Annals of Operations Research

, Volume 127, Issue 1–4, pp 333–358 | Cite as

Call Center Staffing with Simulation and Cutting Plane Methods

  • Júlíus Atlason
  • Marina A. Epelman
  • Shane G. Henderson


We present an iterative cutting plane method for minimizing staffing costs in a service system subject to satisfying acceptable service level requirements over multiple time periods. We assume that the service level cannot be easily computed, and instead is evaluated using simulation. The simulation uses the method of common random numbers, so that the same sequence of random phenomena is observed when evaluating different staffing plans. In other words, we solve a sample average approximation problem. We establish convergence of the cutting plane method on a given sample average approximation. We also establish both convergence, and the rate of convergence, of the solutions to the sample average approximation to solutions of the original problem as the sample size increases. The cutting plane method relies on the service level functions being concave in the number of servers. We show how to verify this requirement as our algorithm proceeds. A numerical example showcases the properties of our method, and sheds light on when the concavity requirement can be expected to hold.

simulation optimization call centers cutting planes sample average approximation 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Júlíus Atlason
    • 1
  • Marina A. Epelman
    • 1
  • Shane G. Henderson
    • 2
  1. 1.Department of Industrial and Operations EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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