3.3. The Operational
Policy Problem (Problem
III)
Iteration 3
Arc
χ.·
— π,·
-6
Qa
hi
State In kilter?
(1, 2)
0
-2
2
0
2 = 1*12 Β
Yes
(1, 3)
0
-2
5
3
0 = ?1S
A
Yes
(2, 3)
2
-2
1
1
0 = ^23
A
Yes
(2, 4)
2
-2
3
3
2 > ItK
A 2
No
(3, 2)
2
-2
1
1
0 = l»2
A
Yes
(3, 4)
2
-2
6
6
0 < h*
Αχ
No
(4,1)
2
0
0
2
2 < Ux Ax
No
1. Pick the next out-of-kilter arc (2, 4).
2. State of arc (2, 4) is A 2 ; decrease fa to i 2 4.
3. Find path from node 2 to node 4 by labeling procedure.
Labeling procedure
Node
Label
2
(4- 2)
1
(2-, 2)
3
Cannot be labeled; (1, 3) is in kilter
4
Cannot be labeled; flow decrease drives
(4, 1) more out of kilter
Nonbreakthrough has occurred.
X = {1, 2}, X r
{3, 4}, Μ = {(1, 3), (2, 3), (2, 4)}, Μ = Φ, D
min(3, 1, 3) = 1, D = does not exist, D f = 1.
New π values: π χ = 0, x 2 = 2,7r 3 = τ 4 = 3.
Recompute state of each arc.