New simple constructive heuristic algorithms for minimizing total flow-time in the permutation flowshop scheduling problem

This paper develops a set of new simple constructive heuristic algorithms to minimize total flow-time for an n-jobs×m-machines permutation flowshop scheduling problem. We first propose a new iterative algorithm based on the best existing simple heuristic algorithm, and then integrate new indicator variables for weighting jobs into this algorithm. We also propose new decision criteria to select the best partial sequence in each iteration of our algorithm. A comprehensive numerical experiment reveals that our modifications and extensions improve the effectiveness of the best existing simple heuristic without affecting its computational efficiency.