Purpose: The incorporation of environmental objective into the conventional supplier selection practices is crucial for corporations seeking to promote green supply chain management (GSCM). Challenges and risks associated with green supplier selection have been broadly recognized by procurement and supplier management professionals. This paper aims to solve a Tetra “S” (SSSS) problem based on a fuzzy multi-objective optimization with genetic algorithm in a holistic supply chain environment. In this empirical study, a mathematical model with fuzzy coefficients is considered for sustainable strategic supplier selection (SSSS) problem and a corresponding model is developed to tackle this problem. Design/methodology/approach: Sustainable strategic supplier selection (SSSS) decisions are typically multi-objectives in nature and it is an important part of green production and supply chain management for many firms. The proposed uncertain model is transferred into deterministic model by applying the expected value measure (EVM) and genetic algorithm with weighted sum approach for solving the multi-objective problem. This research focus on a multiobjective optimization model for minimizing lean cost, maximizing sustainable service and greener product quality level. Finally, a mathematical case of textile sector is presented to exemplify the effectiveness of the proposed model with a sensitivity analysis. Findings: This study makes a certain contribution by introducing the Tetra ‘S’ concept in both the theoretical and practical research related to multi-objective optimization as well as in the study of sustainable strategic supplier selection (SSSS) under uncertain environment. Our results suggest that decision makers tend to select strategic supplier first then enhance the sustainability. Research limitations/implications: Although the fuzzy expected value model (EVM) with fuzzy coefficients constructed in present research should be helpful for solving real world problems. A detailed comparative analysis by using other algorithms is necessary for solving similar problems of agriculture, pharmaceutical, chemicals and services sectors in future. Practical implications: It can help the decision makers for ordering to different supplier for managing supply chain performance in efficient and effective manner. From the procurement and engineering perspectives, minimizing cost, sustaining the quality level and meeting production time line is the main consideration for selecting the supplier. Empirically, this can facilitate engineers to reduce production costs and at the same time improve the product quality. Originality/value: In this paper, we developed a novel multi-objective programming model based on genetic algorithm to select sustainable strategic supplier (SSSS) under fuzzy environment. The algorithm was tested and applied to solve a real case of textile sector in Pakistan. The experimental results and comparative sensitivity analysis illustrate the effectiveness of our proposed model.