Heuristics for Multi-Item Two-Echelon Spare Parts Inventory Control Problem with Batch Ordering in the Central Warehouse

We consider a multi-item two-echelon inventory system in which the central warehouse operates under a (Q,R) policy, and each local warehouse implements (S − 1, S) policy. 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 facility. We propose a Lagrangian heuristic that employs a column generation method and a greedy algorithm. We also consider variants of this heuristic, which are based on the sequential determination of policy parameters (first the order quantities and then the reorder points and basestock levels), as done frequently in practice. As opposed to the heuristics for multi-echelon inventory optimization problems in the literature, our heuristics guarantee feasibility. We propose a lower bound for the optimal expected total cost and show that this bound is asymptotically tight in the number of parts. In an extensive computational study, we test the performances of the heuristics against this lower bound. The performance of the Lagrangian heuristic is found to be extremely well, which improves even further as the number of parts increases. Finally, we show numerically that sequential determination of policy parameters performs less satisfactorily while the computational benefits are limited.