A note: Maximizing the weighted number of just-in-time jobs on a proportionate flowshop

In most cases, an extension of a polynomial time solution of a scheduling problem on a single machine to a proportionate flowshop leads to a similar (polynomial time) solution. One of the rare cases where the problem becomes hard, is that of maximizing the weighted number of Just-in-Time jobs on a proportionate flowshop. We introduce a (pseudo-polynomial) solution algorithm for this problem, which is faster by a factor of n than the algorithm published in the literature. We also introduce a (polynomial time) solution algorithm for the "no-wait" proportionate flowshop.