Prominent influence of transportation costs on supply chain overall profit indicates the importance and emer-gence of transportation optimization models. Regarding this issue and in view of realistic situation consisting of non-de-terministic information, in this research optimizing inbound and outbound transportation costs of a multi echelon supply chain has been considered. To deal with uncertain time deliveries and pricing strategies adopted by different members of supply chain, in conjunction with unpredictable demand rate, fuzzy logic and specifically Trapezoidal Fuzzy Numbers (TrFNs) are included. After designing a fuzzy binary multi objective model based upon structural assumptions, the solving approach is proposed and the model is employed on Iranian steel supply network to illustrate the potential and advantages of our scheduled model. The bi-objective mixed integer fuzzy programming model presents and encompasses many realis-tic circumstances making the model applicable in network transportation cases.