A multi-skill staffing problem in a call center where the agent skill sets are exogenous and the call routing policy has well-specified features of overflow between different agent types is addressed. Constraints are imposed on the service level for each call class, defined here as the steady-state fraction of calls served within a given time threshold, excluded. An approximation of these service levels is developed that allows an arbitrary overflow mechanism and customer abandonment. A two-stage heuristic that finds good solutions to mathematical programs with such constraints is developed. The first stage uses search methods supported by the approximation. Because service level approximation errors may be substantial, the solution is adjusted in a second stage in which performance is estimated by simulation. Realistic problems of varying size and routing policy are solved. The proposed approach is shown to be competitive with (and often better than) previously available methods
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