Solving linear programming relaxations associated with lagrangean relaxations by Fenchel cutting planes

Article Abstract:

Issues relating to the usage of Lagragean relaxations are examined in detail, with a comparison between Lagangean and Fenchel cutting planes.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Lagrangian functions

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Graph theoretic relaxations of set covering and set partitioning problems

Article Abstract:

Alternative graph theoretic relaxations to the scheduling and planning problems known as set covering problem and set partitioning problem are investigated. They are based on an assignment, a shortest route and a minimal spanning tree. Other relaxations in the literature are also reviewed. They include the network flow, the maximum matching and the graph covering relaxations.

Operations research, Management science, Case studies, Graph theory, Relaxation methods (Mathematics)

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Tight linear programming relaxations of uncapacitated p-hub median problems

Article Abstract:

New mixed zero-one linear models with tight linear programming relaxations for solving uncapacitated multiple and single allocation p-hub median problems that arise in the design of airports, courier networks and communication networks are introduced. The approach, which was implemented on real problems, results in mostly integral solutions and in LP relaxations of between 10,010-391,250 variables and 2,101-31,901 constraints.

Linear programming

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