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In this paper, we consider multi-item inventory systems that contain repair kits of spare parts and tools and may include an inventory of spare machines as well. Demands occur in the form of field repair jobs, each requiring some collection of parts and tools for completion. If any required part or tool is not in the repair kit, the repair job is “broken.” The penalty or inconvenience cost is assumed to be proportional to the number of broken jobs, regardless of the number of items short. Previous work on job completion based systems is summarized and new results for the optimal solutions are derived. A more general job completion based system is also analyzed, which allows a pool of spare machines to be used to satisfy demands which cannot be met with the repair kits. Techniques are presented for optimizing the trade-off between the inventory cost of repair kits plus spare machines and the overall level of service.
Mamer et al. (Sat,) studied this question.