Geoscience Reference
In-Depth Information
(
24.13
) with a budget constraint and assume that the facilities have different protec-
tion costs and flexible capacity (i.e., the capacity can be expanded to accommodate
the demand of customers previously assigned to interdicted facilities).
Another interesting variation of the r-IMPF is the problem investigated by
Liberatore et al. (
2012
), which optimizes protection plans in the face of large
area disruptions. The problem includes capacitated facilities, partial interdiction
(interdiction reduces the amount of demand that can be served by a facility) and
correlated disruptions (when a facility is hit, nearby facilities are affected as well).
The problem was formulated as a tri-level program, and solved by dualization
integrated in the implicit enumeration algorithm devised by Scaparra and Church
(
2008a
)forther-IMPF.
All the problems cited so far are static which means that they do not consider
the effect of disruptions over time. In reality, disrupted facilities may have different
recovery times and the duration over which system operations are degraded should
be considered when modeling worst-case disruption scenarios. To redress this
shortcoming, Losada et al. (
2012a
) proposed a different protection model for median
systems where protection does not necessarily prevent facility failure altogether, but
speeds up recovery time following a potential disruption. The resulting model also
incorporates the possibility of multiple disruptions over time and is solved using
three different decomposition approaches.
An underlying assumption of the r-IMPF and all its variations is that protection
is always successful and, therefore, protected facilities are never interdicted in a
worst-case scenario. Bricha and Nourelfath (
2013
) relaxed this assumption and
proposed a model where a protected facility is immune to disruption only with a
given probability. The initial model was then extended to consider protection against
concerted attacks by multiple interdictors.
Whereas most of the focus has been on protection models for median systems,
Zhu et al. (
2013
) proposed a game theoretical model to identify optimal defense
strategies for an uncapacitated fixed-charge location model. In this model, the
defender has several investment strategies (or levels of investment) available and
aims at minimizing the expected damage to the systems along with the protection
expenditure. Similarly, the interdictor can choose different attack levels on each
facility and aims at maximizing a utility function, which combines damage and
attack expenditures.
24.5
Planning Robust Systems: Design Models
Hardening existing facilities can be an effective way of mitigating the impact of
facility failures. An alternative approach is to incorporate the risks of potential
failures in the initial design of a system by identifying location strategies which
are both cost-efficient and robust to external disruptions. Several studies have
demonstrated that significant improvements in reliability can often be obtained
without significant increases in operating costs (Snyder and Daskin
2005
).
