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In this contribution, for the first time, an efficient model of multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station is formulated. Transfer station inserts transfer cost and type-I fixed-charge. Our aim is to analyze an extra cost that treats as type-II fixed-charge and truck load constraints in the designed model that required when the amount of items exceeds the capacity of vehicle for fulfilling the shipment by more than one trip. Type-II fixed-charge is added with transportation cost and other cost from transfer station. We consider here an important issue of the multi-objective transportation problem as product blending constraints for transporting raw materials with different purity levels for customers’ satisfaction. In realistic point of view, the parameters of the model are imprecise in nature due to existing several unpredictable factors. These factors are apprehended by incorporating the fuzzy-rough environment on the parameters. Expected-value operator is utilized to derive the deterministic form of fuzzy-rough data, and the model is experienced with help of fuzzy programming, neutrosophic linear programming and global criteria method. Two numerical examples are illustrated to determine the applicability of the proposed model.

Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station