We study an uncapacitated facility location model where customers are served by facilities of level one, then each level one facility that is opened must be assigned to an opened facility of level two. We identify a polynomially solvable case, and study some valid inequalities and facets of the associated polytope.
We present a Branch-and-Cut algorithm where the volume algorithm is applied instead of the traditionally used dual simplex algorithm to the linear programming relaxations in the root node of the search tree. This means that we use fast approximate solutions to these linear programs instead of exact but slower solutions. We present computational results with the Steiner tree and Max-Cut problems. We show evidence that one can solve these problems much faster with the volume algorithm based...
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