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emergency, including the exceedingly variable demand of the warehouse supply items
[18]. The model allows for two types of order lot sizes: Q
1
for a regular order and Q
2
for an urgent order. Q
1
is ordered when the inventory reaches level r
1
and Q
2
is ordered
when the inventory level reaches r
2
, where r
1
> r
2
.
A Markovian process is also used to solve the demand distribution of inventory.
This idea is initiated by Karlin and Fabens [19], claiming that if each demand state is
defined by different numbers, a base stock type inventory policy can be obtained.
Taskin and Lodree [20] use stochastic programming to determine an optimal order
policy so that the demand in each pre-hurricane season period is met, and reserve
supplies are stored for the ensuing hurricane season, in a cost-effective way.
Bryson et al. [12] use optimal and heuristic approaches to solve a number of hypo-
thetical problems. Mixed integer programming is applied to establish the disaster
recovery capability of an organisation. The aim of the model is to determine the
resources that should be used in order to maximise the total expected value of the
recovery capability. The use of mathematical modelling provides an appropriate deci-
sion support tool for the successful development of a Disaster Recovery Plan (DRP).
This model provides a generic approach which considers different types of resources
required to satisfy demand induced by any relevant disaster.
Various models have been developed and applied to the SADC countries [13,20].
VanWyk et al. [13] apply a stochastic inventory model to the SADC countries to ob-
tain the quantities of aid supplies to keep at an acceptable minimum cost. Van Wyk et
al. [22] developed a mixed integer decision model which selects sub-plans to supply a
country with immediate disaster relief. In addition, a Euclidean Distance Algorithm
was formulated to determine the most similar case when compared to a target case
disaster [22].
The research done for disaster management problems and specifically the SADC
applications, provide useful methods, but only limited research considers case studies
applicable to developing countries. This research is aimed at focusing on the capacity
required to ensure that a sufficient area within Somalia is covered by a pre-positioning
facility. It is therefore a good starting point to develop an innovative model to deter-
mine the capacity required to ensure that a sufficient area within Somalia is covered
by the pre-positioned facility.
2.3
Preemptive Multiobjective Programming
Rardin [23] explains that although practical problems almost always involve more
than one measure of solution merit, many can be modelled quite satisfactorily with a
single cost or profit objective. Other criteria are either presented as constraints or
weighted in a composite objective function to produce a model efficient enough for
productive analysis. Many applications such as those in disaster management must be
treated as multiobjective. When goals cannot be reduced to a similar scale of cost or
benefit, trade-offs have to be addressed. To obtain useful results from such a problem,
the multiobjective model must be reduced to a sequence of single objective optimiza-
tions [23]. This leads to preemptive multiobjective optimization by considering
