The issue of optimization with multiple competing objectives that must be met at the identical period has been referred to as multifaceted optimization. The purpose of this effort is to create an integrated decision support system for the optimization considering a supply chain network with three stages using fuzzy logic and a novel multi-objective genetic algorithm. Generally speaking, decisions that are inherently conflicting are what define all supply chain issues. The devisor can select from a group of Pareto-optimal outcomes when these situations are modeled with numerous objectives. The implementation of multi-objective evolutionary algorithm to address Pareto-optimality in supply chain optimization problems is suggested in this paper, which also analyzes relevant supply chain optimization literature. Implementation of NSGA-II is carried out to a fictitious three-stage supply chain scenario in this article. Additionally, a fuzzy logic method is employed to choose the final response from the Pareto-optimal collection of possibilities. This method yields a fuzzy index that corresponds to each answer. The outcome showed that the fuzzy logic and genetic algorithm created in this work are reliable and strong as they may yield encouraging outcomes.