Geoscience Reference
In-Depth Information
i
i
;
i
2
I;j
2
J (17.57)
x
ij
0
I
i
0
I
y
i
2f
0;1
gI
integer
;
i
2
I;j
2
J: (17.58)
The objective function (
17.44
)-(
17.47
) represents the total profit which includes
the revenue, travel, congestion, and facility fixed and capacity costs, respectively.
Constraints (
17.48
) define the expected waiting time for M/G/1 queues. These
can be substituted with constraints defining other relevant congestion measures,
different queueing mechanisms or both. Specifications (
17.49
) are only relevant
for elastic demand models of type DR and FR type; when the demand rate is
assumed to be inelastic, one should omit these and set
j
D
ma
j
. Similarly,
specifications (
17.50
) are only relevant for user-choice models of AR and FR
type. Constraints (
17.53
)-(
17.57
) enforce the basic interconnections between the
decisions variables and are typically present in some form in all models.
To the best of our knowledge, no published work contains all components listed
in the general formulation above. The specific SLCIS models considered in the
literature typically include only some of the terms in the objective function, differ in
terms of the queueing assumptions and performance measures, as well as in which
(if any) of the specifications (
17.49
)-(
17.52
) to include. The models also differ in
terms of the decision variables. While variables y
i
and x
ij
are present in all models
we are familiar with (though x
ij
may be restricted to binary values only), most
models will assume that the number of facilities is m and not a decision variable.
Many models also assume that all facilities have identical capacity , thus dropping
the decision variables
i
as well.
It is clear that the variety of SLCIS models one can define by mixing and
matching different parts of the general formulation above is almost unlimited. In the
next section we try to bring some structure to the models considered in the literature
by grouping them around some common themes and describing the key challenges
and solution techniques that have been developed for them.
17.5
SLCIS Models in the Literature: Overview
and Classification
Our primary focus (with a few exceptions) is on relatively recent SLCIS models that
have appeared since the survey of Boffey et al. (
2006
).
As noted earlier, the published SLCIS models constitute a rather bewildering
pattern of different assumptions, constraints and response mechanisms. However,
several common themes do emerge, allowing us to identify four common types
of models: Coverage-Oriented, Service-Objective, Balanced-objective, and Explicit
Customer Response. These are described in more details in the following sections.
The relevant references are summarized in Tables
17.2
,
17.3
,and
17.4
.These
tables have the following format: the first column identifies the reference by the
list of authors/year of publication; the next two columns identify the Model Class
