Integration of an Improved Grey-Based Method and Fuzzy Multi-Objective Model for Supplier Selection and Order Allocation

For multi-attribute decision making (MADM) problems, a grey based approach (LI) had been developed to evaluate, rank and select the best suppliers. The method calculates a grey possibility degree between compared suppliers alternatives set and positive ideal referential alternative. The drawback of the method is that the negative ideal referential alternative is not considered in evaluating and ranking of the alternatives. Moreover, the method can only consider interval fuzzy number as input data and real number is neglected. Based on this model and other MADM methods, all demand was sold by the best supplier. In other cases, if the best supplier cannot satisfy all demand, multi-objective programming is used to formulate the problem and assign optimum order quantities to the best suppliers (multi-sourcing). Some techniques, such as goal programming (GP) approach, ε-Constraint method, Reservation level (RL) driven Tchebycheff procedure (RLTP) method had been proposed to solve the multi-objective models. It may be a problem that these techniques traced back to more than 10 years ago. Therefore, there may be still the need to produce a new technique in order to solve the multi-objective models. In this study, to overcome the first drawback, the LI method was improved based on the concepts of technique for order preference by similarity to ideal solution (TOPSIS) to consider both the positive and the negative ideal referential alternative for evaluation of the suppliers. The improved version of the LI method is called the I.LI method. Based on the concepts of TOPSIS, the chosen alternative should have the shortest distance from the positive ideal solution and the farthest from the negative ideal solution. Moreover, in order to solve the problems, a new grey based method (NG) based on the TOPSIS concepts was proposed that can easily consider both interval fuzzy number and real number simultaneously. Afterwards, an innovative comparative approach was proposed to compare the three MADM methods, the LI, the I.LI and the NG methods, and to show that which method is more optimal than the other methods. Subsequently, in this thesis, an integration of the NG method and fuzzy multi-objective model was suggested for multi-sourcing and multi-product supplier selection problem. The score of suppliers calculated by the NG method was served as coefficients in one objective function of the multi-objective model. In this fuzzy multi-objective model, the products are divided into two independent and dependent products so that (1) the price breaks (discounts) depend on the size of the order quantities, (2) independent products’ sales volume affect the prices and discounts of the dependent products and (3) all products must be sold as a bundle. Finally, to overcome the third problem, a new weighted additive function, which is able to consider relative importance of each objective as well as condition of fuzzy situation, is proposed to solve the fuzzy multi-objective model and assign optimum order quantities to the suppliers evaluated and ranked by the NG method. The results of the innovative comparative approach showed that the result of the NG method is more optimal than the I.LI method and the latter is more optimal than the LI method. Therefore, the NG method was selected to be integrated with the fuzzy multi-objective model. Also, the fuzzy multi-objective model was solved by the new weighted additive function, and the results demonstrated that besides considering the relative importance of the objectives, the new technique is also able to consider the condition of fuzzy situation.

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