Staffing a call center with interactive voice response units and impatient calls

A call center consists of telephone trunk lines, a switching machine known as the automatic call distributor (ACD), an interactive voice recording unit (IVRU), and telephone sales agents. Calls enter the center whenever a trunk line is available; otherwise it is lost. Once a trunk line is seized, the call is instructed to choose among several options provided by the call center, via the IVRU. After completing the instructions at the IVRU, the call may leave the center or be routed to an available agent. If all agents are busy, the call is queued at the ACD until one is free. While waiting for the agents, calls may abandon the queue if their waiting time becomes unreasonably long. The reason for impatience and abandonment varies from call to call and it is difficult to quantify. In this paper, we assume that each call abandons the queue independently of each other while waiting for agents after a random amount of time.With this assumption, a serial network model is introduced to determine the optimal quantities of the number of trunk lines and agents subject to given service level. It is shown that abandonment of calls will influence the waiting time and hence the number of agents needed to meet a specific service level. With abandonment, this model provides a reasonable way to determine the number of trunk lines and agents required simultaneously. Numerical examples will illustrate the effects of abandonment on design parameters.