Robust Design and Control of Call Centers with Flexible IVR Systems

We consider the robust design and control of call center systems with flexible interactive voice response (IVR) systems. In a typical call center equipped with an IVR system, customers are handled first by the IVR system, which is a computerized system that often enables customers to self-serve. Those customers whose service cannot be handled by the IVR system are sent to the second stage to be served by agents. In order to address the design of a call center with a flexible IVR system, we consider a call center whose IVR system can operate in two different service delivery modes that have statistically different outcomes. We formulate a stochastic program to determine the number of agents needed in the second stage as well as the proportion of customers that should be selected for each IVR service mode under different demand levels with the objective of minimizing the total staffing and abandonment costs. We also propose dynamic control policies to achieve the optimal proportions without the knowledge of the exact arrival rate. We show that the staffing levels found by the stochastic program combined with the proposed routing policies are asymptotically optimal in large systems. We present extensive numerical and simulation results to illustrate the effectiveness of the proposed solutions