Civil Engineering Reference
In-Depth Information
subject to:
{
}
=
(
[
)
]
R
n
Γ
=∈
γ
:
γ
fGVE
,
,
Θ
[17.9]
g
g
{
}
=
() ()
[
]
kk k
=∈
R
n
:
fTG RG
,
[17.10]
k
k
where
Cb
i
is the cost of the
i
th facility (out of
M
facilities) and
Ca
j
is the
cost for the
j
th user (out of
n
users); and
are the sets of operational
and hierarchical constraints, respectively. The fi rst set is associated with
issues, such as specifi c costs, and maximum allowed distances and capacities,
whereas the second one deals with topological features, such as centroid
mapping and conditions within the hierarchy. For this reason, the con-
straints
Γ
and
κ
γ
g
are (linear) functions of the graph itself (
G
) and a set of attributes
κ
k
depend on the
tree representing the hierarchical structure of the graph (
T
(
G
)) and the
distribution of centroids (
R
(
G
)). Notice that an essential constraint is that
users are assigned only to installed support centres. See Gómez
et al.
(2011d)
for details on the hierarchical constraints.
Θ
(e.g., costs, distances, capacities), whilst the constraints
17.5.3 Illustrative example
Consider a variation of the CFLP. The objective is to provide a support
network for victims after a major earthquake disaster. A transportation
network with 64 nodes (urban regions) and a diameter of approximately
1500 km is generated by using the Delaunay triangulation algorithm
(Khanban
et al.
, 2002). The population associated with every node was
assigned based on a random function. Earthquake scenarios (i.e., assistance
demand) are generated randomly.
The aim of the model is to minimize the cost of installing support centres
throughout the network such that the demand is satisfi ed at every node.
Additionally, the designed support network must cover a percentage
(e.g.,
20%) of the population, even if the demand is below that level; this is
enforced so that a minimum level of assistance is guaranteed everywhere
for the sake of robustness.
Then, a solution is designed for a specifi c disaster, whose performance is
measured in terms of the assistance defi cit when faced with new disasters;
assistance defi cit is computed as the difference between the demand (popu-
lation affected) and the availability of services provided (i.e., available
capacity of the support designed network).
The decision-making problem focuses on allocating two types of centres
with different capacities: type-1 centres have greater capacity than type-2
centres. Additionally, in order to complete the support network, type-2
centres must be connected to a type-1 centre within a distance
d
1
, and users
must be connected to at least one centre within a distance
d
2
; these distances
λ
Search WWH ::
Custom Search