The scheduling of flexible job shop systems is one of the most important issues in the various fields of production and is currently being addressed by many researchers in the field of optimization issues. The present research includes flexible job shop scheduling problem (FJSSP) with multi-objective, minimizing maximum completion time (makespan), maximum machine workload, total machines workload and also, earliness/tardiness penalty with different constraints. In this research, the researcher is looking to design a mathematical model that can cover all the constraints and assumptions related to the problem. Therefore, the mathematical model was designed with multi-objective and different constraints with exact details and different assumptions that are consistent with the actual situation of the problem and implemented at Comex Company. What that distinguishes this research from other similar researches is the approach of multi-objective with different constraints, which, at the same time, it raises the complexity of the problem but the problem gets closer to the actual situation, with less research done. Finally, the results of the study showed that this mathematical model designed, as well as in the real environment which has the flexible job shop system, can be implemented within a reasonable time with the highest efficiency before the implementation of the model.

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