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by using conditional Value-at-risk as the risk measure. O'Hanley and Church
(2011) is one of the few papers that takes an interdiction (worse-case) approach
when considering location of emergency facilities. As far as we know, no system-
atic optimization-based approach exists that provides an anticipatory tri-level
framework as the one presented in this paper.
3Mod lFormu on
In this section, we present a formulation for the tri-level disaster preparedness
planning model. The first and third levels correspond to decision-making in
the preparedness stage and the response/recovery stage, respectively, while the
second level corresponds to the damage inflicted by the disaster. The three levels
are linked by the fact that decisions at each level are affected by decisions taken
in the previous level, and also the fact that the objectives anticipate subsequent
costs. Our model includes the following
parameters and sets:
I
= the set of possible locations for evacuation centres,
J
= the set of communities,
p
j
= size of population of community
j
,
d
ij
= distance from community
j
to location
i
,
C
i
= capacity of evacuation centre at location
i
,
m
= maximum distance between a community and its assigned centre,
E
= maximum number of evacuation centres to be established,
f
i
= fixed cost of establishing an evacuation centre at location
i
,
h
i
= cost per unit of inventory pre-positioned at location
i
,
D
= number of evacuation centres destroyed by the disaster,
F
i
= fixed cost of (re)-establishing a centre at location
i
post-disaster,
H
i
= cost per unit of delivering inventory to location
i
post-disaster, and
T
ik
= cost per unit of transferring inventory from location
i
to
k
post-disaster;
and the following binary and continuous
decision variables:
x
ij
=
1 if community
j
is assigned to evacuation centre in location
i
,
0otherwise;
y
i
=
1, if an evacuation centre is established in location
i
,
0, otherwise;
z
i
= amount of inventory pre-positioned in location
i
,
δ
i
=
1, if the evacuation centre in location
i
is destroyed by the disaster,
0, otherwise;
u
i
=
1 if an evacuation centre is (re-)established in location
i
post-disaster,
0otherwise;
r
ij
= proportion of population of community
j
(re-)assigned to location
i
post-disaster,
w
i
= amount of inventory available in location
i
post-disaster,
s
i
= amount of new inventory supplied to location
i
post-disaster, and
t
ik
= amount of inventory transferred from location
i
to location
k
post-disaster.
