Abstract
This paper investigates the impact of problem formulation on Dantzig—Wolfe decomposition for the multicommodity network flow problem. These problems are formulated in three ways: origin-destination specific, destination specific, and product specific. The path-based origin-destination specific formulation is equivalent to the tree-based destination specific formulation by a simple transformation. Supersupply and superdemand nodes are appended to the tree-based product specific formulation to create an equivalent path-based product specific formulation. We show that solving the path-based problem formulations by decomposition results in substantially fewer master problem iterations and lower CPU times than by using decomposition on the equivalent tree-based formulations. Computational results on a series of multicommodity network flow problems are presented.
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This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.
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Jones, K.L., Lustig, I.J., Farvolden, J.M. et al. Multicommodity network flows: The impact of formulation on decomposition. Mathematical Programming 62, 95–117 (1993). https://doi.org/10.1007/BF01585162
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DOI: https://doi.org/10.1007/BF01585162