Please notice that the solution below is just a possible one. Any different solutions
which make sense are also welcomed.
In the stochastic case, the new model is as below:
Maximize
3
1
2
3
4
5
6
7
8
9
1
[1000(
)
750(
)
250(
)]
j
j
j
j
j
j
j
j
j
j
j
P
y
y
y
y
y
y
y
y
y
=
+
+
+
+
+
+
+
+
Suppose Scenario 1 refers to the normal water allocation, Scenario 2 the 10% higher
case and Scenario 3 the 40% lower case. Therefore,
1
2
3
0.5,
0.4,
0.1
P
P
P
=
=
=
.
And the constraints for
,
1,2,3;
1,2
9
j
i
y
j
i
=
=
K
are
And for each i, 0
j
i
i
y
x
P
.
The constraints for
i
x
are
the same as the constraint 1,
3, 4, 5 in the textbook.
Solving
this
linear
programming,
we
can
derive the optimal planting
decisions shown in table
below
Allocation (Acres)
Kibbutz
Crop
1
2
3
Sugar beets
100
180
130
Cotton
180
240
80
Sorghum
0
0
0
And the optimal watering decision under Scenario 1 is (80, 106.7, 71.7, 180, 240, 80,
0, 0, 0); under Scenario 2 is (100, 133.3, 84.2, 180, 240, 80, 0, 0, 0); under Scenario 3
is (0, 0, 21.7, 180, 240, 80, 0, 0, 0). The expected return is $63333.3.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 SteinW.Wallace
 Optimization, optimal planting decisions, stochastic case

Click to edit the document details