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subproblem, denoted by PL, and its aggregated upper bound subproblern. denoted by PLU,
and the aggregated upper bound subproblem into its aggregated lower bound subproblem,
denoted by Pur, and its aggregated upper bound subproblem, denoted by Puu This bifurcation
process continues until there are no subproblems left for funher decomposition. Figure 4.1
shows this bifurcation process for N=9 with the number of parts at each level. Since the total
number of parts is not a power of two in this exmple. the choice of the parts number at each
level is ;ubitmy. However, to keep the number of bifurcation levels as small as possible. each
bifurcation cm be done such that the number of parts in the two subproblems are equd or
different by one, depending on whether the total number of parts is even or odd.
Fipre 1.1 The bifurcation process for N=9 (9-parts)
At each level. a new linking prima1 variable (A vector) is included in the lower bound
tye subproblem and a new linking dual variable (p vector) is included in the upper bound
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