The two- and m-machine flowshop scheduling problems with bicriteria of makespan and mean flowtime

This paper considers the flowshop scheduling problem with the objective of minimizing the weighted sum of makespan and mean flowtime. Even though the two-machine problem has been addressed and several heuristics have been established in the literature, these heuristics have not been compared. In this paper, a comparison of these available heuristics in the literature is conducted. Moreover, three new heuristic algorithms are proposed, which can be utilized for both the two-machine and m-machine problems. Computational experiments indicate that the proposed heuristics are superior to all the existing heuristics in the literature including a genetic algorithm. Two dominance relations are also developed; one for the two-machine and the other for the three-machine problem. Experimental results show that both relations are efficient.