  Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving
large-scale linear programs whose constraint matrix involves a set of
independent blocks coupled with a set of linking rows. The algorithm decomposes
such a model into a master problem and a set of independent subproblems that
can be solved in a distributed manner. In a typical implementation, the master
problem is solved centrally. In certain settings, solving the master problem
centrally is undesirable or infeasible, such as in the case of decentralized
storage of data, or when independent agents who are responsible for the
subproblems desire privacy of information. In this paper, we propose a fully
distributed DWD algorithm which relies on solving the master problem using a
consensus-based Alternating Direction Method of Multipliers (ADMM) method. We
derive error bounds on the optimality gap and feasibility violation of the
proposed approach. We provide preliminary computational results for our
algorithm using a Message Passing Interface (MPI) implementation on cutting
stock instances from the literature and synthetic instances where we obtain
high quality solutions.
