Tran Quoc Chien1
and Ho Van Hung2
1The University of Education, University of Danang, Danang, Vietnam
2Quangnam University, Tamky, Vietnam
ABSTRACT
The Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In an ordinary graph, the weights of edges and vertexes are considered
independently where the length of a path is the sum of weights of the edges and the vertexes on this path.
However, in many practical problems, weights at a vertex are not the same for all paths passing this vertex
but depend on coming and leaving edges. The presented paper develops a model of the extended linear
multi-commodity multi-cost network that can be more exactly and effectively applied to model many
practical problems. Then, maximal limit cost flow problems are modeled as implicit linear programming
problems. On the base of dual theory in linear programming, an effective approximate algorithm is
developed.
KEYWORDS
Graph, Network, Multi-commodity Multi-cost Flow, Optimization, Linear-Programming.
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