This paper deals with a particular scheduling problem. We consider unit-time jobs and in-tree precedence constraints while minimizing the mean flow time. This problem is observed as $$P|p_{j}=1,\text {in-tree}|\sum C_{j}$$ with the use of the 3-filed notation. To the best of our knowledge, its complexity is still open. Through a reduction from 3-Partition, we show that this problem is strongly $$ \mathcal {NP} $$ -hard.