
Vijay Mehrotra
Samuel G. Steckley
Affiliation:
The Mitre Corporation, McLean, VA 22102-7508 E-mail: sgsteckley@gmail.com
Shane G. Henderson
Affiliation:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853 E-mail: sgh9@cornell.edu
Vijay Mehrotra
Affiliation:
Department of Decision Sciences, San Francisco State University, San Francisco, CA 94132-4156 E-mail: vjm@sfsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the presence and impact of forecast errors in the arrival rate of customers to a service system. Analysis of a large dataset shows that forecast errors can be large relative to the fluctuations naturally expected in a Poisson process. We show that ignoring forecast errors typically leads to overestimates of performance and that forecast errors of the magnitude seen in our dataset can have a practically significant impact on predictions of long-run performance. We also define short-run performance as the random percentage of calls received in a particular period that are answered in a timely fashion. We prove a central limit theorem that yields a normal-mixture approximation for its distribution for Markovian queues and we sketch an argument that shows that a normal-mixture approximation should be valid in great generality. Our results provide motivation for studying staffing strategies that are more flexible than the fixed-level staffing rules traditionally studied in the literature.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 2 , April 2009 , pp. 305 - 332
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.)

Article purchase

Temporarily unavailable

References

1.Avramidis, A.N., Deslauriers, A. & L'Ecuyer, P. (2004). Modeling daily arrivals to a telephone call center. Management Science 50(7): 896–908.Google Scholar
2.Bassamboo, A., Harrison, J. & Zeevi, A. (2006). Design and control of a large call center: Asymptotic analysis of an LP-based method. Operations Research 54: 419–435.CrossRefGoogle Scholar
3.Billingsley, P. (1968). Convergence of probability measures. New York: Wiley.Google Scholar
4.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.Google Scholar
5.Brown, L.D., Zhang, R. & Zhao, L. (2001). Root un-root methodology for non parametric density estimation. Technical report, Department of Statistics, University of Pennsylvania, Philadelphia.Google Scholar
6.Brown, L.D. & Zhao, L.H. (2002). A test for the Poisson distribution. Sankhya 64 (A-3): 611–625.Google Scholar
7.Chen, B.P.K. & Henderson, S.G. (2001). Two issues in setting call center staffing levels. Annals of Operations Research 108: 175–192.Google Scholar
8.Cinlar, E. (1972). Superposition of point processes. In Lewis, P.A.W., (ed.) Stochastic point processes: Statistical analysis, theory, and applications. New York: Wiley Interscience.Google Scholar
9.Deslauriers, A., L'Ecuyer, P., Pichitlamken, J., Ingolfsson, A. & Avramidis, A.N. (2007). Markov chain models of a telephone call center in blend mode. Computers and Operations Research 34(6): 1616–1645.CrossRefGoogle Scholar
10.Gans, N., Koole, G. & Mandelbaum, A. (2003). Telephone call centers: Tutorial, review and research prospects. Manufacturing Service Operations Management 5: 79–141.CrossRefGoogle Scholar
11.Gans, N. & Zhou, Y.-P. (2007). Call-routing schemes for call-center outsourcing. Manufacturing & Service Operations Management 9(1): 33–50.CrossRefGoogle Scholar
12.Grassmann, W.K. (1988). Finding the right number of servers in real-world queuing systems. Interfaces 18(2): 94–104.Google Scholar
13.Harrison, J.M. & Zeevi, A. (2005). A method for staffing large call centers using stochastic fluid models. Manufacturing & Service Operations Management 7: 20–36.CrossRefGoogle Scholar
14.Jongbloed, G. & Koole, G. (2001). Managing uncertainty in call centers using Poisson mixtures. Applied Stochastic Models in Business and Industry 17: 307–318.CrossRefGoogle Scholar
15.Liptser, R.S. & Shiryayev, A.N. (1989). Theory of Martingales. Boston: Kluwer Academic.CrossRefGoogle Scholar
16.Mehrotra, V., Ozluk, O. & Saltzman, R. (2009). Intelligent procedures for intra-day updating of call center agent schedules. Production and Operations Management.Google Scholar
17.Meyn, S.P. & Tweedie, R.L. (1993). Markov chains and stochastic stability. London: Springer-Verlag.Google Scholar
18.Milner, J. & Lennon-Olsen, T.M. (2007). Service level agreements in call centers: Perils and prescriptions. Management Science 54(2): 238–252.CrossRefGoogle Scholar
19.Robbins, T.R., Medeiros, D.J. & Dum, P. (2006). Evaluating arrival rate uncertainty in call centers. In Perrone, L.F., Wieland, F.P., Liu, J., Lawson, B.G., Nicol, D.M. & Fujimoto, R.M., (eds.) Proceedings of the 2006 winter simulation conference. Piscataway NJ: IEEE, pp. 2180–2187.CrossRefGoogle Scholar
20.Ross, A.M. (2001). Queueing systems with daily cycles and stochastic demand with uncertain parameters. Ph.D. dissertation, University of California, Berkeley, Berkeley.Google Scholar
21.Serfling, R.J. (1980). Approximation theorems of mathematical statistics. New York: Wiley.CrossRefGoogle Scholar
22.Shen, H. & Huang, J.Z. (2008). Interday forecasting and intraday updating of call center arrivals. Manufacturing & Service Operations Management 10(3): 391–410.Google Scholar
23.Steckley, S.G., Henderson, S.G. & Mehrotra, V. (2005). Performance measures for service systems with a random arrival rate. In Kuhl, M.E., Steiger, N.M., Armstrong, F.B. & Joines, J.A., (eds.) Proceedings of the 2005 winter simulation conference. Piscataway, NJ: IEEE, pp. 566–575.CrossRefGoogle Scholar
24.Thompson, G.M. (1999). Server staffing levels in pure service environments when the true mean daily customer arrival rate is a normal random variate. Unpublished manuscript.Google Scholar
25.Weinberg, J., Brown, L.D. & Stroud, J.R. (2006). Bayesian forecasting of an inhomogeneous poisson process with applications to call center data. Journal of the American Statistical Association 102(480): 1185–1198.CrossRefGoogle Scholar
26.Whitt, W. (1976). Bivariate distributions with given marginals. Annals of Statistics 4: 1280–1289.CrossRefGoogle Scholar
27.Whitt, W. (1999). Dynamic staffing in a telephone call center aiming to immediately answer all calls. Operations Research Letters 24: 205–212.CrossRefGoogle Scholar
28.Whitt, W. (2002). Stochastic-process limits. Springer Series in Operations Research. New York: Springer.Google Scholar
29.Whitt, W. (2006). Staffing a call center with uncertain arrival rate and absenteeism. Production and Operations Management 15: 88–102.CrossRefGoogle Scholar
30.Wolff, R.W. (1989). Stochastic modeling and the theory of queues. Englewood Cliffs, NJ: Prentice Hall.Google Scholar