Group scheduling in flexible flow shops

Flexible flow shops are becoming increasingly common in industry practice due to higher workloads imposed by jobs. As a result, one or more stages in a flexible flow shop will have two or more units of the same machine type. The group scheduling problem, comprised of two levels of scheduling, is investigated in this paper to minimize the makespan in a flexible flow shop. At the first level, a sequence of jobs in each group is determined, while at the second level a sequence of groups themselves is determined. A statistical model based on split-plot design is developed to conduct the experiments to compare the performance of three different heuristic solution algorithms. These comparisons are based on either single setup or multiple setups on machines for processing jobs in the same group. The single setup assumes that only one machine in a stage can be setup for a group, while the multiple setups assumes that more than one machine in a stage can be setup for a group. Three different problem structures representing sizes ranging from small, medium to large have been considered as the main factor along with flexibility introduced in the shop, setup-to-run time ratio, and solution algorithm as sub plot factors, thus resulting in a 3⁴ factorial split-plot design. The higher the number of stages and the number of parallel machines in each stage, higher is the flexibility introduced in the shop. The results show that for small and medium size problems whether or not a computationally more demanding algorithm is employed to solve the level 1 or level 2 problem does not have any bearing on the makespan evaluated. This situation changes dramatically when large size problems are attempted, as a single-setup algorithm which combines the use of single- and multiple-pass heuristic for the level 2 and level 1 problems, respectively, outperform another single-setup algorithm with the order of use reversed at all levels of flexibility. Test results also show that a multiple-setup algorithm is no worse than the single-setup algorithms and is sometimes much better. Hence, it is recommended for solving group scheduling problems in flexible flow shops.