  The minimization of makespan in open shop with time lags has been shown
NP-hard in the strong sense even for the case of two machines and unit-time
operations. The minimization of total completion time however has remained open
for that case though it has been shown NP-hard in the strong sense for weighted
total completion time or for jobs with release dates. This note shows that the
minimization of total completion time for two machines and unit-time operations
is NP-hard in the strong sense which answers the long standing open question.
