Generalization of a Signature Method to Transportation Problems


Kostas Dosios, Konstantinos Paparizzos




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 $\mu = min \{m - 1, n - 1 \}$.