Geoscience Reference
In-Depth Information
S
1
,
1
S
1
,
2
1
C
1
A
1
B
1
R
1
g
a
c
f
b
e
Fig. 15.3
Supply chain network topology for the illustrative numeric al example—Variant I
15.2.3.2 Illustrative Example—Variant I
We then considered the following variant of the above illustrative example. We
assumed a worst case scenario in the form of unavailability of ground transport.
Hence, link
d
would no longer be available in the supply chain (See Fig.
15.3
).
The data were as above with the expressions (and constraints) associated with path
p
1
and link
d
removed.
The new solution had to satisfy the following equations, under the assumption
that
x
p
2
>
0,
z
p
2
>
ˉ
p
2
>
0, and
0:
R
1
P
R
1
x
p
2
1
P
R
1
x
p
2
þ ˉ
¼
0,
∂ C
p
2
xðÞ
R
1
p
2
þ λ
λ
g
e
þ g
f
þ g
g
∂
x
p
2
zðÞ
∂ʳ
R
1
p
2
¼
0, and
ˉ
∂
z
p
2
¼
0
T
R
1
p
2
þ z
p
2
x
p
2
g
e
þ g
f
þ g
g
:
Similar to the original example, substitution of the partial derivatives and the
numerical values into the above equations leads to the following system of
equations:
8
<
1054
x
p
2
ˉ
p
2
¼
10083
þ
8
:
5
16
z
p
2
ˉ
p
2
¼
0
:
5
x
p
2
þ z
p
2
8
:
¼
64
:
Solution of the above system of equations yields:
x
p
2
¼
8
:
50
:
Hence,
f
a
¼ f
b
¼ f
c
¼ f
e
¼ f
f
¼ f
g
¼
8
:
50
:
Also, the optimal value of the projected demand at demand point
R
1
,
v
R
1
¼
8
:
50.
Therefore, removal of the ground transportation link slightly decreased the
projected demand.
