Steady-state approximations for a multi-echelon multi-indentured repairable-item inventory system

In this paper the authors model a two-echelon multi-indentured repairable-item inventory system. Each of several ‘bases’ has a maximum number of identical online machines, and each machine consists of several module types. At random times these machines fail because of module failures. When a machine fails, the failed module is determined and is replaced by an identical spare module if one is available. Otherwise, the module is backordered. Depending on the type of failure, the failed module is repaired at a central depot or at the base where the failure occurs. The authors assume that separate repairmen are devoted to each module type. Thus, when a module fails, it is repaired by one of its designated repairmen. In calculating the steady-state operating characteristics of this system, the usual Markovian approach leads to a multidimensional state space that is extremely large even for relatively small problems. Solving this multidimensional system exactly is virtually impossible because of the huge number of states. Consequently, the authors propose an approximation method that enables them to solve large problems relatively quickly. Although the present solution is only approximate, results from a variety of test problems indicate that the approximation is quite accurate.