On the complexity of open shop scheduling with time lags

The minimization of makespan in open shop with time lags has been to be 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 it be 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.