Geoscience Reference
In-Depth Information
p
-Hub Median Problems
assume that the number of hubs to locate is given as an
input of the problem. They consist of locating a set of p hub facilities with the
objective of minimizing the total flow cost for routing the flows through the hub
network.
Hub Location Problems
consider that the number of hubs to locate is not known
a priori, but a fixed set-up cost for each hub is considered. The objective is to
minimize the sum of hub fixed costs and of demand flow costs over the hub
network.
p
-Hub Center Problems
are minmax problems that focus on the minimization of
a maximum service or cost measure between O/D pairs. Some of these measures
are:
(i)
the maximum flow cost (or travel time) of all O/D pairs,
(ii)
the maximum
flow cost (or travel time) of all arcs of the hub network, and
(iii)
the maximum
flow cost (or travel time) associated with an access arc.
Hub Covering Problems
impose a maximum threshold value on the service level
(travel time) and focus on the minimization of the set-up cost of the hub network.
They assume demand is covered if both origin and destination nodes are within
a specified distance of a hub node. They differ on their considered coverage
criteria. An O/D pair .i;j/ is covered by hubs k and m if:
(i)
the length of the
path .i;k;m;j/is within a specified value,
(ii)
the length of each arc in the path
.i;k;m;j/does not exceed a specified value, or
(iii)
each of the access arcs meet
different specified values.
Both single and multiple assignment models, as well as uncapacitated and
capacitated models have been considered in the literature for most of these classical
objectives. We refer to Campbell (
1994a
), Campbell et al. (
2001
), and Alumur and
Kara (
2008
) for a detailed overview of these models.
HLPs considering more complex classes of objective functions have also been
studied. Costa et al. (
2008
) and Köksalan and Soylu (
2010
) consider HLPS with
multiple objectives. Puerto et al. (
2011
) introduce a general class of HLPs that
consider an ordered median function (see Chap. 10) for which the above mentioned
objectives (and others) are particular cases. O'Kelly (
2012
) considers objectives
related to the fuel burn and environmental impact in airline hub networks. Campbell
and O'Kelly (
2012
) review some recent HLPs that integrate both cost and service
objectives.
12.3
Formulating Hub Location Problems
One of the major modeling challenges in HLPs is that knowing the hub network
structure is not necessarily sufficient to evaluate the objective function. Formula-
tions must be able to model the path used for routing each flow to determine the
flow cost. Significant progress has been made toward the development of
Mixed
Integer Programming
(MIP) formulations for fundamental HLPs. These exploit
the structure of the solution network obtained when considering the modeling
