Allocating Pooled Inventory According to Contributions and Entitlements - Gerchak, Yigal (Decision Making in Manufacturing and Services, 2016)
Inventory pooling, whether by centralization of stock or by mutual assistance, is known to be beneficial when demands are uncertain. But when the retailers are independent, the question is how to divide the benefits of pooling. We consider a decentralized inventory pooling scheme where retailers’ entitlements to allocation in case of shortage depend on their contributions to the pool. We derive the Nash equilibrium, and specialize it to symmetric cases.