Preliminary normalization is central to the decision process of several popular, recent or completely new multi-attribute decision-making (MADM) methods. However, a number of authors have pointed out serious pitfalls attributed to normalization methods. One major pitfall, which has been identified, is that normalization methods may lead to different final rankings of alternatives when a ranking procedure (RP) based on them is used for solving a MADM problem. The current paper aims to ascertain and illustrate the effectiveness of some RPs based on prominent primary WEighted Self-NORmalizing Distance (WESNORD) metrics and their averages. The effectiveness of the selected RPs is demonstrated by solving a logistics service provider (LSP) selection problem taken from the literature. The results reveal that the RPs considered deliver final rankings of alternatives, which are very similar to the SAW-produced reference ranking.