We consider a multi-item two-echelon spare parts inventory system in which the central warehouse operates under a (Q, R) policy and local warehouses implement (S-1,S) policy. The objective is to find the policy parameters minimizing expected system-wide inventory holding and fixed ordering subject to aggregate and individual response time constraints. Using an exact evaluation we provide a very efficient and effective heuristic, and also a tight lower bound for real-world, large-scale two-echelon spare parts inventory problems. An extensive numerical study reveals that as the number of parts increases - which is usually the case in practice - the relative gap between the cost of the heuristic solution and the lower bound approaches zero. In line with our findings, we show that the heuristic and the lower bound are asymptotically optimal and asymptotically tight, respectively, in the number of parts. In practice, this means we can solve real-life problems with large numbers of items optimally. We propose an alternative approach between system and item approaches, which are based on setting individual and aggregate service level constraints, respectively. Using our alternative approach, we show that it is possible to keep the cost benefit of using aggregate service levels while avoiding long individual response times. We also show that the well-known sequential determination of policy parameters, i.e., determining the batch sizes first, and then finding the other policy parameters using those batch sizes, which is known for its high performance in single-item models, performs relatively poor for multi-item systems. (C) 2016 Elsevier B.V. All rights reserved.