In the present industrial environment, there is fierce competition, which has resulted in a growing demand for highly precise machining of various materials using advanced machining techniques. Electric discharge machining (EDM) is a widely used and extremely efficient advanced machining method that is particularly suitable for working with difficult materials, such as super-alloys, composites, and heat-resistant steels. This study focuses on examining the correlation between the input and output variables of electric discharge machining. Three adjustable machining parameters, specifically current, pulse on time, and voltage, have been selected to determine the material removal rate and surface roughness of AISI304 stainless steel. The experiment is conducted using the Taguchi technique orthogonal array (L27) and the response surface approach is employed to determine the optimal process parameters that minimize surface roughness (SR) and maximize material removal rate (MRR). The efficacy of the present mathematical models has been tested using analysis of variance. This research aims to simultaneously optimize the material removal rate and surface roughness by utilizing the grey entropy weight approach. The experimental results demonstrated that the utilization of the grey entropy methodology significantly improved the output responses in the EDM process compared to the mean method. Furthermore, the grey relational grade was measured to be 0.9641. Hence, the choice of a mechanism for allocating weights to responses and the optimization method itself are pivotal elements in the process of making decisions for multi-objective optimization. The experimental verification validates the effectiveness of the proposed strategy in enhancing the overall machining performance.