Cost allocation in inventory pools of spare parts with service-differentiated demand classes

Holding inventory of spare parts is critical to assure safety and production. In order to save costs, different producers may collaborate through an inventory pool. We consider an inventory pool of spare parts, subject to a service level constraint, where the members of the pool may have different target service levels, so that they represent different demand classes. The pool is implemented either by round-up or rationing policies. The members should agree on how to share the costs. Based on cooperative game theory concepts, we show the important effects that different targets can have in the core stability for this problem. We perform a computational study in a large number of instances, providing insights on the emptiness of the core and the performance of seven allocation methods. We also propose the novel Minimum Deviation from Service Level Referential Cost Method (MIND). This method looks for a stable allocation such that the maximum difference between a cost allocated to a player and its service level referential cost is minimised. The MIND allocation is the solution to a linear programming model and is core guaranteed, in the sense that if the core is not empty, the allocation belongs to the core.