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In the Discounted Generalized Transportation problem (DGT) the cost of transporting a type of product from a source to a destination depends on the amount of transported commodity. Based on this property, in this paper a genetic algorithm is developed to find a high-quality solution of the DGT problem. A numerical example is also presented. The proposed method could be easily integrated into a decision support platform intended to help transport planners to solve problems and make decisions in very limited timeframes.