Geoscience Reference
In-Depth Information
Decision variables
y
i
D
1 if a facility is located at site i
0 otherwise
s
i
D
1 if a facility located at i is interdicted
0 otherwise
z
i
D
1 if a facility located at i is protected
0 otherwise
x
ij
D
1 if the demand of customer j is supplied from facility i
0 otherwise
u
j
D
1 if customer j is covered before disruption
0 otherwise
v
j
D
1 if customer j is covered after disruption
0 otherwise
24.3
Identifying Critical Facilities: Interdiction Models
Interdiction models date back a few decades and were originally designed to assess
the impact of losing critical links in transportation networks for military applications
(see, for example, Wollmer
1964
and Wood
1993
). The first interdiction models
within the facility location literature were introduced by Church et al. (
2004
)
to identify the most critical facility assets in median and covering systems. The
first problem, called the r-Interdiction Median Problem (r-IMP), can be seen as
the antithesis of the p-median problem and aims at identifying the best set of r
facilities to remove, among the existing ones, in order to maximize the overall
demand-weighted cost for serving the customers from the remaining facilities
(these are referred to as non-interdicted facilities). Similarly, the r-Interdiction
Covering Problem (r-ICP) can be seen as the antithesis of the maximal covering
problem and involves finding the subset of r facilities, which when removed,
minimizes the total demand that can be covered within a specified distance or
travel time. In essence, both models identify the subset of facilities whose loss
has the greatest impact on service delivery, where the impact is measured either
in terms of cost increase or in terms of lost coverage to mirror two different service
protocols.
