A queueing-inventory system with a repeated-orbit policy during the service

We consider a service system in which customers who arrive at a service station and place an order, are not involved in the processing of their order, which can therefore be executed in their absence. Consequently, customers may leave the service station for some period of time during the processing of their order (i.e., go to orbit), and then return. While the customers are in orbit, they can utilize their time efficiently. If the service is completed before the customer's return from orbit, the ready service (RS) is stored in a designated storage facility until the customer returns and retrieves the RS from the inventory. If, however, the service is not yet completed when the customer returns, the customer can leave to orbit again. Accordingly, the policy is called "repeated orbit" (during the service). We formulate and analyze the queueing-inventory-repeated-orbit (QIRO) system using the matrix geometric method. The optimal orbiting time is calculated by maximizing the customer's expected utility. In addition, the optimal RS storage capacity and the optimal investment in preservation technologies (to store the RSs) are derived, both of which serve to increase demand and thus maximize the system's expected profit.