In this paper, we have developed an integrated production inventory model for a two echelon supply chain consisting of one manufacturer and one retailer. Purchase cost for the manufacturer is dependent on inventory lot size; production cost of the manufacturer is dependent on production rate. Also purchase cost of the retailer is dependent on demand rate of the customer. The proposed multi objective supply chain inventory model has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership function (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP), weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is provided to illustrate the proposed model. Finally sensitivity analysis and graphical representation have been shown.