Information Technology Reference
In-Depth Information
objectives one at a time. The most important objective is optimized subject to a re-
quirement that the first has achieved its optimal value; and so on [23].
The preemptive approach to multiobjective optimization is that it results in solu-
tions that cannot be improved in one objective without degrading another. If each
stage of the preemptive optimization yields a single-objective optimum, the final solu-
tion is an efficient point of the full multi-objective model. The preemptive process
uses one objective function at a time to improve one without worsening others. At the
completion of this process, no further improvement is possible. As usual, infeasible
and unbounded cases can produce complications, but the typical outcome is an
efficient point [23].
3
Research Methodology
3.1
Preemptive Optimization
Humanitarian relief organizations aim to provide relief for as many disaster victims as
possible, subject to limited funding. It is therefore useful to consider a model that
helps the decision-maker with inventory decisions at the lowest possible cost. The
notation of the preemptive model [6] for Somalia is addressed below:
1 if aid supply i is required for disaster k
0 otherwise
x
ik
q
k
The probability that disaster
k
will occur
n
k
The number of people affected by disaster
k
c
i
The unit cost of aid supply
i
h
i
The holding cost of supply
i
s
i
The number of people affected if supply
i
is not available
The number of people affected if supply
i
is not available
u
i
v
i
The number of aid supply
i
in excess
Q
i
The number of aid supply
i
required
(1)
(2)
The objective functions have been formulated as follows:
Q
i
c
i
+
h
i
v
i
I
i
=
min Z
1
=
1
s
i
u
i
I
i
min Z
2
=
=
1
s.t.
,
i
∈ I
(3)
xnq
s
K
ki
k
k
Q
i
-
v
i
+
u
i
=
k
=
1
i
