The scheduling of flexible job shop systems is one of the important problems in various fields of production and is currently considered by many researchers in the field of optimization problems. The main purpose of the present study is to design a flexible multi-objective job shop scheduling model by considering earliness/tardiness penalties along with fuzzy processing time and finally inserting a new job. This study is applied-exploratory research in terms of research methodology. The present study includes the flexible job-shop scheduling problem (FJSSP) with multiple objectives, minimizing maximum completion time (makespan), maximum machine workload, total machines workload, and also earliness/tardiness penalty with different constraints. The designed fuzzy linear programming was coded in CPLEX software and implemented in sample problems with small, medium, and large dimensions. Then, the mathematical model designed using the Non-dominated Sorting Genetic Algorithm II (NSGA II) meta-heuristic algorithm, which is an algorithm suitable for multi-objective models, was designed and coded in MATLAB software and implemented in the same sample problems. The results of the implementation of mathematical and meta-heuristic methods showed that in terms of implementation time and solution quality in problems with different dimensions, the proposed meta-heuristic method is efficient. Afterward, the two-step NSGA II algorithm was used to insert the new job. Also, the results of the research showed that the mathematical solution method could be considered as the optimal method for the company under study. But, if the need for rescheduling is due to the insertion of the new job(s) during the current schedule and the volume of jobs and operations is larger (medium or large size), it is suggested that the two-stage NSGA II algorithm can be considered as the preferred method for the company under study. As in the study company, with the insertion of the new job, the result of the two-stage NSGA II algorithm was better than the mathematical model.

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