## Contributions to the methodology of decomposition and fixed charge problems |

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### Contents

Hierarchical Decomposition | 5 |

A Method to Obtain the Optimal Dual Solution to | 35 |

The Fixed Charge Problem | 45 |

Copyright | |

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### Common terms and phrases

0-1 integer programming 5x10 problems activity activity x adjacent extreme point aircraft type approximate algorithms blem cargo loading problem Chapter commodity computationally concave functions concave objective function constraints convex set Cooper and Drebes Cornell University critical leg Dantzig 9 Dantzig-Wolfe decomposition dual prices dual solution dual variables associated dynamic programming enter the basis extreme point solution feasible loading pattern feasible solution fixed charge algorithm fixed charge formulation fixed charge problem fixed charge transportation fixed cost forcing go to step Heuristic ID ID integer programming problems k=l i=l knapsack problem large linear programs large number linear programming problem lower bound non-basic columns number of flights objective value Operations Research payload capacity piecewise linear route sec./CDC simplex method solution to 4.1 solved specially structured steepest descent Steinberg straints subproblem Suppose SWIFT algorithms SWIFT-2 test problems Theorem vector to enter warehouse location problem weight-feasible loading zero