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

摘要

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 consideredindependently 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 vertexbut depend on coming and leaving edges. The presented paper develops a model of the extended linearmulti-commodity multi-cost network that can be more exactly and effectively applied to model manypractical problems. Then, maximal limit cost flow problems are modeled as implicit linear programmingproblems. On the base of dual theory in linear programming, an effective approximate algorithm isdeveloped.