Risk assessment and management of civil infrastructure networks: a systems approach - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 449

are fi xed around 350 km so that large clusters are not neglected due to
distance constraints.
The cost is divided into the cost of building and operating support centres,
and the user's cost for accessing the service; the latter is quantifi ed propor-
tionally to the distance travelled by a person and refl ects both the actual
transportation cost and the impact of travelling (i.e., time delay for the
service). Therefore, the objective function from Equation 17.8 becomes:

∑ ∑ ∑ ∑

min cx + p wd [17.11]

hhq a ij ij

hH ∈ qQ ∈ iV ∈ jV ∈

where c h is the cost of installing a support centre of type h ; p a denotes the
number of people to be accommodated; and d ij is the distance between
support centres. The terms in Equation 17.11 account for the aforemen-
tioned parts of the cost:

￿ Installation/operation cost: This is related to the decision variable
x hq that denotes whether alternative h is placed at cluster (fi ctitious
node) q .

￿ User-access cost: This is linked to the decision variable w ij that repre-

sents whether user i is attended at a centre at node j .

A recursive clustering process is carried out in order to fi nd the intrinsic
structure of the network. The algorithm leads to a fi ve-level hierarchy. The
second and fourth levels of the hierarchical decomposition of the proposed
network are shown in Fig. 17.7.
A robustness-oriented simulation is carried out, aiming to estimate the
performance of the designed network due to unforeseen damaging events.
For this purpose, a set of S disasters are simulated and then S solutions for
the resource allocation are obtained by running the optimization algorithm.
For each solution, P additional disastrous events are generated indepen-
dently and the assistance defi cit (AD) of the network is computed as the
amount of people unattended for each event. Monte Carlo simulation was
used; however, more powerful alternatives can be used. Figure 17.8 shows
the strategy for generating disastrous events, as well as the obtained solu-
tions with a heuristic variation of the linear programming and the hierarchi-
cal approach.
Qualitatively, the solution for the proposed approach exhibits greater
decentralization; i.e., the clustering structure of the network is refl ected and
groups with different scales appear in the solution according to optimality.
This fact is important, because it enhances properties, such as robustness
and scalability in the solution.
The formulation of the linear program with the proposed approach
helps reduce the computational burden, i.e., fewer decision variables are
considered by using only the centroids as candidate solutions. Moreover,