Multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse under compound Poisson demand

We consider a multi-item two-echelon spare part inventory system in which the central warehouse operates under an (nQ, R) policy and the local warehouses implement order-up-to S policy, each facing a compound Poisson demand. The objective is to find the policy parameters minimizing expected system-wide inventory holding and fixed ordering costs subject to an aggregate mean response time constraint at each warehouse. In this paper, we propose four alternative approximations for the steady state performance of the system; and extend a heuristic and a lower bound proposed under Poisson demand assumption to the compound Poisson setting. In a computational study, we show that the performances of the approximations, the heuristic, and the lower bound are quite satisfactory; and the relative cost saving of setting an aggregate service level rather than individually for each part is quite high.