Stochastic control of inventory and scheduling decisions in an open network of repairables

We study maintenance operations for capital goods with repairable components. Because the downtime of a capital good is costly, the maintenance provider keeps an inventory of spare parts to quickly replace broken parts of the capital goods. After the replacement, the broken part is added to the repair facility’s repair queue. Upon a part breakdown, if there is no spare part in the inventory, then the maintenance provider has two options: (i) it can backorder the spare part demand, (ii) it can execute an emergency repair, which is done immediately and quickly, and is followed by a quick installation of the part to the capital good. The objective is to minimize the summation of the long-run average costs of emergency repairs, demand backorders, and inventory holding. We study an open network of repairable parts in which the demand for the repair facility is exogenous. Due to the curse of dimensionality, exact analysis is challenging; therefore, we consider the system in the heavy-traffic asymptotic regime. In the heavy-traffic limit, we formulate a Brownian control problem (BCP). Because the BCP is multidimensional, we establish a state-space collapse result showing that the multidimensional BCP is equivalent to a single-dimensional stochastic control problem. We solve the latter control problem analytically using stochastic calculus. By mimicking the optimal solution, we propose a straightforward heuristic control policy that can be easily implemented in practice.