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be damaged and rendered un-usable should somehow be considered in prepared-
ness planning. The interdiction approach used in the tri-level model presented in
this paper allows the consideration of “worst-case” damage scenarios, instead of
an expected-value approach. This provides a framework where the trade-offs be-
tween the effectiveness of relief efforts and preparedness costs can be explored as
a function of the extent of damage caused by the disaster.
In the following section, we give a brief literature review. In Section 3, we
present the tri-level programming framework. We show that the framework can
be re-formulated as a bi-level programme in Section 4. For a simplified model,
this can be reduced further to an equivalent mixed-integer programme. In Section
5, we present an iterative dual ascent solution approach using cutting planes. In
Section 6, computational results indicate that our solution approach is ecient
and viable for realistic-sized problems. From these preliminary computations, we
can also draw some insights on disaster relief planning.
2 Brief Literature Review
We give below a brief literature review of papers related to disaster relief op-
erations. The reader is also referred to the following tutorial and review pa-
pers: Tomasini and van Wasenhove (2009), Balcik et al. (2010) and Celik et al.
(2012). Disaster management can be classified into four main stages:
mitigation,
preparedness, response
and
recovery
. In the past two decades, researchers have
investigated problems arising in each of these stages.
Much research on disaster relief operations focussed on evacuation route plan-
ning, for example, Lu et al. (2005). Huang et al. (2012) discussed the importance
of equity considerations in route planning for humanitarian logistics. As early
as 1991, Sherali and Carter (1991) recognized the impact of shelter locations on
evacuation time, and developed a joint location-route planning model. Jia et al.
(2007) presented a scenario-based facility-location model for large-scale emer-
gencies. Doerner et al. (2008) studied a multi-criteria model for public-facility
location in tsunami-prone areas. Some practitioners and researchers have be-
gun to address the ecacy of good preparedness planning on the effectiveness
of response. Rawls and Turnquist (2010, 2011, 2012) considered the issues re-
lated to pre-positioning and delivery of supplies in the immediate aftermath of
the disaster. Balcik and Beamon (2008) considered the network design prob-
lem for relief distribution. Yushimoto and Ukkusuri (2008) considered the lo-
cation and pre-positioning of supplies by considering the reliability of delivery
paths. Bozorgi-Amiri et al. (2012) developed a mixed-integer non-linear pro-
gramming model for location and inventory pre-positioning. Nurre et al. (2012)
considered the problem of restoration of infrastructure post-disaster. Mete and
Zabinsky (2010) developed a stochastic model for the location and delivery of
medical supplies. Some authors have addressed the linkage between asset pre-
positioning and post-disaster logistics deployment (e.g. Salmeron and Apte, 2010;
Doyen, et al., 2012), but these models adopted a stochastic approach by consid-
ering expected cost over all scenarios. Noyan (2012) considered risk-averseness
