Front-office multitasking between service encounters and back-office tasks

We model the work of a front-line service worker as a queueing system. The server interacts with customers in a multi-stage process with random durations. Some stages require an interaction between server and customer, while other stages are performed by the customer as a self-service task or with the help of another resource. Random arrivals by customers at the beginning and during an encounter create random lengths of idle time in the work of the server (breaks and interludes respectively). The server considers treatment of an infinite amount of back-office tasks, or tasks that do not require interaction with the customer, during these idle times. We consider an optimal control problem for the server’s work. The main question we explore is whether to use the interludes in service encounters for treating back-office, when the latter incur switching times. Under certain operating environments, working on back-office during interludes is shown to be valuable. Switching times play a critical role in the optimal control of the server’s work, at times leading the server to prefer remaining idle during breaks and interludes, instead of working on back-office, and at others to continue back-office in the presence of waiting customers. The optimal policy for use of the interludes is one with multiple thresholds depending on both the customers queueing for service, and the ones who are in-service. We illustrate that in settings with multiple interludes in an encounter, if at all, the back-office work should be concentrated on fewer, longer and later interludes.