In call centers, agents may handle calls at different speeds, and also may be more or less successful at resolving customers’ inquiries. We investigate this speed-quality trade-off, where speed is defined as the average waiting time and quality is defined as the percentage of calls that do not result in callbacks. The routing control is the decision concerning which agent should handle an arriving call when more than one agent is available. In an inverted-V model, we formulate an optimization problem with the dual performance objective of minimizing average waiting time and maximizing the call resolution and solve it asymptotically.
The main practical implication of this work is that focusing on minimizing average waiting time as the sole performance objective, as in the most literature, may not deliver the best customer experience, especially when slow agents may have high service quality. Hence it is important to consider objective functions that take into account call resolution. Theoretically, we identify a graphic algorithm to reduce the number of server pools in trade-off and a nice threshold structure of the optimal routing policy.