### 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 language | English (US) |
---|---|

Pages (from-to) | 125-144 |

Number of pages | 20 |

Journal | Naval Research Logistics |

Volume | 21 |

Issue number | 1 |

State | Published - Jan 1 1974 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Naval Research Logistics*,

*21*(1), 125-144.

}

*Naval Research Logistics*, vol. 21, no. 1, pp. 125-144.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER LINEAR PROGRAMS.

AU - Richmond, Tyronza R.

AU - Ravindran, Arunachalam

PY - 1974/1/1

Y1 - 1974/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0016034347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016034347&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0016034347

VL - 21

SP - 125

EP - 144

JO - Naval Research Logistics

JF - Naval Research Logistics

SN - 0894-069X

IS - 1

ER -