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


  • Esmat Taghipour Alzahra University
  • Mehdi Seifbarghy Alzahra University
  • Mostafa Setak K. N. Toosi University of Technology


Vendor-Managed Inventory (VMI), Pricing, Replenishment Frequency, Defective Items, Inspection Errors, Stackelberg game


In this article, the production-inventory-marketing model for two-stage manufacturer-retailer supply chain under VMI policy with a price-sensitive demand is studied. The imperfect production at the manufacturer and the inspection process incorporating Type I, II error at the retailer are considered. We assume that the manufacturer sends the produced lot to the retailer in a number of equal-size 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. Therefore, this model under VMI policy is formulated by the aim of optimizing the producing, shipment and pricing policies at the same time in production system in the condition of defective items product and inspection errors in order to maximizing the total profit of each member of the supply chain. The solution procedure is proposed to find the Stackelberg game equilibrium. The equilibrium makes the manufacturer and the retailers’ profits maximized. The performance of the model is assessed by a numerical example. The numerical results show that it is more beneficial for the manufacturer and the retailer when the demand is fewer prices sensitive.