Critical paths of non-permutation and permutation flow shop scheduling problems

A Parallel Permutation Flow-Shop Scheduling Model by Using a Two-Step Evolutionary Algorithm to Minimize Intermediate Storage with Tolerable Maximum Completion Time

“…Unfortunately, this permutation FSP may cause longer total completion time. Meanwhile, in the nonpermutation FSP, job overlapping is permitted [11]. The goal of non-permutation FSP is to reduce total completion time.…”

“…In most FSP research, intermediate storage was considered as a limitation rather than an objective. Several studies assumed that intermediate storage is limitless, whereas others considered that it is limited [11] or nil [7], resulting in the possibility of blocking [12].…”

“…As a parallel FSP, there are a set number of identical production lines [13], and any job can be processed on any line of the system. As a permutation FSP, a task cannot overlap with other jobs in a sequence once it has been arranged [11].…”

Multi-objective Batch Scheduling in Collaborative Multi-product Flow Shop System by using Non-dominated Sorting Genetic Algorithm

“…In the permutation flow shop, once these jobs are sequenced, this sequence will be fixed for all stages [13]. In the non-permutation flow shop, the jobs sequence among stages may be different [14]. In the batch scheduling in a flow shop system, the jobs are batched first before sequenced.…”

“…There are several parameters that were used as objective in a batch scheduling studies. The most common parameter is make-span [14,15]. Other parameters are total actual flow time (TAFT) [9,10], total tardiness [18], total earliness [18], revenue [17], overstocking [16], delay [16], inefficiency cost [16], total completion time [5,12], total energy cost [19], number of late jobs [6], run time [20], and so on.…”