Agents’ Self‐Routing for Blended Operations to Balance Inbound and Outbound Services

This study aims to evaluate the cost of agents’ self‐routing in a service system with inbound and outbound customers. We assume that inbound customers arrive over time depending on the waiting time offered, while outbound customers can be contacted at all times. Furthermore, agents are in control of routing decisions and are aware of the state of the system. Accordingly, they decide whether to serve an inbound or outbound customer, or to idle. The system manager seeks to provide a suitable trade‐off between agents’ choice of serving inbound and outbound customers by incentivizing their actions through linear payouts. Hence, there arises a problem of determining the cost of agents’ self‐routing, which can be interpreted as a variant of the principal‐agent problem where the agents’ efforts are directed toward selecting their routing policy. Through a Markov decision process, we show that the agents’ optimal policy is a reservation threshold policy for inbound customers, and express the compensation parameters that minimize staffing cost. We conclude that motivating idling decisions through linear payouts incurs high costs. This justifies the current practice of using automated routing in call centers. Moreover, paying for idling cannot reduce staffing cost. However, discriminating between delayed and non‐delayed customers in the reward structure presents a high potential of reducing agents’ pay. Finally, in situations where agents do not know the status of their colleagues, our analysis argues in favor of not revealing the state of the system to them through delay announcements when the objective waiting time is low.