KEYWORDSMulti-objective supplier selection problem; Coverage; Fuzzy logic; MOPSO; NSGA-II.Abstract. In this paper, a fuzzy multi-objective model is presented to select and allocate order to the suppliers in uncertain conditions, considering multi-period, multisource, and multi-product cases at two levels of a supply chain with pricing considerations. Objective functions considered in this study as the measures to evaluate the suppliers are the purchase, transportation, ordering costs, and timely delivering (or deference shipment quality, or wastages) which are amongst major quality aspects. Partial and general coverage of suppliers with respect to distance and nally suppliers' weights makes the amounts of product orders more realistic. Deference and coverage parameters in the model are considered as uncertain and random triangular fuzzy number. Since the proposed mathematical model is NP-hard, Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is presented. To validate the performance of MOPSO, we applied non-dominated Sorting Genetic Algorithm (NSGA-II). Taguchi technique is executed to tune the parameters of both algorithms. A practical case study in an agricultural industry is shown to demonstrate that the proposed algorithm can be applied to the real-world problems. The results are analyzed using quantitative criteria, performing parametric, and non-parametric statistical analyses.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.