Flexible Flow Shop Scheduling Problem with Reliable Transporters and Intermediate Limited Buffers via considering Learning Effects and Budget Constraint

In this study, a new mathematical model is presented to solve the flexible flow shop problem where transportation is reliable and there are constraints on intermediate buffers, budgets, and human resource learning effects. Firstly, the model is validated to confirm the accuracy of its performance. Then, since it is an NP-hard one, two metaheuristic algorithms, namely, MOSA and MOEA/D, are rendered to solve mid- and large-scale problems. To confirm their accuracy of performance, two small-scale problems are solved using GAMS exact solution software, and the obtained results have been compared with the output of the algorithms. Since the problem in this study is multiobjective, five comparative indices are used to compare the performance of algorithms. The results show that the answers achieved using the metaheuristic algorithms are very close to the ones achieved via the GAMS exact program. Therefore, the proposed algorithms are validated, and it is proved that they are accurately designed and useable in solving the real-world problems (which have mid- and large-scale) in logical calculation time. By comparing the obtained results, it can be seen that the MOEA/D algorithm performs better in terms of computational time (CPU time) and Mean ideal distance (MID). The MOSA algorithm also performs better according to the index Spread of nondominated solutions (SNS), diversity metric (DM), and number of Pareto solutions (NPS). Considering the confirmation of precision and accuracy of performance of the proposed algorithms, it can be concluded that MOSA and MOEA/D are useful in solving the mid- and large-scale modes of the problem in the study, which is very applicable in the real world.