Threshold Routing to Trade Off Waiting and Call Resolution in Call Centers

In a call center, agents may handle calls at different speeds, and also may be more or less successful at resolving customers’ inquiries, even when only considering customers calling with similar requests. One common measure of successful call resolution is whether or not the call results in the customer calling back. This presents a natural trade-off between speed and quality, where speed is defined as the average time before an incoming call is answered (the average waiting time) and quality is defined as the percentage of all arriving calls that do not result in callbacks (the call resolution). The relevant control is the routing; that is, the decision concerning which agent should handle an arriving call when more than one agent is available. In an inverted-V model setting, we formulate an optimization problem with the dual performance objective of minimizing average customer waiting time and maximizing the call resolution. We solve this optimization problem asymptotically in the Halfin-Whitt many-server limit regime, interpret its solution as a routing control for the discrete-event system, and show via simulation that the interpreted routing control is on the efficient frontier. In particular, any routing control that has a lower average waiting time (higher call resolution) must also have a lower call resolution (higher average waiting time).