Centralizing Inventory in Supply Chains by Using Shapley Value to Allocate the Profits

How should the excess profit because of inventory pooling be shared amongst firms at different levels along the supply chain? Suppose each of several retailers observes local demand for a common item and places an order at the supplier, which is immediately filled if the supplier has the item in stock. The supplier can fill retailer orders either from their reserved inventories or from a shareable pool of inventory. Using terminology from cooperative game theory, we say that the supplier and the retailers whose orders are filled from the common pool have formed an inventory-pooling coalition and study the use of Shapley value to allocate the expected excess profit because of pooling. We find that under Shapley value allocations the retailers have incentive to join the inventory-pooling coalition, and the supplier carries the level of inventory that is optimal for the coalition. Shapley value allocations might not lie within the core of the game, but the grand coalition of all players is stable in the farsighted sense. And, although the supplier's share of the expected excess profit is largest when all the retailers participate in the inventory-pooling coalition, the allocations to the retailers may diminish as the coalition grows. Colluding against the supplier (by merging and forming larger retailers) may seem like an appealing strategy for the retailers to increase their share of the total supply chain profit, but we find that the total expected after-pooling profits of retailers may instead go down because of collusion.