In the emergency production of medical products, the supplier with raw materials is often the leader in the game and has the advantage of determining the supply chain structure. Previous research on supply chain structure mostly focuses on how the leader uses this advantage to obtain the optimal profit, ignoring the strategic compensation of the follower under this disadvantage. This paper explores how the follower can get the optimal profit through contract design and production time in a supply chain composed of two buyers (integrated buyer and non-integrated buyer) and a supplier. In the case of shortage of medical products, firms form a completely decentralized or partially decentralized (the supplier and a buyer form a vertically integrated entity) structure for emergency production. The results show that the integrated buyer can obtain more profits in the partially decentralized structure. In addition, in the partially decentralized structure, the non-integrated buyer is more sensitive to production time. Surprisingly, in emergency production, the more purchases the non-integrated buyer makes, the higher the wholesale price of the supplier. However, under certain conditions, this abnormal phenomenon increases the possibility of the buyer obtaining the optimal profit, and weakens the influence of supply chain structure.
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