A two-echelon repairable inventory system with stocking-center-dependent depot replenishment lead times

Consider a two-echelon repairable inventory system consisting of a central depot and multiple stocking centers. The centers provide parts replacement service to customers and replenish their inventory from the depot, following a one-for-one policy. The depot fills center replenishment orders on a first-come-first-serve basis. Defectives received at the centers are passed to the depot for repair and depot inventory replenishment. For this system, existing models (e.g., the METRIC model) usually assume that the depot replenishment lead times (DRLTs) are independent, identically distributed (i.i.d.), which however, does not fit well into the service parts logistics system that motivated this research. Because the DRLTs consist of the sum of repair times, defective return times, and transportation times, they are different across stocking centers, which are located globally. We study the impact of such center-dependent DRLTs on system performance. We derive probability distributions of the random delays at the depot experienced by center replenishment orders. We prove that a center with shorter DRLTs experiences shorter delays, and therefore, delivers better customer service. We show that for such systems, using the i.i.d. DRLT assumption introduces errors in estimating system performance. These errors become significant when both the demand rates and the depot planned inventory level are low.