In inventory strategy companies employ to increase efficiency and decrease waste by receiving goods only as they are needed in the production process, thereby reducing inventory costs. Normally, the vendor and the buyer problems treated separately. In this paper, we discuss a joint integrated vendor buyer model for both in crisp and in fuzzy sense. This integrated approach is the success of supply chain management to minimize the joint total cost. This proposed model is based on the joint total cost of both the vendor and the buyer. Holding cost of the vendor, holding cost of the buyer, production cost of the vendor and purchasing cost of the buyer are taken as triangular fuzzy numbers. In this model, we reduce the inventory and waste considerations through Just-In-Time. Finally, a numerical example and sensitivity analysis are given to illustrate this model. Graded mean integration representation method is used for defuzzification.