Risk Pooling and Cost Allocation in Spare Parts Inventories

We present a problem on risk pooling and cost allocation in inventory of spare parts motivated in the oil and gas sector. Spare parts are held to facilitate operational conditions. Multiple inventory plants control their stock per separate. In practice, however, they supply each other when needed. Risk pooling is a source of savings in this situation. Under a centralized inventory solution, the plants should agree on how to share costs for taking advantage of the benefits of pooling. We report computations where the centralized inventory achieves significant savings over the decentralized solution, considering ordering and holding costs subject to a service level constraint. We then test five cost allocation methods and analyse their outcomes, using game theory principles. We show examples where a method results in stable allocations when the plants use the same target service levels, but not when at least one plant use a different target.