Testing the suitability of vector normalization procedure in topsis method: application to wheel loader selection

The object of the research consists of testing the suitability of the vector normalization procedure (NP) in the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method.One of the most problematic steps of the Multi-Criteria Decision Making (MCDM) process is related to the application of NPs by default to transform different measurement units of criteria into a comparable unit. This is because of the absence of a universal agreement that defines which NP is the most suitable for a given MCDM method. In the literature, there are thirty-one available NPs, each one of them has its strengths and weaknesses and, accordingly, can efficiently be applied to an MCDM method and even worst to another. Let’s note that many NPs (e. g., NPs of sum, max-min, vector, and max) have been used by default (i. e., without suitability study) in the TOPSIS method. Consequently, outcomes of multi-criteria evaluation and rankings of alternatives considered in the decision problems could have led to inconsistent solutions, and, therefore, decision-makers could have made irrational or inappropriate decisions. That’s why suitability studies of NPs become indispensable.Moreover, a description of the methodology, proposed in this research, is outlined as follows:1) method of weighting based on an ordinal ranking of criteria and Lagrange multiplier (for determining criteria weights);2) TOPSIS method (for ranking considered alternatives);3) a statistical approach with 3-estimate (for comparing effects generated by the used NPs).In the research, twelve different NPs are compared to each other in the TOPSIS method via a numerical example, which deals with the wheel loader selection problem.The results of the comparison indicate that, amongst the twelve different NPs analyzed in this suitability study, vector NP has the lesser effect on the considered alternatives’ evaluation outcomes, when used with the TOPSIS method.The vector NP-TOPSIS approach can therefore be applied to solve multi-criteria decision problems. Its application further allows the decision-makers and users to better select efficient solutions and, consequently, to make conclusive decisions.