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model is the set of assumptions made about how customers and facilities interact,
specifically how customer demand is “allocated” to facilities and how much of
the potentially available demand is “captured”. These issues are explored in detail
in Sect. 17.3 , where we also introduce a classification of SLCIS models based on
the types of customer response. All model components come together in Sect. 17.4
where we formulate a “general” SLCIS model and review the main features that are
typically included in various sub-classes. In Sect. 17.5 we provide an overview of
SLCIS models discussed in the literature, providing a unifying structure organized
around four main “themes”. We also discuss the key challenges that arise for
different model classes and computational approaches that have been developed.
In the last section we discuss conclusions and suggestions for future research.
17.2
Key Model Components
As noted earlier, SLCIS models describe the system consisting of customers,
facilities and their interactions. We start by describing each of these components
in more detail.
17.2.1
Customers
Customers are assumed to be located in a set J, with customer location j 2 J
capable of generating a demand stream with maximum intensity of ma j per unit
time. In the vast majority of models described in the literature, J isassumedtobe
a discrete set, often conceptualized as the set of nodes of some underlying network
G D .J;A/,whereA is the set of links. Other common alternatives in location
(but not in SLCIS) literature include J being a sub-region of the real plane R 2 ,or
consisting of both links and nodes of a network G. The most general SLCIS setting
we are aware of is given in Baron et al. ( 2008 ), where J is a bounded sub-space of
R N and can contain a mixture of discrete points and continuous regions. To keep
the presentation as transparent as possible, we will retain the common assumption
that J is discrete and n Dj J j is the number of customer demand points, which we
will frequently refer to as “nodes”.
Let u j represents the utility derived by customers at node j 2 J from services
offered by the facilities. The demand stream generated by j is assumed to be a
Poisson process with rate . u j / 2 Œ0; ma j . We will postpone the description of
utility functions until Sect. 17.3.1 , since other system components need to be defined
first. However, we can already identify two different classes of SLCIS models: the
elastic demand models, where . u j / is a non-constant function, i.e., . u j / 6D max
j
for some values of u j ,andthe inelastic demand models where the demand rate is
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