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Staffing Multiskill Call Centers via Linear Programming and Simulation

GERAD and Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal H3C 3J7, Canada
GERAD and Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal H3C 3J7, Canada
mehmetc{at}amazon.com
lecuyer{at}iro.umontreal.ca

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).

Key Words: call centers; staffing; optimization by simulation; integer programming; cutting planes; skill-based routing; subgradient cuts
History: Received: November 11, 2004;

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