Geoscience Reference
In-Depth Information
second assumes that uncertainty is given by a single parameter equally influencing
the flow cost for all links of the network. The third considers the more general
case in which the uncertainty of transportation costs is independent for each link
of the network. the authors show that the first to variants are equivalent to their
associated expected value problem in which uncertain amount of flows and flow
costs are replaced with their expected value. However, this equivalence does not
hold for the third case. Alumur et al. (
2012b
) consider HLPs under uncertainty in
the set-up cost for the location of hubs and in the demand flows for both single
and multiple assignments models. The first class of models deals with uncertainty
on the set-up costs in the absence of a known probability distribution for these
random parameters. The authors propose the use of a minimax regret model in
which the objective is to minimize the worst-case regret over a finite set of scenarios.
The second class considers uncertainty on the demand flows and uses a two-stage
stochastic program with recourse. However, as shown in Contreras et al. (
2011a
)
these problems are equivalent to their associated expected value problem. The third
class considers uncertainty in both set-up costs and demand flows and are modeled
as two-stage minmax regret programs with recourse.
Demand uncertainty has also been studied in hub location from a congestion
perspective. When demand flows increase unexpectedly within a short time, they
are likely to congest the hub network. This causes an increase in the operational
cost of the network due to delays at hub facilities. Elhedhli and Hu (
2005
)present
a single allocation hub location model that considers hub congestion-related costs
as an exponential function of the hub flow. Camargo et al. (
2009
) propose the
multiple allocation analogue of the previous model. Elhedhli and Wu (
2010
) study
a different approach in which the hub network is modeled as a network of M=M=1
queues where each hub behaves as a single server with a given exponential service
rate determined by its capacity. The congestion cost is modeled using a Kleinrock
average delay function. Camargo and Miranda (
2012
) provide extensions to the
previous single allocation models by considering two different perspectives: a
network owner perspective in which the goal is to design a hub network with the
least congestion cost, and a user perspective in which the goal is to minimize the
maximum congestion effect.
An important uncertainty aspect neglected until very recently is the reliability of
hub networks. Kim and O'Kelly (
2009
) presents a reliable p-hub location problem
arising in the design of telecommunication networks. This problem considers
the reliability of O/D paths by taking into account the probability of successful
communication to deliver traffic without congestion or loss between O/D pairs. It
focuses on maximizing the total network flow that can be routed when incorporating
the reliability of O/D paths. An et al. (
2011
) and Aziz et al. (
2014
) study models
in which disruptions at hub nodes are taken into account when designing the hub
network. The proposed models mitigate the resulting hub unavailability by using
backup hubs and alternative routes for demand flows. The objective of this model
is to minimize the total expected flow cost considering both the regular and the
disruptive situation.
