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In this paper, we consider the evaluation of the best tender in a public procurement process. According to the Most Economic Advantageous Tender criterion, in order to analyze a number of tenders, a group of experts has to consider different criteria, both of qualitative and quantitative nature. Selecting the best tender involves the solution of a multi-criteria choice problem. Indeed, in Italy, the National Anti-Corruption Authority suggested the use of traditional multiple criteria methods to evaluate the qualitative component and provided details on how aggregate the evaluations related to single criteria to derive the ranking of tenders. However, they are rarely used in practice and may have some application drawbacks. This paper aims at proposing the use of ELECTRE (ELimination Et Choix Traduisant the Realité) III and P-AHP (parsimonious analytic hierarchy process) as the more effective methods for analyzing public tenders when a great number of alternatives and/or the heterogeneity of scales are involved. The use of the proposed methodologies is completely innovative in the practice, in the Italian context. Furthermore, we carry out a comparative study among these multi-criteria methods and analyze the strengths and the weaknesses of each method in order to help the DMs to identify the more appropriate method. Moreover, we aim to develop easier and user-friendly models that sound practical in the public tender context. The potential advantages of the proposed approach are validated by a real-life contractor-selection case. The results show that the rankings obtained by ELECTRE III and P-AHP are almost the same. [ABSTRACT FROM AUTHOR]