Abstract
This paper proposes a heuristic method to minimize makespan in a machining-assembly flowshop where there are two parallel flow lines with two machines per line at a machining stage and one robot at an assembly stage. Each job has two major component-parts to be processed in parallel at the machining stage, and a flow line to be used for machining each part is specified individually in advance. No assembly operation of these parts for any job involving various other parts supplied independently by some contracting companies can start until all the related component-parts have been completed at the machining stage. This scheduling problem is NP-complete and an optimal schedule for this problem is not always a permutation schedule. In the proposed method, an NEH-based heuristic algorithm first provides a set of promising permutation schedules, and then a Johnson-rule-based heuristic algorithm generates a non-permutation schedule for each of the five best permutation schedules. To avoid falling into a local optimal, the Johnson-rule-based heuristic algorithm allows that the performance of schedule becomes worse than that of the previous one in its searching process. The performance of the proposed method is compared with a branch and bound algorithm with one hour limitation in computation time. Numerical experiments to solve 100 instances generated randomly for each problem with at most 50 jobs show that the proposed heuristic algorithm can provide a near-optimal non-permutation schedule efficiently with high accuracy such as mean relative error being less than 0.3% and the maximum relative error being less than 3%.
