Inventory Sharing and Rationing in Decentralized Dealer Networks

Hui Zhao · Vinayak Deshpande · Jennifer K. Ryan

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Supply Chain and Inventory Management Sustainable Supply Chain Management Logistics and Transportation Systems

Abstract

An increasing number of manufacturers have started to pursue a strategy that promotes inventory sharing among the dealers in their distribution network. In this paper we analyze a decentralized dealer network in which each independent dealer is given the flexibility to share his inventory. We model inventory sharing as a multiple demand classes problem in which each dealer faces his own customer demand with high priority, and inventory-sharing requests from other dealers with low priority. Assuming that each dealer uses a base-stock and threshold-rationing policy for his inventory-stocking and inventory-sharing decisions, we explicitly model the interactions between the dealers through inventory sharing and obtain a closed-form cost function for each dealer based on the steady-state distribution of the inventory levels at the two dealers. We then provide a detailed supermodularity analysis of the inventory-sharing and inventory-rationing game in which each dealer has a two-dimensional strategy set (stocking level and rationing level). We show that the full-sharing game (in which dealers precommit to sharing all of their on-hand inventory) and the fixed-sharing-level game (in which dealers precommit to sharing a portion of their on-hand inventory) are supermodular, and thus a pure-strategy Nash equilibrium is guaranteed to exist. For the rationing game (in which dealers precommit to their stocking levels), we show that there exists a dominant strategy equilibrium on the dealers’ sharing (rationing) levels. Finally, a comprehensive computational study is conducted to highlight the impact of the manufacturer’s incentives, subsidies, and/or transshipment fees on the dealers’ sharing behavior.

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References

2011Supermodularity and Complementarity 2000Foundations of Inventory Management 1990Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities 1979Equilibrium Points in Nonzero-Sum n -Person Submodular Games 1999Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain 1999Decentralized Multi-Echelon Supply Chains: Incentives and Information 2001Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers 1997The Competitive Newsboy

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