66 Int. J. Applied Decision Sciences, Vol. 7, No. 1, 2014 Copyright © 2014 Inderscience Enterprises Ltd. Multi-objective supplier selection and order allocation under quantity discounts with fuzzy goals and fuzzy constraints Nima Kazemi* Young Researchers and Elite Club, Karaj Branch, Islamic Azad University, Karaj, Iran E-mail: nimakzm@gmail.com *Corresponding author Ehsan Ehsani Young Researchers and Elite Club, Sari Branch, Islamic Azad University, Sari, Iran E-mail: ehsani.ie2010@gmail.com Christoph H. Glock Carlo and Karin Giersch Endowed Chair ‘Business Management: Industrial Management’, Department of Law and Economics, Technische Universität Darmstadt, Hochschulstr. 1, 64289 Darmstadt, Germany E-mail: glock@bwl.tu-darmstadt.de Abstract: This paper investigates a multi-objective supplier selection and order allocation problem under quantity discounts in a fuzzy environment. Prior research on supplier selection and order allocation with quantity discounts mainly considered partial fuzziness of the decision problem; a situation where both the objectives of the decision maker and the constraints are fuzzy has not been studied up to now. This paper closes this gap by integrating both aspects into a single model. First, a combination of fuzzy preference programming and interval-based TOPSIS is proposed for evaluating suppliers. Secondly, based on the scores obtained in the first step, a fuzzy multi-objective linear programming model is developed. Subsequently, a new solution procedure for solving the fuzzy multi-objective linear programming model is presented. The procedure first transforms fuzzy constraints and coefficients into deterministic coefficients, and then three different fuzzy programming approaches, namely interactive fuzzy multi-objective linear programming, and the weighted additive as well as the weighted max-min method are implemented. Finally, the performance of each method is evaluated by computing the distance between each solution and the preferred solution. Keywords: supplier selection; order allocation; quantity discount; fuzzy preference programming; FPP; interval-based TOPSIS; α-cut approach; interactive fuzzy linear programming; i-FMOLP; weighted additive method; weighted max-min method.