Notes on Linear Programming

Part XLVII Solving Linear Programs in Integers

by George Bernard Dantzig

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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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