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The Steiner tree problem with revenues, budgets and hop constraints (STPRBH)is a variant of the classical Steiner tree problem. This problem asks for asubtree in a given graph with maximum revenues corresponding to its nodes,where its total edge costs respect the given budget, and the number of edgesbetween each node and its root does not exceed the hop limit. We introduce anew binary linear program with polynomial size based on partial-ordering, which(up to our knowledge) for the first time solves all STPRBH instances from theDIMACS benchmark set to optimality. The set contains graphs with up to 500nodes and 12500 edges.

A new Integer Linear Program for the Steiner Tree Problem with Revenues, Budget and Hop Constraints