Optimal Service Policy for a Workstation Subject to Breakdown

This paper considers a service system with one workstation, where arriving defective items are either repaired by the station or replaced by the available items in the warehouse. We model the system as a dynamic programming with the objective minimizing the total operational cost. The workstation is subject to breakdown and repair. We show the existence of a switching curve which is an increasing function. The switching curve forms an optimal policy for the decision on whether an arriving defective item should be repaired by the workstation or replaced by the available item in stock. The properties of the optimal policy are also studied.