Scheduling in the two-machine flowshop with due date constraints

The problem of minimizing either the maximum tardiness or the number of tar dy jobs in a two-machine flowshop with due date considerations is known to be strongly NP-hard. A recent paper presented polynomial-time reductions fr om Partition to some restricted cases and concluded their ordinary NP-hardn ess. However, no pseudo-polynomial-lime algorithm was developed. In this pa per, we conduct polynomial-time reductions from 3-Partition to these specia l cases. The results confirm the strong NP-hardness of the problems under s tudy. We also identify some other special cases as polynomially solvable by presenting their solution methods. (C) 2001 Elsevier Science B.V. All righ ts reserved.