Notes on Linear Programming

Part XLVII Solving Linear Programs in Integers

George Bernard Dantzig

ResearchPublished 1958

The development of a variant to a recent result of Gomory (Princeton). In solving linear programs in integers, Gomory showed how to add linear inequality constraints to a linear-programming problem automatically in such a way that the extreme points of the resulting convex contain only integral solutions in the neighborhood of the minimum. The present study gives an alternative method for generating additional constraints in a way easy to justify and apply. It is not known, however, whether these conditions will lead to a solution in a finite number of iterations as is true for the stronger Gomory conditions. Anyone considering their practical use should therefore weigh the ease of generation against the extra number of iterations required for convergence.

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  • Copyright: RAND Corporation
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  • Year: 1958
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Dantzig, George Bernard, Notes on Linear Programming: Part XLVII Solving Linear Programs in Integers, RAND Corporation, RM-2209, 1958. As of October 11, 2024: https://www.rand.org/pubs/research_memoranda/RM2209.html
Chicago Manual of Style
Dantzig, George Bernard, Notes on Linear Programming: Part XLVII Solving Linear Programs in Integers. Santa Monica, CA: RAND Corporation, 1958. https://www.rand.org/pubs/research_memoranda/RM2209.html. Also available in print form.
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