## DECOMP: an implementation of Dantzig-Wolfe decomposition for linear programmingFor linear optimization models that can be formulated as linear programs with the block-angular structure, i.e. independent subproblems with coupling constraints, the Dantzig-Wolfe decomposition principle provides an elegant framework of solution algorithms as well as economic interpretation. This monograph is the complete documentation of DECOMP: a robust implementation of the Dantzig-Wolfe decomposition method in FORTRAN. The code can serve as a very convenient starting point for further investigation, both computational and economic, of parallelism in large-scale systems. It can also be used as supplemental material in a second course in linear programming, computational mathematical programming, or large-scale systems. |

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### Contents

INTRODUCTION | 1 |

PROGRAM SUBROUTINES | 33 |

PORTABILITY ISSUES | 168 |

Copyright | |

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### Common terms and phrases

algorithm BTRAN BUMP CALL FORMC candidate column CHUZR columns selected compute constraints convex combinations corresponding cost vector coupling rows current cycle D-W Phase Dantzig-Wolfe decomposition data array DECOMP decomposition direct access file DSUM dual variable dual vector elementary matrix entering column eta file eta vector extreme ray feasible Gaussian elimination IF(LSUB IF(MSTAT INDATA indicates infeasible input INVERT IPROS IROWP iteration JH(I KCYC KFASE KMULT KSTR KVEC LCOUNT linear programming lines lines 60 LMAX LMAXP1 LSUB MAST master problem matrix MAXCA proposals Maximum number MPS format MSTAT multiple pricing NCAND NCASUB NCNZ 0 ETAS NCOL NELEM NETA non-zero elements NORMAL NPROS NROW NROWO number of columns Number of coupling number of proposals Number of rows Number of subproblems objective value optimal parameter pivot row ratio reduced cost selected for multiple simplex Solving subproblem STRUCTURAL COLUMNS Subroutine unbounded UNPACK update WRITE(6 YA(I zero