Abstract
We study the facial structure of a polyhedron associated with the single node relaxation of network flow problems with additive variable upper bounds. This type of structure arises, for example, in network design/expansion problems and in production planning problems with setup times. We first derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet-defining. Then we generalize our results through sequence independent lifting of valid inequalities for lower-dimensional projections. Our computational experience with large network expansion problems indicates that these inequalities are very effective in improving the quality of the linear programming relaxations.
This research is supported, in part, by NSF Grant DMI-9700285 to the Georgia Institute of Technology.
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© 1999 Springer-Verlag Berlin Heidelberg
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Atamtürk, A., Nemhauser, G.L., Savelsbergh, M.W.P. (1999). Valid Inequalities for Problems with Additive Variable Upper Bounds. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_5
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DOI: https://doi.org/10.1007/3-540-48777-8_5
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