NETWORK OPTIMIZATION WITH PIECEWISE LINEAR CONVEX COSTS

The problem of finding the minimum cost multi-commodity flow in an undirected and complete network is studied when the link costs are piecewise linear and convex. The arc-path model and overflow model are presented to formulate the problem. The results suggest that the new overflow model outperforms the classical arc-path model for this problem. The classical revised simplex, Frank and Wolf and a heuristic method are compared for the problem.