Decomposition approaches in permutation scheduling problems with application to the M-machine flow shop scheduling problems

In this article, we consider three decomposition techniques for permutation scheduling problems. We introduce a general iterative decomposition algorithm for permutation scheduling problems and apply it to the permutation flow shop scheduling problem. We also develop bounds needed for this iterative decomposition approach and compare its computational requirements to that of the traditional branch and bound algorithms. Two heuristic algorithms based on the iterative decomposition approach are also developed. extensive numerical study indicates that the heuristic algorithms are practical alternatives to very costly exact algorithms for large flow shop scheduling problems.