A note on the proportionate flow shop with a bottleneck machine

Choi, B.-C., Yoon, S.-H., Chung, S.-J., 2007. Minimizing maximum completion time in a proportionate flow shop with one machine of different speed. European Journal of Operational Research 176, 964–974 consider the proportionate flow shop with a slow bottleneck machine and propose the SLDR heuristic for it. Choi et al. (2007) derive a data-dependent worst-case ratio bound for the SLDR heuristic which is then bounded by two. In this note, we show that the tight worst-case ratio bound of the SLDR heuristic is 3/2.