Routing analyses for call centers with human and automated services

We analyze a call center with robot and human agents. Customers arrive over time and have a preference for being served by an agent. Thus, although robots are infinite in number, it might be preferable to let some customers wait so as to give them a human service. The aim of this paper is to determine how agents and robots should be placed in the call center architecture to deliver the lowest wait- and service-dissatisfaction. We prove that in terms of expected wait- and expected service-dissatisfaction, a preventive policy where scheduling to robots or to agents is made at arrival, outperforms corrective policies, where scheduling is made after a certain wait, or policies where the robot service can be interrupted. This conclusion is only true with respect to expectation, however. When considering higher moments of the wait, a corrective policy appears to be preferable. Service interruption leads to less variability in service-dissatisfaction, which can be appreciated when customer fairness is sought.