Geodesic
Generalization of a Signature Method to Transportation Problems
Yugoslav journal of operations research, Tome 6 (1996) no. 1, p. 55
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Balinski's strong dual feasible bases for assignment problems are generalized to transportation problems. They are celled dual feasible super bases or trees. The super trees (not necessarily dual feasible) are also a generalization of Cunningham's (primal feasible ) strong bases. A simplex algorithm for transportation problems which generates dual feasible super bases is presented. Transportation problems with total supply (demand) $D>O$, m supply and n demand nodes are solved in at most $\mu(\mu - 1)/2 + \mu(D - \alpha - \beta - \mu + 1)$ iterations and in at most $O( \mu(m + n)(D - \alpha - \beta))$ elementary steps, where n is the maximum supply, $\beta$ is the minimum demand and $\mu = min \{m - 1, n - 1 \}$.
Keywords: Dual simplex method, transportation and assignment problems, signatures, strong bases, pivoting, complexity 
@article{YJOR_1996_6_1_a4,
     author = {Kostas Dosios and Konstantinos Paparizzos},
     title = {Generalization of a {Signature} {Method} to {Transportation} {Problems}},
     journal = {Yugoslav journal of operations research},
     pages = {55 },
     year = {1996},
     volume = {6},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_1996_6_1_a4/}
}
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Kostas Dosios; Konstantinos Paparizzos. Generalization of a Signature Method to Transportation Problems. Yugoslav journal of operations research, Tome 6 (1996) no. 1, p. 55 . http://geodesic.mathdoc.fr/item/YJOR_1996_6_1_a4/