Abstract
The problem of minimizing either the maximum tardiness or the number of tardy jobs in a two-machine flowshop with due date considerations is known to be strongly NP -hard. A recent paper presented polynomial-time reductions from Partition to some restricted cases and concluded their ordinary NP -hardness. However, no pseudo-polynomial-time algorithm was developed. In this paper, we conduct polynomial-time reductions from 3-Partition to these special cases. The results confirm the strong NP -hardness of the problems under study. We also identify some other special cases as polynomially solvable by presenting their solution methods.
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