Using simulation-based Stochastic Approximation to optimize staffing of systems with Skills-Based-Routing

In this paper, we consider the problem of minimizing the operational costs of systems with Skills-Based-Routing (SBR). In such systems, customers of multiple classes are routed to servers of multiple skills. In the settings we consider, each server skill is associated with a corresponding cost, and service level can either appear as a strong constraint or incur a cost. The solution we propose is based on the Stochastic Approximation (SA) approach. Since SBR models are analytically intractable in general, we use computer simulation to evaluate service-level measures. Under the assumption of convexity of the service-level as functions in staffing levels, SA provides an analytical proof of convergence, together with a rate of convergence. We show, via numerical examples, that although the convexity assumption does not hold for all cases and all types of service-level objectives, the algorithm nevertheless identifies the optimal solution.