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Table 5.4 The subproblem sires
The lower-lower bound subproblem keeps adding proposais corning from dl the previous
upper and lower level itentions and the upper-upper bound subproblem accumulates the cuts
corning from al1 the previous upper and lower level itentions. However. the lower-upper bound
and upper-lower bound subproblems don't keep ail the information; they forget the lower level
information when they have upper level information exchmge due to die problems mentioned in
the previous chiipter. The lower-lower bound and lower-upper bound subproblems used prima1
simplex method and the upper-lower bound and upper-upper bound subproblems utilized dual
simplex method.
The stopping criterion used by the decomposition algorithm is that the relative duality gap
(Le. the gap as a fraction of the avenge of the upper and lower bounds) is smaller than or equal
to 1.0~10~. which is a very rigomus condition. By this stopping criterion, ail tested pmblerns
using the puailel decornposition algorithm converged to optimal solutions and they are exactly
the siune as those obtained by the direct methods by CPLEX 6.0. Tables 5.5 and 5.6 show the