Joint Inventory and Scheduling Control in a Repair Facility

We study inventory and repair scheduling decisions of a maintenance service provider for repairable capital goods. Because of high downtime costs, the service provider keeps spare parts on stock to replace broken parts quickly. The service provider should determine the inventory level of spare parts for each component and the repair scheduling policy. Furthermore, in case of a stock-out, the service provider should decide whether to back-order the demand or execute an emergency repair, which is an urgent but expensive repair operation for a broken part followed by a fast form of installation. The objective is to minimize the long-run average inventory holding, back-order, and emergency repair costs. We formulate the repairable network as a closed queueing system and consider an asymptotic regime in which the repair facility is in the conventional heavy-traffic regime. Then, we formulate and solve a Brownian control problem (BCP). From the optimal BCP solution, we derive a simple and intuitive decision rule stating if the emergency repairs are necessary to achieve a close-to-optimal system performance. Moreover, we propose a simple, intuitive, and easy-to-implement heuristic control policy and demonstrate its close-to-optimal performance via numerical experiments.