Abstract
This paper presents some modifications of Ford-Fulkerson’s labeling method for solving the maximal network flow problemwith application in solving the transportation and assignment problems. The modifications involve the tree representationof the nodes labeled and the edges used them. It is shown that after each flow adjustment some of the labels canbe retained for the next labeling process. Through certain computational aspects it has been suggested that to indicatethat with theses the primal-dual approach for solving the transportation and assignment problems is improved to certainextent.
Highlights
New solution techniques have been suggested to solve transportation, mainly in the tree representation of a basis, location of a better adjacent basis, and labeling and relabeling of trees (Glover, 1982; Klingman, 1983)
Each label computed in the labeling method of Ford-Fulkerson (Ford, L.R., 1962) for the maximum flow problems consists of two element
All labels are discarded and the labeling process starts from the source again
Summary
New solution techniques have been suggested to solve transportation, mainly in the tree representation of a basis, location of a better adjacent basis, and labeling and relabeling of trees (Glover, 1982; Klingman, 1983). In this paper some of theses ideas are incorporated into the primal-dual approach to the transportation and assignment problems. Each label computed in the labeling method of Ford-Fulkerson (Ford, L.R., 1962) for the maximum flow problems consists of two element. All labels are discarded and the labeling process starts from the source again. For the assignment problem our computational experience with these modifications has been very encouraging and since the primal-dual approach is similar in the spirit to Hungarian Method, it appears that we have accelerated the Hungarian Method. For instance; algorithms for solving the Bottleneck Assignment and Bottleneck Transportation problems (Garfinkel, R.S., 1981) involve the solution of maximal flow problems
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
