Integration of pricing and inventory decision in a supply chain under vendor-managed inventory with defective items and inspection errors: a game-theoretic approach

In this paper, the production-inventory-marketing model for a two-stage manufacturer-retailer supply chain under VMI policy with a price-sensitive demand is studied. An imperfect production at the manufacturer and inspection process involving with Type I and II errors at the retailer are considered. We assume that the manufacturer gives products to the retailer in a number of equal-sized shipments. This model is formulated as a Stackelberg game in which the retailer retains a certain degree of autonomy by reserving the right to choose the retail price and the manufacturer determines replenishment frequency, replenishment quantity and wholesale price. The critical supply chain decision factors including the manufacturer’s wholesale price, the retailer’s price, shipment frequencies and number of shipments are determined maximizing the total profit of each member of the supply chain. A solution procedure is proposed to find the Stackelberg game equilibrium. The performance of the model is assessed by a numerical example. The numerical shows that it is more beneficial for both the manufacturer and the retailer when the demand is less price sensitive