I have a directed acyclic graph $ G = (V, A) $, I want to cover the vertices of $ G $ with a minimum number of roads so that each vertex $ v_i $ is covered by $ b_i $ different paths

When $ b_i = 1 $ For all vertices, the problem can be solved in polynomial time. But I am looking for the complexity of the problem when $ b_i> 1 $ for at least one vertex $ v_i $Do you know any results that can help me?