Semi on-line scheduling on three processors with known sum of the tasks

We consider a semi on-line version of the multiprocessor scheduling problem on three processors, where the total size of the tasks is known in advance. We prove a lower bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1+\frac{\sqrt{129}-9}{6}>1.3929$\end{document} on the competitive ratio of any algorithm and propose a simple algorithm with competitive ratio equal to 1.5. The performance is improved to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1+\frac{8}{19}<1.4211$\end{document} by a preprocessing strategy. The latter algorithm is only 2% away from the lower bound.