A bi-objective flexible flow shop scheduling problem with machine-dependent processing stages: Trade-off between production costs and energy consumption

Abstract

This paper aims to propose a flexible flow shop scheduling problem (FFSP) with machine-dependent processing stages. The parallel machines in the first stage are considered unrelated with different technology levels and some of them are multifunctional that can do several processes on jobs. Therefore, the jobs that are assigned to these machines don't require to be processed in some next stages. We conduct the problem considering production costs and energy consumption as two conflict objective functions. Furthermore, setup times are assumed as sequence-dependent and are need when a machine starts to process a new job. This problem is described with a numeric example, and its parameters and decision variables are defined. Then a linear mathematical model based on MIP is developed to solve the problem in small-sized scales. Since the problem is discussed in an NP-hard environment, a new approach based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) is introduced to find optimal or near-optimal solutions. Some numerical examples in different conditions are tuned as test problems and different metrics that are popular in multi-objective optimization environment such as ER, GD, and ONVG are used to demonstrate performance of the proposed algorithm. The computational result indicates appropriate performance of the algorithm in solving this bi-objective problem. Moreover, the comparison result shows superiority of this algorithm over SPEA 2 as another multi-optimization method in solving the problem. Finally, supplementary analysis is presented by adjusting different amount of the makespan as the pre-known index for controlling completion time. The result indicates that the solution approach can provide proper alternatives for managers in different various situations.