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As such, all firms should select the best suppliers by applying appropriate methods through different selection criteria. An appropriate supplier reduces all purchasing costs as well as increases customer satisfaction to improve the final product and strengthen corporate competitiveness. Due to the natural uncertainty of this dilemma, most of recent works show a great deal of interest in applying uncertainty approaches. The main innovation of this paper is to develop a new multi-objective model for both supplier selection and order allocation operations considering incremental discount in a fuzzy environment. The proposed model considers the material cost with incremental discount and the transportation cost, holding costs along with its control and interest as well as the possibility of payment, brought back, and replacement costs, simultaneously, for the first time in this research area. Based on the proposed fuzzy model, the Zimmermann fuzzy approach is used in order to covert the model in a single objective form. Accordingly, a Genetic Algorithm (GA) is applied to solve the proposed problem. Based on the multi-objective optimization proposed, a Non-dominated Sorting GA (NSGA-II) is also employed to solve the developed model through the multi-objective assessment methodologies. Finally, a comprehensive evaluation and discussion based on the results are provided to reveal the performance of developed methodology.<\/jats:p>","DOI":"10.3233\/jifs-182843","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T15:45:18Z","timestamp":1560527118000},"page":"1435-1455","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":37,"title":["A multi-objective supplier selection and order allocation through incremental discount in a fuzzy environment"],"prefix":"10.1177","volume":"37","author":[{"given":"Mojgan","family":"Safaeian","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amir Mohammad","family":"Fathollahi-Fard","sequence":"additional","affiliation":[{"name":"Department of 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