Coalition or decentralization: a game-theoretic analysis of a three-echelon supply chain network

Abstract

Supply chains have become the major and dominant paradigm of business and competition. The main challenge is how to act in multi-echelon supply chains considering the levels involved. Making a choice independently or integrating with some or all levels will be a critical decision, and therefore affects the overall profit of the chain. This article proposes a non-cooperative game theory approach to helping in making a better decision in the supply chain and gaining the most accessible benefit. Our research considers unlimited three-echelon supply chains with S suppliers, M manufacturers and K retailers. The Nash equilibrium and definition are used bearing in mind inventory and pricing and marketing cost as decision variables for this matter. This paper studies a three-echelon supply chain network and focuses on the value of integrating a pair of partners in the chain. In the decentralized case, the supplier sets its own price, the manufacturer points out order quantity, wholesale price and backorder quantity, and the retailer charges the final retail price of the product and marketing product. Though there are multiple players at a single echelon level, each manufacturer supplies only a specific product to a given retailer. In addition to the decentralized case, two integration scenarios have been taken into account: manufacturer-retailer and supplier-manufacturer. As for manufacturer-retailer integration, inventory/holding cost issues diminish to a single warehouse and the retailer does not have to enforce marketing effort any more. Supplier-manufacturer integration brings similar benefits. Under each scenario, all parties involved simultaneously set their strategies. Through a numerical experiment, 17 design cases (through designing experiments) have been developed and the total profit of the supply chain under each scenario has been evaluated. Statistical tests on the above introduced 17 experiments have found that the decentralized system performs significantly worse than the integration of the supplier with the manufacturer, whereas no significant difference can be observed regarding other combinations.

Keyword : supply chain, coalition, non-cooperative games, Nash equilibrium, design of experiment, Levenberg-Marquardt algorithm