A note: flowshop scheduling with linear deterioration and job-rejection

We study a scheduling problem on an m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document}-machine flowshop with linear deterioration of job processing times and job rejection. The objectives are minimum makespan and minimum total load, subject to an upper bound on the total permitted rejection cost. The problems are NP-hard (since the single machine makespan minimization version was shown to be hard), and we introduce pseudo-polynomial dynamic programming algorithms, thus proving that both problems are NP-hard in the ordinary sense.