Abstract: This paper focus on two stage supply chain model with a single vendor and a single buyer for a single product, taking into consideration the effect of deterioration and credit period incentives. We study and analyze the benefits of order cost reduction and credit period incentives in a co-ordinated supply chain . Shortage for the buyer is allowed and it is completely backlogged. The demand and shortage cost were taken as fuzzy parameters. Graded mean integration representation method is applied for defuzzification. This paper also includes a detailed numerical examples for more understanding of the proposed strategy.