Steady-state approximation of a multiechelon multi-indentured repairable-item inventory system with a single repair facility

The authors model a two-echelon multi-indentured repairable-item inventory system where each ‘base’ has a maximum number of identical online machines, and each machine consists of several module types. Machine failures are due to module failures and occur according to an exponential distribution. When a machine fails, the failed module is replaced by an identical spare module if one is available. Otherwise, the module is backordered. All failed modules go to a single ‘depot’ repair facility which consists of a finite number of identical repairmen who are able to repair any module type in an exponentially distributed time, although the repair rates for different module types may differ. The principal contribution of this article is an approximation algorithm for calculating the steady-state characteristics of the system. In comparison with simulation results, the algorithm is quite accurate and computationally efficient.