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Abstract
A fast, robust and efficient algorithm for solving the Location routing problem (LRP) for one of the largest companies in Greece, which distributes wood products, is developed. To solve the company's problem, a new formulation of the LRP based on bilevel programming is proposed. Based on the fact that in the LRP, decisions are made at a strategic level and at an operational level, we formulate the problem in such a way that in the first level, the decisions of the strategic level are made, namely, the top manager finds the optimal location of the facilities: while in the second level, the operational level decisions are made, namely, the operational manager finds the optimal routing of vehicles. For this problem, a Bilevel Genetic Algorithm is proposed. The algorithm manages to provide practical solutions and significant economic benefits for the company. The algorithm is also tested on a set of benchmark instances. The results of the algorithm are also very satisfactory for those instances and, for six of them, a new best solution has been found.