The single-machine family scheduling problem of minimizing the number of la
te jobs has been known to be NP-hard, but whether it is NP-hard in the stro
ng sense is cited as an open problem in several reviews. In this note, we p
rove that this problem is strongly NP-hard even if all set-up times and pro
cessing times are one unit. Copyright (C) 2001 John Wiley & Sons, Ltd.