This short paper addresses the problem of testing equality of means across multiple samples in one-way designs with unequal variances. Specifically, the focus is on assessing the null hypothesis \(H_0: \mu _1 = \mu _2 = \ldots = \mu _S\) against ordered alternatives, as this problem is of practical interest. However, justifying the assumption of homogeneity of variances in practical applications presents a significant challenge. To handle with this problem, various solutions have been proposed in the literature. Recently, parametric bootstrap approaches have been introduced, demonstrating good performances, particularly for symmetric distributions. In this paper, we put forward a novel approach based on permutations, utilizing the Non-Parametric Combination (NPC) methodology. We aim to compare this new approach with the aforementioned methods in a real case study.