A Mixed Integer Linear Program for a Precedence-Constrained Minimum-Cost Arborescence Problem

The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial algorithms for solving the problem. In this paper we introduce a new variation of the problem called the Precedence-Constrained Minimum-Cost Arborescence Problem, in which precedence constraints are enforced on pairs of nodes. Such constraints prevent some node to be reachable from another node in the arborescence if there is a precedence relationship between the two nodes. The problem has applications in infrastructure designs for oil and gas distribution. We propose a mixed-integer linear programming model for the problem. Experimental results are finally presented and discussed