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 - ε 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 - ε)-approximation algorithm for it implies P = NP.
Ageev, A. (2018). Inapproximability lower bounds for open shop problems with exact delays. In Communications in Computer and Information Science (Vol. 871, pp. 45–55). Springer Verlag. https://doi.org/10.1007/978-3-319-93800-4_4