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.

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.

Currently, the supplier selection process is considered as an integral part of the supply chain. The appropriate selection of suppliers plays a preponderant role in the performance chain of supply as it determines relevant aspects such as cost management and flexibility of most production processes. Background: It is considered a multi-criteria and multi-objective problem because it includes both qualitative and quantitative factors. Method: To solve the Supplier Selection and Fair Order Allocation Problem (SSFOAP), a hybrid solution methodology based on the best–worst method (BWM) and MMD-TOPSIS techniques in the first phase has been developed to find a robust ranking of suppliers. In the second phase to determine the weight of the objective function, the Linear Programming (LP) approach is used. Results: This proposed model can help decisionmakers find the right orders for each supplier and enable purchasing managers to manage supply chain performance in terms of cost, quality, and service. To test the performance of our solution methodology, we apply our hybrid technique to solve a real case of the Tunisian Electric Society (TSE). Cplex software is used to solve bi-objective programming and to answer strategic questions. Conclusions: The experimental results indicate that the combination of MMD-TOPSIS and bi-objective programming provide effective gain concerning solution quality compared with the given solution of the administrator of TSE.

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