## Semi-Simultaneous Flows and Binary Constrained (Integer) Linear Programs

- Linear and integer programs are considered whose coefficient matrices can be partitioned into K consecutive ones matrices. Mimicking the special case of K=1 which is well-known to be equivalent to a network flow problem we show that these programs can be transformed to a generalized network flow problem which we call semi-simultaneous (se-sim) network flow problem. Feasibility conditions for se-sim flows are established and methods for finding initial feasible se-sim flows are derived. Optimal se-sim flows are characterized by a generalization of the negative cycle theorem for the minimum cost flow problem. The issue of improving a given flow is addressed both from a theoretical and practical point of view. The paper concludes with a summary and some suggestions for possible future work in this area.

Author: | Alexander Engau, Horst W. Hamacher |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-14361 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (99) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 2006 |

Year of Publication: | 2006 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2006/07/12 |

Tag: | consecutive ones matrix; integer programming; linear programming; network flows |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |