On Integer and Partial Integer Linear Programming Problems

by George Bernard Dantzig

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A study concerned with solving a linear program in which some variables must have integer values. If the integer condition is ignored, the linear-programming solution often yields integer solutions and the problem is solved. However, if the solution turns out fractional, it is necessary to add additional linear constraints and to repeat the procedure until an integer solution is achieved. A recent result of R. E. Gomory showed how to add additional constraints if all variables must have integer values. The present paper discusses the partial integer problem and extends Gomory's procedure to the case in which all but one variable must have integer values.

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