Geoscience Reference
In-Depth Information
d
S
1
,
1
S
1
,
2
1
C
1
A
1
B
1
R
1
g
a
c
f
b
e
Fig. 15.2
Supply chain network topology for the illustrative numerical example
c
a
fðÞ¼
3
f
a
þ
2
f
a
,
c
b
fðÞ¼f
b
þ
3
f
b
,
c
c
fðÞ¼
2
f
c
þ f
c
,
c
d
fðÞ¼
4
f
d
þ
3
f
d
,
c
e
fðÞ¼
7
f
e
þ
5
f
e
,
^
^
c
f
f
f
¼ f
f
þ
4
f
f
,
c
g
f
g
¼
3
f
g
þ
2
f
g
:
^
^
There are two paths in this network defined as:
p
1
(
a
,
b
,
c
,
d
,
f
,
g
) and
p
2
(
a
,
b
,
c
,
e
,
f
,
g
). The set of paths,
P
, is identical to the set of paths connecting the origin 1 to
the destination,
R
1
, i.e.,
P
R
1
, where
P¼P
R
1
¼
f
p
1
;
p
2
g:
The demand for the relief item at the demand point followed a uniform distribu-
tion on the interval [5,10]; therefore,
the probability distribution function of
demand at the demand point is:
v
R
1
5
10
5
¼
x
p
1
þ x
p
2
5
5
P
R
1
v
R
ðÞ¼
:
The unit shortage and surplus penalties were:
λ
R
1
¼
5000 and
λ
R
1
¼
100.
The organization is interested in the pre-positioning strategy; i.e., it wishes
to determine the amount of the relief item that should be stored beforehand.
Thus, the organization will only ship the pre-positioned supplies of relief goods
and will not procure post the disaster. Consequently, the completion time on links
a
,
b
, and
c
(procurement, transportation, and storage) is set to zero:
˄
a
f ðÞ¼˄
b
f ðÞ¼˄
c
f ðÞ¼
0
:
The completion time functions on the rest of the links were:
˄
d
f ðÞ¼
9
f
d
þ
6,
˄
e
f ðÞ¼
2
f
e
þ
2,
˄
g
f
g
¼
5
f
g
þ
4
˄
f
f
f
¼
1
:
5
f
f
þ
2,
:
The target time at demand point
R
1
was 72 h:
T
R
1
¼
72,
8p
∈P
R
1
:
The decision-maker assigned a higher tardiness penalty to
p
2
in that the
expectation of on-time delivery from the path with the air transportation link was
higher, so the tardiness penalty function at the demand point was:
