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.

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Author:Alexander Engau, Horst W. Hamacher
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
Tag:consecutive ones matrix; integer programming; linear programming; network flows
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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