Revised Dantzig-Wolfe decomposition for staircase-structured linear programs

Staircase structured linear programs arise naturally in the study of engineering economic systems. One general approach to solving such LP's is the technique of nested decomposition of the primal or dual problem. The research described in this paper proposes a revised decomposition algorithm that incorporates knowledge of the structure of the staircase basis in forming the decomposed linear programs. Column proposals from the revised subproblems are shown to achieve maximum penetration against the master problem basis.