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This paper deals with a complex optimization problem, more specifically the two-stage transportation problem with fixed costs. In our investigated transportation problem, we are modeling a distribution network in a two-stage supply chain. The considered two-stage supply chain includes manufacturers, distribution centers, and customers, and its principal feature is that in addition to the variable transportation costs, we have fixed costs for the opening of the distribution centers, as well as associated with the routes. In this paper, we describe a different approach for solving the problem, which is an effective hybrid genetic algorithm. Our proposed hybrid genetic algorithm is constructed to fit the challenges of the investigated supply chain network design problem, and it is achieved by incorporating a linear programming optimization problem within the framework of a genetic algorithm. Our achieved computational results are compared with the existing solution approaches on a set of 150 benchmark instances from the literature and on a set of 50 new randomly generated instances of larger sizes. The outputs proved that we have developed a very competitive approach as compared to the methods that one can find in the literature.

An Efficient Hybrid Genetic Approach for Solving the Two-Stage Supply Chain Network Design Problem with Fixed Costs