In the practical production, after the completion of a job on a machine, it may be transported between the different machines. And, the transportation time may affect product quality in certain industries, such as steelmaking. However, the transportation times are commonly neglected in the literature. In this paper, the transportation time and processing time are taken as the independent time into the flexible job shop scheduling problem. The mathematical model of the flexible job shop scheduling problem with transportation time is established to minimize the maximum completion time. The FJSP problem is NP-hard. Then, an improved genetic algorithm is used to solve the problem. In the decoding process, an operation left shift insertion method according to the problem characteristics is proposed to decode the chromosomes in order to get the active scheduling solutions. The actual instance is solved by the proposed algorithm used the Matlab software. The computational results show that the proposed mathematical model and algorithm are valid and feasible, which could effectively guide the actual production practice.

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