Spare parts management affects significantly costs and service level for supply chains. This paper deals with an inventory management problem for multi-item repairable systems via a systemic perspective based on a new efficient integer black-box optimization model. With respect to the traditionally used marginal allocation that considers items individually, the proposed black-box optimization model is a holistic approach in the fact that it exploits relationships among items. The authors propose a derivative-free algorithm specifically tied to the application which exploits a new selection strategy for choosing entire subsets of items with the aim to get the best expected improvement in the objective function. The approach has been tested on a real case study for optimizing stocks in an airline's inventory network. The case study provides evidence about the good behavior of the exploratory geometry of the proposed approach in finding quickly a feasible and optimal solution for inventory control.