Geoscience Reference
In-Depth Information
Capacitated versions of HLPs with single assignment have also been studied by
Campbell (
1994b
), Ernst and Krishnamoorthy (
1999
), Labbé et al. (
2005
), Correia
et al. (
2010
), Contreras et al. (
2009a
), and Contreras et al. (
2011d
). All these models
only consider capacity constraints on the incoming or outgoing flow at the hub
nodes. Aykin (
1994
,
1995
) have considered HLPs with capacity constraints on the
incoming flow at the hubs as well as on direct O/D links. Carello et al. (
2004
),
Yaman and Carello (
2005
)andYaman(
2008
) have studied capacitated HLPs with
modular link capacities. They considered capacity constraints on the incoming and
outgoing flow at hubs.
All of the above mentioned capacitated models consider that both hub and
arc capacities are exogenous, i.e. capacity levels for potential hub nodes and hub
arcs are determined a priori. Given that capacities can have a determining impact
on locational and routing decisions, some researchers have started studying more
realistic capacitated models in which the amount of installed capacity is part of the
decision process. Correia et al. (
2010
) studied an extension of capacitated HLPs with
single assignment in which the hub capacity is a decision variable. Elhedhli and Wu
(
2010
) introduced a capacitated model in which hub capacity is also a decision
variable. Contreras et al. (
2012
) presented models with multiple assignments in
which the amount of capacity installed at the hubs is part of the decision process,
for both splittable and non-splittable commodity cases.
12.4.4
Uncertainty in Hub Location
The design of hub networks corresponds to long-term strategic decisions which
are typically made within an uncertain environment. That is, costs, demands,
distances, and other parameters may change after location and network design
decisions have been made. Nevertheless, most HLPs treat data as known and
deterministic. This can result in highly sub-optimal solutions given the inherent
uncertainty surrounding future conditions. Some researchers have thus started to
study how different uncertainty aspects can be taken into account when designing
hub networks.
Marianov and Serra (
2003
) is probably the first paper dealing with uncertainty,
focusing on stochasticity at the hub nodes by representing hub airports as M=D=c
queues and limiting through chance constraints the number of airplanes that can
queue at an airport. Sim et al. (
2009
) introduce the stochastic p-hub center problem
and employ a chance-constrained formulation to model the minimum service-level
requirement. This model takes into account the variability in travel times when
designing the hub network so that the maximum travel time through the network
is minimized.
Contreras et al. (
2011a
) study how the classical UHLPMA can be modeled as a
two-stage integer stochastic program with recourse in the presence of uncertainty
on demands and flow costs. In particular, three different stochastic versions are
introduced. The first considers the flow between O/D nodes to be stochastic. The
