Information Technology Reference
In-Depth Information
The righthand side of constraint (8) is the maximum number of centres destroyed
by the disaster, which can be considered as a parameter for the severity of the
damage, on which sensitivity analysis can be performed. Constraints (9) state
that a centre is not destroyed unless it has been established (in the first level).
The third level represents the response and recovery stage after the disaster,
where the decisions involve (re-)establishment of evacuation centres, re-supply
and/or transfer of goods to/between centres, and re-allocation of people to the
centres. It is formulated as follows.
r,u,s,t,w RecoveryCost ( x, y, z ; δ ; r, u, s, t )=
i∈I
( F i u i + H i s i )+
i∈I
( L3 ): min
T ik t ik
k∈I
( y i
δ i )
u i ,
i
I,
subject to
1
(11)
r ij
j
J,
=1
(12)
i
I
u i +( y i
δ i )
r ij
i
I,j
J,
(13)
C i ( y i
δ i )
w i
i
I,
(14)
w i
z i
i
I,
(15)
t ik
w i
i
I,
(16)
k∈J
w i + s i +
k∈J
t ki
t ik
p j r ij
i
I,
(17)
k∈J
j∈J
u i
∈{
0 , 1
}∀
i
I,
(18)
r ij ,t ik ,s i ,w i
0
i,k
I,j
J.
(19)
The RecoveryCost includes cost of (re-)establishing centres and cost of supplying
and transhipping inventory to and among operational centres, in order to cover
the population accommodated at the centres. Constraint (11) states that a centre
canbeestablishedinalocationnotpreviouslyusedorinalocationwherean
established centre has been destroyed. Constraints (12) and (13) indicate in
which evacuation centres (that are operational post-disaster) the population for
each community should be accommodated. In this level, the population of each
community may be split among several centres. The variables w j with constraints
(14) and (15) determine how much inventory is available post-disaster; we assume
all inventory is rendered unusable if a centre is destroyed. Finally, constraints
(17) ensure that the inventory at each centre (including existing, newly-supplied
and transhipped) is sucient to support the population accommodated at the
centre post-disaster.
The linkage between the three levels of the formulation is via the Recov-
eryCost post-disaster. The rationale for the formulation is that the decisions at
the preparedness stage (in the first level) should anticipate the recovery cost
post-disaster. Our formulation also takes an interdiction approach rather than
an expected-value or chance-constrained approach in modelling the disaster.
Probability-based formulations are much affected by the pool of scenarios con-
sidered and their associated probabilities, which may be dicult to ascertain for
 
Search WWH ::




Custom Search