Formal Methods of Value Sharing in Supply Chains

Abstract

We consider a decentralized, two-echelon supply chain where the upper echelon --the supplier-- bears the inventory risk. To service the retailers, the supplier either keeps inventory reserved for each of her customers or else pools inventory to share among her customers. The common insight regarding inventory pooling is that it reduces costs and so increases profits for the supply chain party carrying inventory. However, it has recently been shown that inventory pooling may indeed reduce the total supply chain profits. We further show that inventory pooling may reduce supply chain profits even under traditional service contracts based on the frequently invoked measure of service, probability of stock-out.

We model the inventory transactions among the retailers and the supplier as a cooperative game. The players have the option of reserving inventory or forming inventory-pooling coalitions. The total profit of the coalitions is allotted to the players using a profit-sharing mechanism based on Shapley value. We analyze the properties of the proposed profit-sharing scheme in two steps. We first consider a stylized model with two retailers who are not necessarily identical. Then we extend the analysis to an arbitrary number of identical retailers. In both cases, we assume the demand across retailers is independent.

We find that the Shapley value allocations coordinate the supply chain and are individually rational. However for more than two retailers, they may not be in the core. Even when they satisfy all the stability properties, including membership in the core, they may be perceived unfair since a player's allocation can exceed his contribution to the total supply chain profit. In addition to analyzing the stability properties of the proposed allocation mechanism, we are also interested in the types of behavior the mechanism induces in the players. We find that the retailers prefer pooling partners with either very high or low service level requirements and the supplier prefers retailers with low service requirements since this gives her the ability to maximize her profit allocation. Finally, we analyze the effects of demand variance on the allocations and the profitability of strategic retailer coalitions.