202 Introduction to Linear Optimization and Extensions with MATLAB
R
to guide the subdivisions to a production plan that is systemwide (company-
wide) cost optimal, which represents an equilibrium where supply and demand
are balanced.
5.5.2 Initialization
To start the Dantzig-Wolfe decomposition, the master problem requires an
initial basic feasible solution. The strategy is to develop an auxiliary problem
similar to a Phase 1 approach for the revised simplex method in Chapter
3. First, an extreme point x
k
= v
k
1
is generated for each subproblem SP
k
using the Phase 1 approach for the revised simplex method. If any of the
subproblems do not have a feasible extreme point, then the original problem
is infeasible. Even if all subproblems admit an extreme