Summary: ``In this article, we formulate a population control model, which is based upon the hierarchical size-structure and the incubation delay. For a given ideal population distribution, we investigate the optimal input problem: How to choose a inflow way such that the sum of the deviation between the terminal state and the given one and the total costs is minimal. The well-posedness is established by the method of characteristics, the existence of unique optimal policy is shown by the Ekeland variational principle, and the optimal policy is exactly described by a normal cone and an adjoint system. These results set a foundational framework for practical applications.''