Globalization of business around the world has turned individual firms into groups of collaborating business units whereby companies do not operate in isolation but function as integral part of big supply chain networks (SCN). Organization of SCN is quite complex as they operate with uncertainty in demands and operations. However, supply chain networks are required to be optimized in order to reduce the overall supply chain cost and increase service levels. Since these objectives are normally conflicting and incommensurable, instead of a singular solution, it is preferred to obtain a set of equitable solutions which is commonly referred to as set of Pareto optimal solutions. Subsequently, a suitable solution can be chosen by the user from the set of equitable solutions. In the present research, a multi-echelon SCN problem is formulated and two important objectives are identified. It is desired to minimize the total cost of supply chain network and at the same time maximize customer service level in terms of supply to demand ratio. Simultaneous optimization of these objectives has been carried out using an evolutionary algorithm (EA) called NSGA-II, which works with population of SCN solutions and is more likely to provide set of globally optimized solutions. However, at the conclusion of optimization, user needs to select a final solution from the Pareto optimal set of solutions after careful analysis. Existing approaches to carry out such analysis are complex and time consuming. We propose a novel method involving fuzzy logic in this research by which fuzzy indices corresponding to each of the solutions in the Pareto Front (PF) are obtained. Fuzzy indices of all the Pareto optimal SCN solutions are later compared to reach to a final solution from the Pareto optimal set.