In the 2-Machine Flow Shop problem with exact delays the operations of each job are separated by a given time lag (delay). Leung et al. (2007) established that the problem is strongly NP-hard when the delays may have at most two different values. We present further results for this case: we prove that the existence of (1.25−ε)-approximation implies P=NP and develop a 2-approximation algorithm.
@article{arxiv.1711.00081,
title = {Approximating the $2$-Machine Flow Shop Problem with Exact Delays Taking Two Values},
author = {Alexander Ageev},
journal= {arXiv preprint arXiv:1711.00081},
year = {2022}
}