A note on “parallel machine scheduling with non-simultaneous machine available time”

The purpose of this note is to point out that if there are some machines that do not process any job and hence is inactive in the planning horizon then the lower bound of makespan provided by Lee (1991) in the above mentioned paper may not be a valid one. Furthermore, the error bound of applying the Longest Processing Time (LPT) algorithm to the problem can be tightened if the number of active machines is smaller than the total number of machines.