JOINT OPTIMIZATION OF THE RETAILER'S PRICE, REPLENISHMENT CYCLE AND PRODUCTION RATE IN A VMI SYSTEM WITH DISCOUNTING USING GAME THEORY

We considered a two echelon supply chain with a vendor who manufactures a product to meet the demand for multiple retailers. It is assumed that demands faced by all the retailers are linear decreasing functions of their prices. The production rate is greater than the total demand rate faced by the vendor, consequently, there is no backordering. Cause of the system is under VMI contract, the vendor is responsible for the replenishment decisions of the retailers. He also bears the ordering costs. Thus, the retailers bear only their respective transportation, holding and purchase costs. In this model, the vendor makes n delivers to retailers in a given production setup. However, the size of the delivery batch increases each time by a factor x (x>1) and the purchase cost decreases each time by a factor alpha (0