A FUZZY MATHEMATICAL MODEL FOR MULTI-OBJECTIVE FLEXIBLE JOB-SHOP SCHEDULING PROBLEM WITH NEW JOB INSERTION AND EARLINESS/TARDINESS PENALTY - Seyyedi, Mir Hossein; Fakoor Saghih, Amir Mohammad; Naji Azimi, Zahra (International Journal of Industrial Engineering: Theory, Applications and Practice, 2021)
The scheduling of flexible job shop systems is one of the important problems in various fields of production and has been currently considered in optimization problems. The main purpose of the present study is to design a flexible multi-objective job-shop scheduling model considering earliness/tardiness penalties along with fuzzy processing time and finally inserting a new job. In terms of research methodology, this study can be regarded as an applied-exploratory investigation. The present study includes the flexible job-shop scheduling problem (FJSSP) with multiple objectives to minimize maximum completion time (makespan), maximum machine workload, total machines workload, and earliness/tardiness penalty considering different constraints. The designed fuzzy linear programming was coded in CPLEX software and implemented on small, medium, and large-dimension examples. A mathematical model was designed using the Non-dominated Sorting Genetic Algorithm II (NSGA II) meta-heuristic algorithm, which was then coded in MATLAB software and implemented in the same examples. 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, a two-step NSGA II algorithm was employed to insert the new job. Moreover, the mathematical solution method could be considered as the optimal method for the company under study. However, the two-stage NSGA II algorithm is preferred for the company under study if the need for rescheduling is due to the insertion of the new larger/medium job(s) during the current schedule.