The minimum-cost arborescence problem is a well-studied problem in the area
of graph theory, with known polynomial-time algorithms for solving it. Previous
literature introduced new variations on the original problem with different
objective function and/or constraints. Recently, the Precedence-Constrained
Minimum-Cost Arborescence problem was proposed, in which precedence constraints
are enforced on pairs of vertices. These constraints prevent the formation of
directed paths that violate precedence relationships along the tree. We show
that this problem is NP-hard, and we introduce a new scalable mixed integer
linear programming model for it. With respect to the previous models, the newly
proposed model performs substantially better. This work also introduces a new
variation on the minimum-cost arborescence problem with precedence constraints.
We show that this new variation is also NP-hard, and we propose several mixed
integer linear programming models for formulating the problem
