# A Stochastic Programming Approach for Staffing and Scheduling Call Centers with Uncertain Demand Forecasts

### Mathilde Excoffier, Céline Gicquel, Oualid Jouini, Abdel Lisser

#### Abstract

We consider a workforce management problem arising in call centers, namely a staffing and shift-scheduling problem. It consists in determining the minimum-cost number of agents to be assigned to each shift of the scheduling horizon so as to reach the required customer quality of service. We assume that the mean call arrival rate in each period of the horizon is a random variable following a continuous distribution. We model the resulting optimization problem as a stochastic program involving joint probabilistic constraints. This allows to manage the risk of not reaching the required quality of service at the horizon level rather than on a period by period basis. We propose a solution approach based on linear approximations to provide approximate solutions of the problem. We finally give numerical results carried out on a real-life instance. These results show that the proposed approach compares well with previously published approaches both in terms of risk management and cost minimization.

#### References

- Aksin, Z., Armony, M., and Mehrotra, V. (2007). The modern call center: A multi-disciplinary perspective on operations management research. Production and Operations Management, 16:665-688.
- Cezik, M. T. and L'Ecuyer, P. (2008). Staffing multiskill call centers via linear programming and simulation. Management Science, 54:310-323.
- Cheng, J. and Lisser, A. (2012). A second-order cone programming approach for linear programs with joint probabilistic constraints. Operations Research Letters, 40:325-328.
- Erdog?an, E. and Iyengar, G. (2007). On two-stage convex chance constrained problems. Mathematical Methods of Operations Research, 65:115-140.
- Gans, N., Koole, G., and Mandelbaum, A. (2003). Telephone call centers: Tutorial, review, and research prospects. Manufacturing & Service Operations Management, 5:79-141.
- Gans, N., Shen, H., and Zhou, Y.-P. (2012). Parametric stochastic programming models for call-center workforce scheduling. Working paper.
- Gross, D., Shortle, J. F., Thompson, J. M., and Harris, C. M. (2008). Fundamentals of Queueing Theory. Wiley Series.
- Gurvich, I., Luedtke, J., and Tezcan, T. (2010). Staffing call centers with uncertain demand forecasts: A chanceconstrained optimization approach. Management Science, 56:1093-1115.
- Jongbloed, G. and Koole, G. (2001). Managing uncertainty in call centers using poisson mixtures. Applied Stochastic Models in Business and Industry, 17:307- 318.
- Liao, S., Koole, G., van Delft, C., and Jouini, O. (2012). Staffing a call center with uncertain non-stationary arrival rate and flexibility. OR Spectrum, 34:691-721.
- Liao, S., van Delft, C., and Vial, J.-P. (2013). Distributionally robust workforce scheduling in call centers with uncertain arrival rates. Optimization Methods and Software, 28:501-522.
- Luedtke, J., Ahmed, S., and Nemhauser, G. (2007). An Integer Programming Approach for Linear Programs with Probabilistic Constraints, volume 4513. Springer Berlin Heidelberg.
- Mehrotra, V., Ozlük, O., and Saltzman, R. (2009). Intelligent procedures for intra-day updating of call center agent schedules. Production and Operations Management, 19:353-367.
- Prékopa, A. (2003). Probabilistic programming. Handbooks in Operations Research and Management Science, 10:267-351.
- Robbins, T. R. and Harrison, T. P. (2010). A stochastic programming model for scheduling call centers with global service level agreements. European Journal of Operational Research, 207:1608-1619.

#### Paper Citation

#### in Harvard Style

Excoffier M., Gicquel C., Jouini O. and Lisser A. (2014). **A Stochastic Programming Approach for Staffing and Scheduling Call Centers with Uncertain Demand Forecasts** . In *Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-017-8, pages 80-88. DOI: 10.5220/0004832100800088

#### in Bibtex Style

@conference{icores14,

author={Mathilde Excoffier and Céline Gicquel and Oualid Jouini and Abdel Lisser},

title={A Stochastic Programming Approach for Staffing and Scheduling Call Centers with Uncertain Demand Forecasts},

booktitle={Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2014},

pages={80-88},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004832100800088},

isbn={978-989-758-017-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - A Stochastic Programming Approach for Staffing and Scheduling Call Centers with Uncertain Demand Forecasts

SN - 978-989-758-017-8

AU - Excoffier M.

AU - Gicquel C.

AU - Jouini O.

AU - Lisser A.

PY - 2014

SP - 80

EP - 88

DO - 10.5220/0004832100800088