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A genetic algorithm for solving fourth-party logistics routing optimizing problem with fuzzy duration time

From the beginning of the 21st century, Fourth Party Logistics (4PL) has been attracting more and more attention in many fields. In this paper, a 4PL routing problem with fuzzy duration time is presented, and the fuzzy numbers is used to denote the uncertainty of the duration time. After a simple description of 4PL, a fuzzy programming for it is built and a crisp equivalent is derived by expected value. Then genetic algorithm is designed to solved the problem. Finally, an extensive computational analysis is presented and the numerical results show that which route should be selected in order to get minimum cost in the due date.