Dynamic hybrid flowshop scheduling problem with multiprocessor tasks

Hybrid flowshop scheduling with multiprocessor tasks considering transportation time,machine breakdown and job dynamic arrival was studied.Since this problem was caused by several classical scheduling problems,and was complex and difficult to solve,it was challenged to develop effective approximation algorithms to solve the problem.Two Lagrangian relaxation algorithms were proposed to determine near optimal solutions respectively combined with sub-gradient optimization and interleaved sub-gradient and bundle algorithm.Computational results on the problem with up to 100 jobs indicated that the proposed algorithms could generate good schedules within a reasonable CPU time.