Today I claimed during my presentation that if a job j had forced DOUBLING to increase \Lambda to a value \geq 4 OPT, then the input can be augmented by jobs j+1,..., n that force a factor of 8 (i.e. without changing the value OPT).
I would like to apologize for the misinformation and to thank Prof. Rote for his questions, as this claim is indeed not trivial (unlike what I thought during the presentation) and needs to be (dis)proven thoroughly.