COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 990

"An Implementation of the Generalized Basis Reduction Algorithm
for Integer Programming"

William Cook, Thomas Rutherford, Herbert E. Scarf, Herbert E. and David Shallcross

August 1991

In recent years many advances have been made in solution techniques for specially structured 0–1 integer programming problems. In contrast, very little progress has been made on solving general (mixed integer) problems. This, of course, is not true when viewed from the theoretical side: Lenstra (1981) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of Lovasz and Scarf (1988). This method allows us to avoid the ellipsoidal approximations required in Lenstra’s algorithm. We report on the solution of a number of small (but difficult) examples, up to 100 integer variables. Our computer code uses the linear programming optimizer CPlex as a subroutine to solve the linear programming problems that arise.

Keywords: Linear programming, mixed integer problems

JEL Classification: C61, C63