Capacitated two-indenture models for repairable item systems

A two-indenture maintenance system is considered for a number of identical installations, in use at a single site. The installations are considered as assemblies that are made up of a number of repairable components. A component repair center and an assembly facility are both modeled as product form queuing networks. Failures of the assemblies occur according to a Poisson process. There are stock points for both ready-for-use assemblies and components. The inventory control policy employed at each stock point is a base-stock policy. Upon failure of an assembly, it is replaced by a ready-for-use one, if available. The failed assembly is inspected to identify and disassemble the broken component causing its failure. Next, the broken component is sent to the component repair center and one ready-for-use component is requested from the stock of this component. Once a ready-for-use component is available for the assembly, the request and the available component are merged and sent to the assembly facility. Completion of component repair or an assembly operation results in a replenishment of the corresponding stock point. Requests that cannot be satisfied right away are backordered. Service discipline is first-come-first-serve at each facility. Assuming that only one component is identified at a time as the cause of an assembly failure, first an alternative slightly aggregated (but exact) formulation is given for the system and then a near-product-form solution is proposed as an approximate steady-state distribution of the aggregated system. Comparison of the approximate performance measures computed with the use of the near-product-form solution and the ones obtained with simulation shows that the approximation is quite accurate. Relying on the accuracy, approximate performance measures are used for optimizing base-stock levels with a greedy procedure.