Inventory management in the supply chain has been discovered to be the key to long-term success. Inventory is
important in the supply chain because it balances supply characteristics and consumer demand. In this non-coordinated supply
chain model, the merchant determines the appropriate order quantity based on the various expenses involved. Under quadratic
price dependent demand, an extension of the lagrangian method is used to optimize fuzzy EOQ, total variable cost of the relevant
retailer, and the supply chain. To support the model, a numerical case is solved.