ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Modelling and forecasting of call center arrival process

  • 1.

    Department of Business Administration, School of Management, University of Science and Technology of China, Hefei 230026, China

  • 2.

    Department of Management Science, School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2017.09.009
  • Received Date: 07 April 2016
  • Accepted Date: 29 November 2016
  • Rev Recd Date: 29 November 2016
  • Publish Date: 30 September 2017
    Abstract

  • Abstract

    Fitting arrival process and forecasting future arrivals are crucial to staffing and scheduling in call centers. According to different stages of a call center, arrivals are classified into IVR arrival and agent arrival. Non-homogeneous Poisson process has been widely used overseas for modeling stochastic agent arrival process. However, this study initially proposed IVR arrival fitting and forecasting. The IVR arrival process of this call center appears to be “overdispersed” when comparing the mean arrival rate and its variance with the corresponding Poisson process. Therefore, time series was used to model and predict the IVR arrival process. White noise test of residuals was applied and the MAE (mean absolute error) was adopted to evaluate the goodness of fit. The results show that ARIMA (1,0,1) is preferable for predicting the IVR arrival in a short period of normal days and Winters is preferable for the Spring Festival period. Finally, the regression method was employed to describe the relationship between IVR arrival and agent arrival, and predict the agent arrival.

    Abstract

    Fitting arrival process and forecasting future arrivals are crucial to staffing and scheduling in call centers. According to different stages of a call center, arrivals are classified into IVR arrival and agent arrival. Non-homogeneous Poisson process has been widely used overseas for modeling stochastic agent arrival process. However, this study initially proposed IVR arrival fitting and forecasting. The IVR arrival process of this call center appears to be “overdispersed” when comparing the mean arrival rate and its variance with the corresponding Poisson process. Therefore, time series was used to model and predict the IVR arrival process. White noise test of residuals was applied and the MAE (mean absolute error) was adopted to evaluate the goodness of fit. The results show that ARIMA (1,0,1) is preferable for predicting the IVR arrival in a short period of normal days and Winters is preferable for the Spring Festival period. Finally, the regression method was employed to describe the relationship between IVR arrival and agent arrival, and predict the agent arrival.
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    • References(21)
  • [1]
    GANS N, KOOLE G, MANDELBAUM A. Telephone call centers: Tutorial, review, and research prospects[J]. Manufacturing and Service Operations Management, 2003, 5(2): 79-141.
    [2]
    SHEN H, HUANG J Z. Forecasting time series of inhomogeneous Poisson processes with application to call center work force management[J]. Annals of Applied Statistics, 2008, 2(2): 601-623.
    [3]
    BROWN L, GANS N, MANDELBAUM A,et al. Statistical analysis of a telephone call center: A queueing-science perspective[J]. Journal of the American Statistical Association, 2005, 100(469): 36-50.
    [4]
    KIM S H, WHITT W. Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process[J]. Naval Research Logistics, 2014, 61: 66-90.
    [5]
    KIM S H, WHITT W. Are call center and hospital arrivals well modeled by nonhomogeneous Poisson process? [J]. Manufacturing and Service Operations Management, 2014,16(3): 464-480.
    [6]
    AVRAMIDIS A N, DESLAURIERS A, L’ECUYER P. Modeling daily arrivals to a telephone call center[J]. Management Science, 2004, 50(7): 896-908.
    [7]
    SHEN H. Statistical analysis of call-center operational data: Forecasting call arrivals, and analyzing customer patience and agent service[C]// Wiley Encyclopedia of Operation Research and Management Science, 2010.New York: Wiley, 2010.
    [8]
    MAMAN S, MANDELBAUM A, WHITT W, et al. Queues with random arrival rates: Interface, modelling and asymptotics (C-staffing)[R]. Work in Progress, 2015.
    [9]
    CHANNOUF N, L’ECUYER P. A normal copula model for the arrival process in a call center[J]. International Transactions in Operational Research, 2012, 19: 771-781.
    [10]
    SHEN H, HUANG J Z. Interday forecasting and intraday updating of call center arrivals[J]. Manufacturing and Service Operations Management, 2008, 10(3):391-410.
    [11]
    JAOUA A, L’ECUYER P, DELORME L. Call type dependence in multiskill call centers[J]. Journal
    Simulation, 2013, 89(6): 722-734.
    [12]
    THOMPSON H E, TIAO G C. Analysis of telephone data: A case study of forecasting seasonal time series[J]. The Bell Journal of Economics and Management Science, 1971, 2(2): 515-541.
    [13]
    MABERT V A. Short interval forecasting of emergency phone call work loads[J]. Journal of Operations Management, 1985, 5(3): 259-271.
    [14]
    TAYLOR J W. A comparison of univariate time series methods for forecasting intraday arrivals at a call center[J]. Management Science, 2008, 54(2): 253-265.
    [15]
    IBRAHIM R, L’ECUYER P. Forecasting call center arrivals: Fixed-effects, mixed-effects, and bivariate models[J]. Manufacturing and Services Operations Management, 2013, 15(1): 72-85.
    [16]
    AKTEKIN T, SOYER R. Call center arrival modeling: A Bayesian state space approach[J]. Naval Research Logistics, 2011, 58(1): 28-42.
    [17]
    SHEN H. Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles: Comments[J]. International Journal of Forecasting, 2010, 58: 652-654.
    [18]
    TAYLOR J W. Density forecasting of intraday call center arrivals using models based on exponentially smoothing[J]. Management Science, 2012, 58(3): 534-549.
    [19]
    李诗羽, 张飞, 王正林. 数据分析: R语言实战[M]. 北京：电子工业出版社, 2014: 260-286.
    [20]
    黄荣坦. ARIMA模型建立与应用[EB/OL]. [2016-04-07]. http://wenku.baidu.com/view/ d88f12f3941ea76e58fa0484.html.
    [21]
    Wikipedia. Overdispersion [EB/OL]. [2016-04-07]. https://en.wikipedia.org/wiki/ Overdispersion.
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    [1]
    GANS N, KOOLE G, MANDELBAUM A. Telephone call centers: Tutorial, review, and research prospects[J]. Manufacturing and Service Operations Management, 2003, 5(2): 79-141.
    [2]
    SHEN H, HUANG J Z. Forecasting time series of inhomogeneous Poisson processes with application to call center work force management[J]. Annals of Applied Statistics, 2008, 2(2): 601-623.
    [3]
    BROWN L, GANS N, MANDELBAUM A,et al. Statistical analysis of a telephone call center: A queueing-science perspective[J]. Journal of the American Statistical Association, 2005, 100(469): 36-50.
    [4]
    KIM S H, WHITT W. Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process[J]. Naval Research Logistics, 2014, 61: 66-90.
    [5]
    KIM S H, WHITT W. Are call center and hospital arrivals well modeled by nonhomogeneous Poisson process? [J]. Manufacturing and Service Operations Management, 2014,16(3): 464-480.
    [6]
    AVRAMIDIS A N, DESLAURIERS A, L’ECUYER P. Modeling daily arrivals to a telephone call center[J]. Management Science, 2004, 50(7): 896-908.
    [7]
    SHEN H. Statistical analysis of call-center operational data: Forecasting call arrivals, and analyzing customer patience and agent service[C]// Wiley Encyclopedia of Operation Research and Management Science, 2010.New York: Wiley, 2010.
    [8]
    MAMAN S, MANDELBAUM A, WHITT W, et al. Queues with random arrival rates: Interface, modelling and asymptotics (C-staffing)[R]. Work in Progress, 2015.
    [9]
    CHANNOUF N, L’ECUYER P. A normal copula model for the arrival process in a call center[J]. International Transactions in Operational Research, 2012, 19: 771-781.
    [10]
    SHEN H, HUANG J Z. Interday forecasting and intraday updating of call center arrivals[J]. Manufacturing and Service Operations Management, 2008, 10(3):391-410.
    [11]
    JAOUA A, L’ECUYER P, DELORME L. Call type dependence in multiskill call centers[J]. Journal
    Simulation, 2013, 89(6): 722-734.
    [12]
    THOMPSON H E, TIAO G C. Analysis of telephone data: A case study of forecasting seasonal time series[J]. The Bell Journal of Economics and Management Science, 1971, 2(2): 515-541.
    [13]
    MABERT V A. Short interval forecasting of emergency phone call work loads[J]. Journal of Operations Management, 1985, 5(3): 259-271.
    [14]
    TAYLOR J W. A comparison of univariate time series methods for forecasting intraday arrivals at a call center[J]. Management Science, 2008, 54(2): 253-265.
    [15]
    IBRAHIM R, L’ECUYER P. Forecasting call center arrivals: Fixed-effects, mixed-effects, and bivariate models[J]. Manufacturing and Services Operations Management, 2013, 15(1): 72-85.
    [16]
    AKTEKIN T, SOYER R. Call center arrival modeling: A Bayesian state space approach[J]. Naval Research Logistics, 2011, 58(1): 28-42.
    [17]
    SHEN H. Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles: Comments[J]. International Journal of Forecasting, 2010, 58: 652-654.
    [18]
    TAYLOR J W. Density forecasting of intraday call center arrivals using models based on exponentially smoothing[J]. Management Science, 2012, 58(3): 534-549.
    [19]
    李诗羽, 张飞, 王正林. 数据分析: R语言实战[M]. 北京：电子工业出版社, 2014: 260-286.
    [20]
    黄荣坦. ARIMA模型建立与应用[EB/OL]. [2016-04-07]. http://wenku.baidu.com/view/ d88f12f3941ea76e58fa0484.html.
    [21]
    Wikipedia. Overdispersion [EB/OL]. [2016-04-07]. https://en.wikipedia.org/wiki/ Overdispersion.
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