Modeling and Analysis of Multicommodity Network Flows via Goal Programming

In this work goal programming is used to solve a minimum cost multicommodity network flow problem with multiple goals. A single telecommunication network with multiple commodities (e.g., voice, video, data, etc.) flowing over it is analyzed. This network consists of: linear objective function, linear cost arcs, fixed capacities, specific origin-destination pairs for each commodity. A multicommodity network flow problem with goals can be successfully modeled using linear goal programming techniques. When properly modeled, network flow techniques may be employed to exploit the pure network structure of a multicommodity network flow problem with goals. Lagrangian relaxation captures the essence of the pure network flow problem as a master problem and sub-problems (McGinnis and Rao, 1977). A subgradient algorithm may optimize the Lagrangian function, or the Lagrangian relaxation could be decomposed into subproblems per commodity; each subproblem being a single commodity network flow problem. Parallel to the decomposition of the Lagrangian relaxation, Dantzig-Wolfe decomposition may be implemented to the linear program. Post-optimality analyses provide a variety of options to analyze the robustness of the optimal solution. The options of post-optimality analysis consist of sensitivity analysis and parametric analysis. This mix of modeling options and analyses provide a powerful method to produce insight into the modeling of a multicommodity network flow problem with multiple objectives.Air Force Inst of Tech Wright-Patterson AFB OH School of Engineering and Management is the author of 'Modeling and Analysis of Multicommodity Network Flows via Goal Programming', published 2002 under ISBN 9781423510505 and ISBN 142351050X.