Abstract
A necessary and sufficient condition for unimodularity in the multicommodity transportation problem is established, and the constructive proof yields an equivalent, single commodity network flow problem for the class of problems satisfying the condition. The concept of a graphic matroid is used to establish the transformation.
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Evans, J.R., Jarvis, J.J. & Duke, R.A. Graphic matroids and the multicommodity transportation problem. Mathematical Programming 13, 323–328 (1977). https://doi.org/10.1007/BF01584345
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DOI: https://doi.org/10.1007/BF01584345