This paper analyzes the substructure of linear programming tableaux for capacitated transshipment problems. Specifically, it demonstrates that submatrices of these tableaux correspond in a precise way to certain “contractions” of the transshipment network. The results are couched within the GNET/Depth network data structure of Bradley, Brown and Graves or the predecessor/thread/distance structure of Glover, Klingman, et al. An application to fixed-charge network problems is described.
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Rardin et al. (1979) studied this question.