Vertical channel structure strategy in competing supply chains under third party’s extended warranties based on inverse demand function

This paper established two competing supply chains consisting of two manufacturers and two exclusive retailers, in which two retailers sell substitutable products and also sell extended warranties for the products they sell. We use inverse demand function to describe the product price. It is an interdisciplinary application in the field of mathematics and management. From the perspective that both chain members can be better off, this paper studies how the market competition and third party's extended warranty policy impact the dominance of the vertical channel structure strategy of two symmetrical supply chains which propose the same channel structures. The results show that when the market competition is mild, or when the market competition intensity is moderate and the product initial market size is lower than specific threshold value, pure coordinated channel structure (in which both chains propose coordinated structure) is superior to pure decentralized channel structure (in which both chains propose decentralized structure). When the competition intensity is moderate and the product initial market size is higher than the specific threshold, or when the competition is extremely intensive, pure decentralized channel structure is superior to pure coordinated channel structure. And no matter whether the supply chains choose pure coordination or pure decentralized, there are different fixed areas composed of market competition intensity and initial market size, so that supply chains and third parties can make more profits at the same time.