Staffing Multiskill Call Centers via Linear Programming and Simulation

Mehmet Tolga Cezik · Pierre L’Ecuyer

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Scheduling and Timetabling Solutions Simulation Techniques and Applications Optimization and Mathematical Programming

Abstract

We study an iterative cutting-plane algorithm on an integer program for minimizing the staffing costs of a multiskill call center subject to service-level requirements that are estimated by simulation. We solve a sample average version of the problem, where the service levels are expressed as functions of the staffing for a fixed sequence of random numbers driving the simulation. An optimal solution of this sample problem is also an optimal solution to the original problem when the sample size is large enough. Several difficulties are encountered when solving the sample problem, especially for large problem instances, and we propose practical heuristics to deal with these difficulties. We report numerical experiments with examples of different sizes. The largest example corresponds to a real-life call center with 65 types of calls and 89 types of agents (skill groups).

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References

1983Simulation Modeling and Analysis.1999Simulation modeling and analysis 2003Telephone Call Centers: Tutorial, Review, and Research Prospects 2002An Object-Oriented Random-Number Package with Many Long Streams and Substreams 2002Queueing Models of Call Centers: An Introduction 2005A Staffing Algorithm for Call Centers with Skill-Based Routing 2019Large Deviations For Performance Analysis 1996Server Staffing to Meet Time-Varying Demand

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2015Staffing and scheduling under nonstationary demand for service: A literature review 2009Optimizing daily agent scheduling in a multiskill call center 2009Constrained optimization in expensive simulation: Novel approach 2008Simple Methods for Shift Scheduling in Multiskill Call Centers 2013Operations Research (OR) in Service Industries: A Comprehensive Review 2019When You Work with a Superman, Will You Also Fly? An Empirical Study of the Impact of Coworkers on Performance

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