A divergent two-echelon spare part inventory system with lost sales and compound Poisson demand

This paper investigates a spare parts inventory system in a two-echelon supply chain following a continuous review process. The first echelon has a central warehouse, while the second has multiple local warehouses. The demand for spare parts at the local warehouses follows a Compound Poisson Process. A base-stock policy controls inventory in the supply chain with demand satisfied within a pre-determined waiting time threshold. Failure to do so will result in lost sales, which happens when stockouts occur at both echelons and there is no inventory in transit. The lead time at the central warehouse is a random variable following a general distribution. Empirical evidence suggests that the Compound Poisson Process provides a more accurate fit for the lumpy and intermittent demand of spare parts compared to the Poisson process, which is the approach often adopted in the literature. This paper follows a queueing network modeling approach to find the inventory performance measures in closed-form when the lead time at the central warehouse follows a general distribution. We minimize supply chain costs and improve performance by determining the optimum inventory levels at the central and local warehouses. We simulated our model and found that the numerical results deviated by a maximum of 5.84% error compared to the results from closed-form expressions.