Stackelberg game in VMI system with sufficient capacity considering wholesale and retail prices

This work discusses a VMI (vendor managed inventory) supply chain where one manufacturer produces and supplies a single product at a wholesale price to multiple retailers, maybe its agents, who then sell the product in dispersed and independent markets at retail prices. The manufacturer determines wholesale price, inventory replenishment cycle, and backorder quantity by maximizing its own profit with sufficient capacity. The retailers in turn take the manufacturer's decision results as given inputs to determine the optimal retail prices to maximize their own profits. This problem is modeled as a Stackelberg game where the manufacturer is the leader and retailers are followers. The analysis of the equilibrium of the Stackelberg game and its corresponding algorithm are given. A numerical study is conducted to understand the influence of some parameters.