GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER LINEAR PROGRAMS.

Tyronza R. Richmond, Arunachalam Ravindran

Research output: Contribution to journalArticle

Abstract

This paper investigates a new procedure for solving the general-variable pure integer linear programming problem. A simple transformation converts the problem to one of constructing nonnegative integer solutions to a system of linear diophantine equations. Rubin's sequential algorithm, an extension of the classic Euclidean algorithm, is used to find an integer solution to this system of equations. Two new theorems are proved on the properties of integer solutions to linear systems. This permits a modified Fourier-Motzkin elimination method to be used to construct a nonnegative integer solution. An experimental computer code was developed for the algorithm to solve some test problems selected from the literature. The computational results, though limited, are encouraging when compared with the R. E. Gomory all-integer algorithm.

Original languageEnglish (US)
Pages (from-to)125-144
Number of pages20
JournalNaval Research Logistics
Volume21
Issue number1
StatePublished - Jan 1 1974

Fingerprint

Integer Program
Linear Program
Euclidean
Integer
Non-negative
Linear Diophantine equation
Euclidean algorithm
Linear equations
Linear programming
Sequential Algorithm
Integer Linear Programming
Linear systems
Test Problems
System of equations
Convert
Elimination
Computational Results
Linear Systems
Linear program
Theorem

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

Cite this

Richmond, T. R., & Ravindran, A. (1974). GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER LINEAR PROGRAMS. Naval Research Logistics, 21(1), 125-144.
Richmond, Tyronza R. ; Ravindran, Arunachalam. / GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER LINEAR PROGRAMS. In: Naval Research Logistics. 1974 ; Vol. 21, No. 1. pp. 125-144.
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Richmond, TR & Ravindran, A 1974, 'GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER LINEAR PROGRAMS.', Naval Research Logistics, vol. 21, no. 1, pp. 125-144.

GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER LINEAR PROGRAMS. / Richmond, Tyronza R.; Ravindran, Arunachalam.

In: Naval Research Logistics, Vol. 21, No. 1, 01.01.1974, p. 125-144.

Research output: Contribution to journalArticle

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