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Integer Programming Post-Optimal Analysis with Cutting Planes

Dieter Klein, Søren Holm

Abstract

Sufficient conditions have been developed for testing the optimality of solutions to all-integer and mixed-integer linear programming problems after coefficient changes in the right hand side and the objective function, or after introduction of new variables. The same conditions can be used as necessary conditions for coefficient changes to alter an optimal solution. The tests are based on cutting-plane theory, and the application of the tests requires solution of the original integer problem with a cutting-plane algorithm.

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Key concepts: Cutting-plane method, Integer programming, Integer (computer science), Mathematical optimization, Mathematics, Branch and price, Plane (geometry), Linear programming