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A Simplified Primal (All-Integer) Integer Programming Algorithm

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  • R. D. Young

    (Rice University, Houston, Texas)

Abstract

This paper describes a primal, all-integer algorithm for solving a bounded and solvable pure integer programming problem. The method is a primal analogue to the Gomory All-Integer Algorithm, and is a variant of the simplex method in sense that the Gomory algorithm is a variant of the dual method. The simplified primal algorithm makes these major amendments to the simplex method: (i) a special row, indexed by L , is adjoined to the tableau and is periodically revised by a well-defined procedure; (ii) in most cycles of the algorithm the pivot column, A J , is selected so that a LJ > 0 and (1/ a LJ ) A J is lexicographically smaller than (1/ a Lj ) A j for all nonbasic columns A j that have a Lj > 0; (iii) in all cycles of the algorithm a Gomory cut is adjoined after selection of the pivot column, and the cut is selected so that it will have a unit coefficient in the pivot column and it will qualify (in order to be used) as the pivot row. With comparatively minor restrictions on the selection of the row used to generate the Gomory cut the simplified primal algorithm is shown to be finite.

Suggested Citation

  • R. D. Young, 1968. "A Simplified Primal (All-Integer) Integer Programming Algorithm," Operations Research, INFORMS, vol. 16(4), pages 750-782, August.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:4:p:750-782
    DOI: 10.1287/opre.16.4.750
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    Cited by:

    1. Santanu S. Dey & Jean-Philippe Richard, 2009. "Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 137-150, February.

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