Abstract
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.
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