Modeling and Analysis of Multicommodity Network Flows Via Goal Programming

Abstract

In this work goal programming is used to solve a minimum cost multicommodity network flow problem with multiple objectives. The network consists of; linear objective function.linear cost arcs, fixed arc and node capacities, and specific origin-destination pairs for each commodity. This suggests a classic linear program. When properly modeled. Lagrangian relaxation. Daiitzig-Wolfe decomposition, and network flow techniques may be employed lo exploit the pure network structure. Lagrangian relaxation captures the essence of Ihe pure network flow problem as a master problem and sub-problems. The relaxation may be optimized directly, or be decomposed into subproblems, one tor each commodity with eaeh subproblem a minimum cost single commodity network flow problem. Postoptimalily analyses, viasensitivity analysis and parametric analysis, provide a variety of options under which the robustness of the optimal solution may be investigated. This mix of modeling options and analyses provides a powerful approach for producing insight into the modeling of a multicommodity network flow problem with multiple objeetives.