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The Multi-objective Flexible Job Shop Scheduling (MFJSS) problem, in which the order or processing sequence for a set of jobs through several machines is assigned in an optimal patterns have accepted sizeable attentiveness. Different types of scheduling rules and procedures for certain types of MFJSS have made progress from these endeavors. The scheduling problem is cumbersome to be made consistent due to different types of criteria involved. This is because in MFJSS, after the completion of a job on a machine, it may be transited between different machines and transit time may affect scheduling. However, the transit times are frequently ignored in the literature. In this paper, the transit time and the processing time are considered as the independent time into the MFJSS. In this paper, we propose Combinatory Least Slack and Kuhn Tucker Optimization (CLS-KTO) for the MFJSS problem with the objectives to minimize the mean tardiness, makespan and job completion time. The problem is addressed via assignment and scheduling model. First, by using well-designed processing and transit time and least slack variable, Combinatory Least Slack (CLS) algorithm is adapted for the CLS-KTO. Then, an Additive function is formulated by incorporating Combinatory Dispatching Rules into the adapted CLS, where some good machines are assigned for the corresponding job, therefore reducing mean tardiness. Furthermore, in the proposed sequencing part, an optimization model based on the Kuhn Tucker conditions and Lagrange Multiplier is adopted to handle the three objectives. In the experimental studies, the influence of mean tardiness on the performance of the proposed CLS-KTO is first examined. Afterwards, the effectiveness of makespan and job completion time in CLS-KTO is verified. Finally, extensive comparisons are carried out with the state-of-the-art methods for the MFJSSon benchmark OR instances. The results show that CLS-KTO performs better than other algorithms.

Combinatory Least Slack and Kuhn Tucker Optimization for Multiobjective Flexible Job Shop Scheduling