A Stackelberg game model for optimizing price, service level and inventory decisions in Vendor Managed Inventory system

Vendor management inventory (VMI), as one of the inventory management methods, reduces the cost of inventory in the chain, quick response to customers, increased service level, customer satisfaction, and improve collaboration between the members of the supply chain. In this study, a bi-level supply chain model with one manufacturer and one retailer under a vendor management inventory policy is investigated. The manufacturer produces a single product by the production capacity constraint at wholesale price and delivers the product to the retailer who then sells the product in the dispread market at retail price. The demand rate for the product in the retailer market is assumed to be a decreasing function of the price and an increasing function of the service level. The manufacturer determines its wholesale price, product’s replenishment cycle time, and backorder quantity to maximize its profit. Retailer determines the optimal retail price and service level to maximize its profit. This problem formulated as a Stackelberg game model with consideration manufacture as a leader and retailer as a follower. To search the Stackelberg game equilibrium, a solution algorithm has been proposed. A numerical study has been conducted to demonstrate how the algorithm works and to understand the influences of decision variables and parameters. Also, in order to validate the proposed model, sensitivity analysis has been performed on some parameters.