Leader–follower game in vendor-managed inventory system with limited production capacity considering wholesale and retail prices

Vendor-managed inventory (VMI) is a widely used co-operative inventory policy in supply chains in which each enterprise has its autonomy in pricing. In this paper, a leader–follower Stackelberg game in a VMI supply chain is discussed where the manufacturer, as a leader, produces a single product with a limited production capacity and delivers it at a wholesale price to multiple different retailers, as the followers, who then sell the product in dispersed and independent markets at retail prices. An algorithm is then developed to determine the equilibrium of the Stackelberg game. Finally, a numerical study is conducted to understand the influence of the Stackelberg equilibrium and market-related parameters on the profits of the manufacturer and its retailers. Through a numerical example, our research demonstrates that: (a) the market-related parameters have significant influence on the manufacturer's and its retailers' profits; (b) a retailer's profit may not necessarily be lowered when it is charged with a higher inventory cost by the manufacturer; and (c) the equilibrium of the Stackelberg equilibrium benefits the manufacturer.