For a Maximization IP Problem, B&B reaches the following point:
a) What subproblems cannot possibly yield an optimal solution to the
original (“main”) problem even if they were elaborated further?
b) If you stopped now, what guarantee can you give concerning the best
feasible solution identified so far (in terms of being within a given
percent of optimality)?
c) What constraints would you add to define the subproblems under
Sub-problem #7?
Main Pb.
ZLP = 170
Sub Pb. #1
ZLP = 160
Sub Pb. #3
ZLP = 150
Sub Pb. #2
ZLP = 140
Sub Pb. #4
Sub Pb. #5
ZLP = 130
ZIP = ZLP = 120
Sub Pb. #7
ZLP = 125
X7* = 6.7
Sub Pb. #6
ZLP = 110
Sub Pb. #8
ZLP = 115
For a Minimization IP Problem, B&B reaches the following point:
a) Which sub-problems would be cut-off (not explored) if the tolerance
parameter were 0?
b) Which sub-problems would be cut-off (not explored) if the tolerance
parameter were 10%?
c) Write the tightest possible upper and lower bounds for Z*IP, the
optimal solution value to the original problem.
Original Pb.
ZLP = 170
Sub Pb. #1
ZLP = 180
Sub Pb. #3
ZLP = 310
Sub Pb. #2
ZLP = 240
Sub Pb. #4
Sub Pb. #5
ZLP = 250
ZIP = ZLP = 320
Sub Pb. #7
ZLP = 330
X7* = 6.7
Sub Pb. #6
ZLP = 260
Sub Pb. #8
ZLP = 300