U-shaped line balancing model with an uncertainty time on some tasks

The Allowable Time Approach of the Uncertain Task for Three U-shaped Lines with the Minimum Workstations

“…The uncertain tasks of three U-shaped Lines determine the time as an interval. They differ from the uncertain tasks of three previous papers which were the scenario time [12,[25][26]. The uncertain tasks of UL-1 which correspond to the [25] paper deviate from the normal time between -1 and 1.…”

“…Next, Varnasilpin and Masuchun proposed the UL model that consisted of 11 uncertain tasks. The uncertain time characteristic of this UL model conformed to the uncertain time characteristic of the [25] paper [26]. In both academic works, they formulated both UL models with a binary integer linear programming.…”

“…On a later stage, Varnasilpin and Masuchun proposed the UL model that consisted of 8 certain tasks and 3 uncertain tasks. This UL model indicated the uncertain time which comprised the pessimistic time, the normal time, and the optimistic time [25]. Next, Varnasilpin and Masuchun proposed the UL model that consisted of 11 uncertain tasks.…”

“…Both UL models were a type-1 problem. For the smallest number of workstations, the workstation quantity of the [25] UL model and the [26] UL model was five and four, respectively. The uncertain time of both UL models were the optimistic time.…”

“…The uncertain task time for each UL characterized a different variance. First UL indicated the uncertain time which corresponded to the uncertain time of the UL model in the [25] paper. Second UL indicated the uncertain time which comprised the most pessimistic time, the pessimistic time, the normal time, the optimistic time, and the most optimistic time.…”