Mathematical Programming

, Volume 5, Issue 1, pp 1–28

# Pivot selection methods of the Devex LP code

• Paula M. J. Harris
Article

## Abstract

Pivot column and row selection methods used by the Devex code since 1965 are published here for the first time. After a fresh look at the iteration process, the author introduces dynamic column weighting factors as a means of estimating gradients for the purpose of selecting a maximum gradient column. The consequent effect of this column selection on rounding error is observed. By allowing that a constraint may not be positioned so exactly as its precise representation in the computer would imply, a wider choice of pivot row is made available, so making room for a further selection criterion based on pivot size. Three examples are given of problems having between 2500 and 5000 rows, illustrating the overall time and iteration advantages over the standard simplex methods used today. The final illustration highlights why these standard methods take so many iterations. These algorithms were originally coded for the Atlas computer and were re-coded in 1969 for the Univac 1108.

## Keywords

Selection Method Iteration Process Simplex Method Precise Representation Maximum Gradient
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. [1]
G.B. Dantzig, “Minimization of a linear function of variables subject to linear inequalities”, in:Activity analysis of production and allocation, Ed. T.C. Koopmans (Wiley, New York, 1951) 339–347.Google Scholar
2. [2]
J.C. Dickson and F.P. Frederick, “A decision rule for improved efficiency in solving linear programming problems with the simplex algorithm”,Communications of the Association for Computing Machinery 3 (1960) 509–512.Google Scholar
3. [3]
P.M.J. Harris, “An algorithm for solving mixed integer linear programmes”,Operational Research Quarterly 15 (2) (1964) 117–132.Google Scholar
4. [4]
H.W. Kuhn and R.E. Quandt, “An experimental study of the simplex method”, in:Proceedings of Symposia in Applied Mathematics 15 (American Mathematical Society, Providence, R.I., 1963) 107–124.Google Scholar
5. [5]
P. Wolfe and L. Cutler, “Experiments in linear programming”, in:Recent advances in mathematical programming, Eds. R. Graves and P. Wolfe (McGraw-Hill, New York, 1963).Google Scholar