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Our model, in contrast to much of the above cited literature, does not consider
targets for cost; instead, it minimizes the total operational costs of the activities in
the supply chain network. This, we believe, makes more sense in that the relief
operations budget largely depends on the intensity of damage and the fatality toll
which may be difficult be determine a priori. In addition, our model—unlike the
aforementioned ones—allows for the pre-disaster and the post-disaster procure-
ment of relief items, and involves the time and the cost associated with each
strategy or a combination of both. Moreover, we handle nonlinear costs, which
capture congestion effects, a big issue in disaster relief, and an aspect that has been
missing from much of the literature on the topic (cf. Haghani and Oh 1996 ).
The organization of this paper is as follows. In Sect. 15.2 , we present the supply
chain network topology of the disaster relief organization, construct the optimiza-
tion problem, and establish its variational inequality formulation which provides us
with nice computational features. We also present several illustrative numerical
examples and conduct sensitivity analysis. In Sect. 15.3 , we propose an algorithm
that, when applied, computes the incurred optimal levels of disaster relief product
flows in the supply chain network as well as the optimal path time deviations. The
algorithm is then used to solve a large-scale numerical example in Sect. 15.4 , along
with a variant. In Sect. 15.5 , we summarize the results and present our conclusions.
15.2
The Integrated Disaster Relief Supply Chain Network
Model
In this section, we develop the integrated disaster relief supply chain network
model. We mention that, depending on the structure of the specific disaster relief
(humanitarian) organization, the scale/intensity of the disaster, and the region or the
country that the disaster takes place in, the supply chain network may vary in
specific details. Nevertheless, the general framework of the majority of non-profit
disaster aid organizations follows a pattern similar to the one that we describe
below.
15.2.1 Components of the Disaster Relief Supply Chain Network
The disaster relief supply chain network model, as we shall demonstrate, captures
both the preparedness phase and the response phase of the disaster management
cycle (with the other two phases being mitigation and recovery ) (Tomasini and Van
Wassenhove 2009 ). We take into account the pre-disaster preparations including
the procurement, the pre-positioning, and the storage of disaster relief items given
the estimated demand in disaster-prone areas. We also take into consideration the
relevant issues surrounding the transportation and the ultimate distribution of the
relief goods to the demand points once a potential disaster takes place. Furthermore,
the case where an organization procures the humanitarian aid items after the
occurrence of a disaster is also integrated into our model.
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