Abstract
Known approximation algorithms recommended for the permutation flow-shop problem with the weighted sum of completion times have a worst-case performance ratio which is unknown, or known but unlimited. We propose new algorithms with this ratio equal to [ m k]ϱ k , where ϱ k is the worst-case performance ratio of an algorithm which solves an auxiliary k -machine problem. Worst-case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also presented.
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