Spare parts inventory pooling: how to share the benefits?

We consider a stock point for expensive, low-usage items that is operated by multiple decision makers. Each faces a Poisson demand process, and the joint stock point is controlled by a continuous-review base stock policy with full backordering. We consider penalty costs for backorders and holding costs for stock on hand. For this model, we derive structural properties of the resulting cost function. We use these to prove not only that it is cost effective to share one stock point with all parties involved, but also that collaboration (inventory pooling) can be supported by a stable cost allocation, i.e., the core of the associated cooperative game is non-empty. These results hold under optimized and under exogenously given base stock levels. For the former case, we further identify a stable cost allocation that would be easy to implement in practice and that induces players to reveal their private information truthfully.