Approximate dynamic programming in multi-skill call centers

We consider a multi-skill call center consisting of specialists and fully cross-trained agents. All traffic is inbound and there is a waiting queue for each skill type. Our objective is to obtain good call routing policies. In this paper we use the so-called policy iteration (PI) method. It is applied in the context of approximate dynamic programming (ADP). The standard PI method requires the exact value function, which is well known from dynamic programming. We remark that standard methods to obtain the value function suffer from the curse of dimensionality, i.e., the number of states grows exponentially with the size of the call center. Therefore, we replace the real value function by an approximation and we use techniques from ADP. The value function is approximated by simulating the system. We apply this method to our call routing problem, yielding very good results.