Information Technology Reference
In-Depth Information
Thus, our results indicate that a model that considers recovery cost post-disaster
adds only a modest amount of computation time compared to one that considers
only pre-positioning and location costs pre-disaster.
6.3 Computational Study: Insights
In this section, we present some insights drawn from the computational results.
We illustrate our findings with Instances 1a-c with
= 50;
similar results are observed for the other problem sizes. Figure 1 depicts the
optimal solutions for
D
=0
,
3
,
6 and 9. The established evacuation centres are
denoted by red squares, unused evacuation centre locations by green triangles,
and communities by blue circles. The size of a node is proportional to its capacity
or population size. A blue edge connects a community to its assigned centre.
Note that, in an optimal solution, an established centre carries pre-positioned
inventory if and only if there is a blue edge connecting it to a community. In
Figure 1.a, an evacuation centre is labelled with its cost per unit of inventory
pre-positioned; in Figures 1.b to 1.d, the label indicates the cost per unit of
delivering inventory post-disaster.
|
I
|
=30and
|
J
|
1000
1000
10
36
10
44
2
50
1
31
37
1
800
800
26
4
2
9
9
50
600
9
600
5
4
24
3
7
3
16
9
24
17
8
9
15
2
43
8
35
33
400
6
400
5
8
24
4
6
43
1
48
200
200
7
4
13
22
3
4
10
44
6
8
15
1
7
45
7
48
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
a.
D
=0
b.
D
=3
1000
1000
36
44
36
44
50
50
31
37
31
37
800
800
26
26
9
50
600
5
9
50
600
5
24
7
16
24
7
16
24
17
17
24
15
15
43
43
400
35
33
35
33
400
8
8
24
24
43
43
48
48
200
200
13
45
22
13
22
4
4
44
44
6
6
15
15
45
48
48
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
c.
D
=6
d.
D
=9
Fig. 1.
The locations for the case
|I|
=30
, |J|
=50
Note that the case of
D
= 0 (Figure 1.a) corresponds to (
RM
) without con-
straints (23), that is, when the recovery costs are not considered. In this case,
when no disaster strikes (
D
= 0), the optimal solution has fewer evacuation cen-
tres established to reduce fixed costs and tends to establish evacuation centres of
