Geoscience Reference
In-Depth Information
Location models for planning reliable systems can be broadly grouped into two
main categories which reflect different risk attitudes of the decision maker: risk-
averse and risk-neutral.
24.5.1
Planning for a Risk-Averse Designer
The models in this category identify location strategies for coping with the worst
case in terms of facility loss or disruption. They therefore capture the perspective
of a risk-averse decision maker and are suitable for hedging against deliberate
disruptions and strategic risks. These models typically embed an interdiction model
in a multi-level structure where the upper-level model identifies the optimal location
of the facilities, whereas the lower-level model endogenously generates worse-case
scenario losses.
We illustrate how such location-interdiction models can be formulated by
presenting the Maximal Covering Location-Interdiction Problem (MCLIP). The
idea is to couple the classical Maximal Covering Location problem with the r-ICP
presented in Sect.
24.3
to identify the location of p facilities which maximizes a
weighted combination of (1) the initial coverage and (2) the minimum coverage
level following the loss of the most critical r facilities (O'Hanley and Church
2011
).
The MCLIP model can be formulated as follows:
maximize Ǜ
X
j2J
d
j
u
j
C
.1
Ǜ/H.y/
(24.17)
subject to
X
i2I
y
i
D
p
(24.18)
X
y
i
u
j
8
j
2
J
(24.19)
i2N
j
y
i
2f
0;1
g8
i
2
I
(24.20)
u
j
2f
0;1
g8
j
2
J;
(24.21)
where
H.y/
D
min
X
j2J
d
j
v
j
(24.22)
subject to
X
i2I
s
i
D
r
(24.23)
v
j
y
i
s
i
8
j
2
J;i
2
N
j
(24.24)
s
i
2f
0;1
g8
i
2
I
(24.25)
v
j
2f
0;1
g8
j
2
J:
(24.26)
