Approximation algorithm for A bicriteria multicommodity flow problem

In the present work, one of bicriteria multicommodity flow problem, called as maximum flow problem with minimized maximum of met rates, is proposed to find a certain kind of weak solutions for the operational decisions of many practical situations with multicommodity flow, for instance, the emergency logistics distribution decision stemming from the action of China´s reliving the areas suffering the tremendous snow disaster in the beginning of 2008. For the problem, the existence of solutions is proved, a pseudopolynomial time approximation algorithm to solve it is designed, finally an approximation measure on the algorithm we design is proposed and proved.