We revisit the classical single-machine scheduling problem to minimize total tardiness with deadlines. The problem is binary NP-hard even without the deadline restrictions. It was reported early in Koulamas and Kyparisis (Eur J Oper Res 133:447–453, 2001) that the exact complexity (unary NP-hardness or pseudo-polynomial-time solvability) of the problem is still open. We show that this problem is unary NP-hard.

中文翻译：

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单机调度的一元 NP-hardness 以最小化总延迟与最后期限

我们重新审视经典的单机调度问题，以最大程度地减少总延迟时间。即使没有截止日期限制，问题也是二进制 NP-hard。Koulamas 和 Kyparisis (Eur J Oper Res 133:447–453, 2001) 的早期报道称，该问题的确切复杂性（一元 NP 硬度或伪多项式时间可解性）仍然是开放的。我们证明这个问题是一元 NP-hard 问题。