Monday, February 12, 2018

Extended Linear Multi-Commodity Multicost Network and Maximal Flow Limited Cost Problems

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. 

No comments:

Post a Comment