Testing the equality of means of several skewed populations, particularly in the presence of nuisance parameters, is a central challenge in statistics. While various tests have been proposed for such as log-normal, inverse-normal, and exponential distributions leveraging methods like generalized p-value, parametric bootstrap, and the fiducial approach, there remains a notable gap in the literature, the absence of a computational approach meth-od-based test for the two-parameter exponential distribution. Such a method is essential for achieving robust results in small sample sizes while considering power and Type I error probability. In response to this gap, our paper introduces and implements novel computational approach tests embedded in the doex package in R. Our focus is on assessing the equality of means for several skewed populations following a two-parameter exponential distribution. We conduct a comprehensive comparison of our proposed tests against existing alternatives, evaluating their penalized power and Type I error probability. Notably, our computational approach tests exhibit superior performance, particularly in cases involving small samples and balanced designs. Furthermore, to illustrate the practical relevance of our proposed tests, we present a real-world application using authentic data. This empirical demonstration serves to underscore the efficacy and applicability of our novel computational approach tests in real-world scenarios.