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Joint chance-constrained staffing optimization in multi-skill call centers

Author

Listed:
  • Tien Thanh Dam

    (Phenikaa University)

  • Thuy Anh Ta

    (Phenikaa University)

  • Tien Mai

    (Singapore Management University)

Abstract

This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.

Suggested Citation

  • Tien Thanh Dam & Thuy Anh Ta & Tien Mai, 2022. "Joint chance-constrained staffing optimization in multi-skill call centers," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 354-378, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00830-1
    DOI: 10.1007/s10878-021-00830-1
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    References listed on IDEAS

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    1. Ingolfsson, Armann & Campello, Fernanda & Wu, Xudong & Cabral, Edgar, 2010. "Combining integer programming and the randomization method to schedule employees," European Journal of Operational Research, Elsevier, vol. 202(1), pages 153-163, April.
    2. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.
    3. Júlíus Atlason & Marina Epelman & Shane Henderson, 2004. "Call Center Staffing with Simulation and Cutting Plane Methods," Annals of Operations Research, Springer, vol. 127(1), pages 333-358, March.
    4. Júlíus Atlason & Marina A. Epelman & Shane G. Henderson, 2008. "Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods," Management Science, INFORMS, vol. 54(2), pages 295-309, February.
    5. Wyean Chan & Ger Koole & Pierre L'Ecuyer, 2014. "Dynamic Call Center Routing Policies Using Call Waiting and Agent Idle Times," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 544-560, October.
    6. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    7. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    8. Itai Gurvich & James Luedtke & Tolga Tezcan, 2010. "Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach," Management Science, INFORMS, vol. 56(7), pages 1093-1115, July.
    9. Avramidis, Athanassios N. & Chan, Wyean & Gendreau, Michel & L'Ecuyer, Pierre & Pisacane, Ornella, 2010. "Optimizing daily agent scheduling in a multiskill call center," European Journal of Operational Research, Elsevier, vol. 200(3), pages 822-832, February.
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