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Over the last decade, our world exposed to many types of unpredictable disasters (recently Coronavirus). These disasters have clearly shown the uncertainty and vulnerability of supply chain systems. Also, it confirmed that adopting Just-in-Time (JIT) strategy to reduce the logistic chain cost may lead to inbuilt complexity and risks. Efficient tools are therefore needed to make complexity optimized supply chain decisions. Evolutionary algorithms, including genetic algorithms (GA), have proven effective in identifying optimal solutions that address the trade-offs between total supply chain cost and carbon emissions regulatory policy represented by carbon tax charges. These solutions pertain to the design challenges of supply networks exposed to potential disruption risks. However, GA have a set of parameters must be chosen for effective and robust performance of the algorithms. This paper aims to set the most suitable values of these parameters that used via GA – ased optimization cost and risk reduction model in firms using a JIT as a delivery system. The model has been conceptualized for addressing the design complexities of the supply chain, referred to as SCRRJITS (Simultaneous Cost and Risk Reduction in a Just-in-Time System). A complete analysis of the different parameters and operators of the algorithm is carried out using design of experiments approach. The algorithm performance measure used in this study is convergence of solutions. The results show the extent to which the quality of solution can be changed depending on selection of these parameters.