# User’s Guide

• James K. Ho
• Rangaraja P. Sundarraj
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 338)

## Abstract

DECOMP is a FORTRAN IV code of the Dantzig-Wolfe algorithm for solving linear programming problems of the form
$${\text{Minimize}}\;{\text{z = }}\;\sum {\text{(}}{{\text{c}}_{\text{r}}}{{\text{x}}_{\text{r}}}{\text{)}}$$
(1)
subject to
$$\sum {\text{(A}}{{\text{1}}_{\text{r}}}{{\text{x}}_{\text{r}}}{\text{)}}\;{\text{ = }}\;{{\text{b}}_{\text{0}}}$$
(2)
$${\text{A}}{{\text{2}}_{\text{r}}}{{\text{x}}_{\text{r}}}\;{\text{ = }}\;{{\text{b}}_{\text{r}}}\;{\text{;}}\;{\text{r}}\;{\text{ = }}\;{\text{1,}}...{\text{,}}\;{\text{R}}$$
(3)
$${{\text{x}}_{\text{r}}}\; \geqslant \;{\text{0}}\;{\text{;}}\;{\text{r = 1,}}...{\text{,}}\;{\text{R}}$$
(4)
where c r is 1 by nr, b r is mr by 1 and all other vectors and matrices are of compatible dimensions. DECOMP was first coded by C. Winkler based on J.A. Tomlin’s LPM1 linear programming code at the Systems Optimization Laboratory (SOL) at Stanford University. It has been further developed by J.K. Ho and E. Loute at the Center for Operations Research and Econometrics (CORE), University of Louvain, Belgium.

## Keywords

Auxiliary Variable Master Problem Restricted Master Problem Major Cycle Simplex Iteration
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.