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delivery and resilient when disrupted? This last question deals with the design of
a new system, whereas the first two questions deal with an existing system. All of
these are major issues and are addressed in this chapter.
The main optimization models developed to answer these questions can be
classified as follows:
I. Interdiction models . These models identify vulnerabilities of service/supply
systems and quantify the impacts of potential losses of key components on a
system ability to provide efficient service.
II. Protection models . These models optimize the allocation of protective resources
among the facilities of already existent systems.
III. Design models . These models are used for planning new service and supply
systems which are secure and resilient to disruptions.
In this chapter, we will provide a description of the seminal models in each class and
outline how these models have then been further developed and extended to capture
the additional complexities and interdependencies characterizing real service and
supply systems. The description of the models is paralleled by a brief description of
the solution methodologies which have been proposed for solving them.
The reminder of this chapter is organized as follows. Section 24.2 introduces
the notation used throughout the chapter. Interdiction, protection and design models
are described in Sects. 24.3 , 24.4 and 24.5 , respectively. In Sect. 24.6 , we highlight
future trends in modeling location problems under disaster events. Some conclusive
remarks are finally provided in Sect. 24.7 .
24.2
Notation
In the following description of location models under disruption, we assume that
the reader is already familiar with the classic location problems introduced in the
previous chapters (e.g., median, covering, fixed-charge and hub location problems).
Here we briefly summarize the main notation used throughout the chapter.
Inputs
I D Set of potential locations for the facilities, indexed by i
J D Set of customers, indexed by j
F D Set of facilities in an existing system
d j D Demand of customer j
c ij D Unitary cost for serving customer j from facility i
N j D Set of facilities covering customer j (N j I)
p D Number of facilities to be located
r D Number of facilities to be interdicted
b D Number of facilities to be protected
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