We consider a revenue-generating call center with inbound and outbound calls, where service and sales activities are blended. For maximizing the call center's revenue, the call center manager exercises two levels of control; agent reservation for inbound calls and call outsourcing.

Given the influence of waits on purchase probability, we investigate the strategy of outsourcing customers who have waited already, as opposed to outsourcing customers directly at arrival. We use a single framework to investigate combining agent reservation with outsourcing decisions, and a waiting time-based outsourcing strategy. The existing literature only considers these two strategies in isolation and is restricted to quantity-based decisions. From a practical viewpoint, our results aim to provide decision support tools that are directly implementable in a call center's routing software.

We apply a Markov decision process approach to optimize the manager's decisions. The particularity of our approach is that we use the experienced waiting time as a decision variable. We prove that the optimal policy for reservation and outsourcing is of threshold type. Our main conclusion is that outsourcing customers after letting them wait in-house generates higher revenue than outsourcing calls at arrival. However, it is also detrimental to service quality. In addition, we identify contexts where the difference between the two outsourcing strategies is significant. Contrary to standard call center practices, which either consist of specialized teams for one type of call, or only exercising one specific level of decision-making (reservation or outsourcing), we demonstrate the potential of partial outsourcing with partial reservation.

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