Proportionate flexible flow shop scheduling via a hybrid constructive genetic algorithm

The proportionate flow shop (PFS) is considered as a unique case of the flow shop problem in which the processing times of the operations belonging to the same job are equal. A proportionate flexible flow shop (PFFS) is a machine environment with parallel identical machines at each stage. This study presents an effective hybrid approach based on constructive genetic algorithm (CGA) for PFFS scheduling with the criterion to minimize the total weighted completion time (WCT). Minimizing the WCT in a PFFS problem significantly differs from the parallel-identical-machine scheduling problem, an optimal schedule in which the jobs on each machine are in weighted shortest processing time (WSPT) order. The proposed approach incorporates two fitness functions, and a population trained by a local improvement search based on tabu search with a candidate list strategy into CGA. Simulation results are compared with those of the column generation (CG) approach to demonstrate the effectiveness of the proposed hybrid approach. In particular, the CG approach has been applied successfully to solve various parallel machine scheduling problems, and yields high-quality solutions.