A note on the algorithm LPT-FF for a flowshop scheduling with two batch-processing machines

A flowshop scheduling problem with two batch-processing machines is investigated in this paper, with the optimization goal to minimize the makespan. When the job processing times on the two machines are positively correlated, a 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4$$\end{document}-approximation algorithm for this NP-hard problem was previously proposed. We show that this algorithm has a worst-case performance guarantee of 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}.