Abstract
We study the two-machine Open Shop problem with exact delays. When all delays are equal to zero this problem converts to the no-wait two-machine Open Shop problem, which is known to be NP-hard. We prove that even the proportionate case of Open Shop problem with exact delays does not admit approximations with ratio \(1.5-\varepsilon \) unless P \(=\) NP. We also consider the very special case when the delays take at most two different values and prove that the existence of a \((1.25-\varepsilon )\)-approximation algorithm for it implies P \(=\) NP.
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