Common Terminal Multicommodity Flow with a Concave Objective Function

Abstract

We consider graphs in which there are n source nodes, each a source of a different commodity, and a common terminal node. Associated with each commodity is a nonincreasing function $\alpha _i (.),i = 1, \cdots ,n$. An algorithm is presented which yields a flow pattern that maximizes $Z = \Sigma _{i = 1}^n \int_0^{fi} {\alpha _i (x)dx} $, where $f_i $ is the flow value of the ith commodity.