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The supplier selection and order allocation are two key strategic decisions in purchasing problem. The review presented in this paper focuses on the supplier selection problems (SSP) and order allocation from year 2000 to 2017 in which a new structure and classification of the existing research streams and the different MCDM methods and mathematical models used for SSP will be presented. The review was examined in three aspects: the summaries of the existing evidence concerning the problems, the identification of gaps in the current research to help determine where further investigation might be needed and positioning new research activities.

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Abstract:The TOPSIS method suffers from two major shortcomings (1) the non-meaningfulness of the resulting rankings in mixed data contexts (i.e., the rankings of alternatives may change under admissible transformations of the initial attribute values, in the measurement-theoretic sense of the term), and (2) rank reversals or ranking irregularities(i.e., the rankings of alternatives may change if a new alternative is added to the given offered set of alternatives or an old one is deleted from it or replaced in it). The present research tackles the above shortcomings in order to improve the TOPSIS method by suggesting novel reference points and by extending it to mixed data in a rather defensible manner. Finally, the suggested TOPSIS method (referred to herein as the meaningful mixed data TOPSIS method (TOPSIS-MMD)) is used to solve a mixed data multiattribute supplier selection problem.

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