An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming

William Cook, Thomas Rutherford (), Herbert Scarf and David F. Shallcross

No 990, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Pages: 13 pages
Date: 1991-08
Note: CFP 906.
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in ORSA Journal of Computing (spring 1993), 5(2): 206-221

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d09/d0990.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:990

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().