Performance analysis in a call center with calls’ abandonment and optional feedback

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Authors:

Yan Chen, Faculty of Science, Jiangsu University, Zhenjiang, 212013, China.

Peishu Chen, School of Applied Mathematics, Chaohu University, Chaohu 238000, China.

Yijuan Zhu, School of Business Administration, South China University of Technology, Guangzhou 510000, China.

Abstract:

Purpose. With the increase of the call center business and the equipment update, the Interactive Voice Response Units (IVRU) become widely used in call centers. This research investigated two kinds of call problems (abandonment and optional feedback) and the role of the service channel (servers and the IVRU) in a call center. We have obtained some important performance measures, which are very helpful for optimizing call centers.

Methodology. We formulated the call center with the Interactive Voice Response Units by a two-stage queuing system. Applying the queueing theory, we discussed a call center with the customers’ impatience, optional feedback, and part shutdown of the servers.

Findings. We first get the systems’ Q-matrix, and then by using the Structured Gaussian Elimination method, we obtained the idle probability, the average number of customers in the second-level queue, the leaving probability due to customers’ impatience and some other performance measures.

Originality. We made a study of a call center made up of trunk lines, interactive voice response units (IVRU) and agents. We discussed a partial closing rule, call abandonment and feedback in the center. The research on this aspect has not been found at present.

Practical value. We have also considered the fact that some customers who are dissatisfied with the service may return for service, and they may return to the Interactive Voice Response Units or the servers or both. Our model is more reasonable and close to widely used call centers.

References:

1. Koole, G., & Mandelbaum, A. (2002), “Queueing models of call centers: An introduction”, Annals of Operations Research, vol. 113, no.1-4, pp. 41–59.

2. Gans, N., Koole, G., & Mandelbaum, A. (2003), “Telephone call centers: Tutorial, review, and research prospects”, Manufacturing & Service Operations Management, vol.5, no.2, pp. 79–141.

3. Aguir, S., Karaesmen, F., Akşin, O.Z., & Chauvet, F. (2004), “The impact of retrials on call center performance”, OR Spectrum, vol.26, no.3, pp. 353–376.

4. Shin, Y.W., & Choo, T. (2009), “M/M /s queue with impatient customers and retrials”, Applied Mathematical Modelling, vol.33, pp. 2596–2606.

5. Srinivasan, R., Talim, J., & Wang, J. (2004), “Performance analysis of a call center with interactive voice response units”, Top, vol.12, no.1, pp. 91–110.

6. Wang, J., & Srinivasan, R. (2008), “Staffing a call center with interactive voice response units and impatient calls”, IEEE International Conference on Service Operations and Logistics, and Informatics, vol. 1, pp. 514–519.

7. Huaqing, Z. (2010), “Performance analysis in call centers with IVR and impatient Customers”, Journal of East China Normal University (Natural Science), vol.1, pp. 69–78.

8. Yan C., Yijuan Z., & Peishu, C. (2010), “Analysis of a call center with a closing rule and impatient calls”, International Conference on application of mathematics and physics, pp. 342–346.

9. Kawanishi, K. (2008), “QBD approximations of a call center queueing model with general patience distribution”, Computers & Operations Research, vol. 35, no.8, pp. 2463–2481.

10. Ke, J.C., Lin, C.H., Yang, J.Y., & Zhang, Z.G. (2009), “Optimal (d, c) vacation policy for a finite buffer M/M/c queue with unreliable servers and repairs”, Applied Mathematical Modelling, vol.33, no.10, pp. 3949–3962.

 

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ISSN (print) 2071-2227,
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