Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach
We consider the problem of staffing call centers with multiple customer classes and agent types operating under quality-of-service (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability with respect to the uncertainty in the demand rate. We contrast this chance-constrained formulation with the average-performance constraints that have been used so far in the literature. We then propose a two-step solution for the staffing problem under chance constraints. In the first step, we introduce a random static planning problem (RSPP) and discuss how it can be solved using two different methods. The RSPP provides us with a first-order (or fluid) approximation for the true optimal staffing levels and a staffing frontier. In the second step, we solve a finite number of staffing problems with known arrival rates--the arrival rates on the optimal staffing frontier. Hence, our formulation and solution approach has the important property that it translates the problem with uncertain demand rates to one with known arrival rates. The output of our procedure is a solution that is feasible with respect to the chance constraint and nearly optimal for large call centers.
Volume (Year): 56 (2010)
Issue (Month): 7 (July)
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- repec:spr:compst:v:65:y:2007:i:1:p:115-140 is not listed on IDEAS
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- Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
- Refik Soyer & M. Murat Tarimcilar, 2008. "Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach," Management Science, INFORMS, vol. 54(2), pages 266-278, February.
- Weinberg, Jonathan & Brown, Lawrence D. & Stroud, Jonathan R., 2007. "Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1185-1198, December.
- Haipeng Shen & Jianhua Z. Huang, 2008. "Interday Forecasting and Intraday Updating of Call Center Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 391-410, July.
- 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.
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