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The multi-objective supplier selection problem with fuzzy parameters and solving the order allocation problem with coverage

Mohammad Khalilzadeh (CENTRUM Católica Graduate Business School, Pontificia Universidad Católica del Perú, Lima, Peru)
Arya Karami (Faculty of Industrial Engineering, Sharif University of Technology, Tehran, Iran)
Alborz Hajikhani (Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran)

Journal of Modelling in Management

ISSN: 1746-5664

Article publication date: 30 April 2020

Issue publication date: 4 August 2020




This study aims to deal with supplier selection problem. The supplier selection problem has significantly become attractive to researchers and practitioners in recent years. Many real-world supply chain problems are assumed as multiple objectives combinatorial optimization problems.


In this paper, the authors propose a multi-objective model with fuzzy parameters to select suppliers and allocate orders considering multiple periods, multiple resources, multiple products and two-echelon supply chain. The objective functions consist of total purchase costs, transportation, order and on-time delivery, coverage and the weights of suppliers. Distance-based partial and general coverage of suppliers makes the number of orders of products more realistic. In this model, the weights of suppliers are determined by fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, as a multi-criteria decision analysis method, in the objective function. Also, the authors consider the parameters related to delays as triangular fuzzy numbers.


A small-sized numerical example is provided to clearly show the proposed model. The exact epsilon constraint method is used to solve this given multi-objective combinatorial optimization problem. Subsequently, the sensitivity analysis is conducted to testify the proposed model. The obtained results demonstrate the validity of the proposed multiple objectives mixed integer mathematical programming model and the efficiency of the solution approach.


In real-life situations, supplier selection parameters are uncertain and incomplete. Hence, the fuzzy set theory is used to tackle uncertainty. In this paper, a multi-objective supplier selection problem is formulated taking into consideration the coverage of suppliers and suppliers’ weights. Integrating coverage of suppliers to select and allocate the order to them can be mentioned as the main contribution of this study. The proposed model considers the delay from suppliers as fuzzy parameters.



Khalilzadeh, M., Karami, A. and Hajikhani, A. (2020), "The multi-objective supplier selection problem with fuzzy parameters and solving the order allocation problem with coverage", Journal of Modelling in Management, Vol. 15 No. 3, pp. 705-725.



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