Approximate dynamic programming techniques for skill-based routing in call centers*

We consider the problem of dynamic multi-skill routing in call centers. Calls from different customer classes are offered to the call center according to a Poisson process. The agents are grouped into pools according to their heterogeneous skill sets that determine the calls that they can handle. Each pool of agents serves calls with independent exponentially distributed service times. Arriving calls that cannot be served directly are placed in a buffer that is dedicated to the customer class. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on approximate dynamic programming techniques. In particular, we perform one-step policy improvement using a polynomial approximation to relative value functions. We compare the performance of this method with decomposition techniques. Numerical experiments demonstrate that our method outperforms leading routing policies and has close to optimal performance.