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a related hub covering problem to locate two types of hub nodes and hub arcs
associated with ground and air transportation. The model uses a cost-oriented
objective while ensuring time-definite deliveries.
12.4.6
Competition and Collaboration
Most HLPs studies assume that the decision maker is a monopolist firm in a
market and thus can capture all demand flow in the market, regardless of the
design of the hub network. As a result, location and network design decisions
are usually determined by the firm's cost-based objective without taking into
account customer preferences. However, in practice many telecommunication and
transportation networks operate in a competitive environment where several firms
exist in a market and compete to provide service to customers. Customers must
determine which competing firm to use based on several criteria such as the travel
time and the costs charged. Competitive hub location models focus on the design
of hub networks so as to maximize the market share of competing firms. In these
models, customers (or demand flow) are captured from competitor's hub networks
whenever the new hub network offers a reduction of the travel time or distance
needed by the customers to go from their origins to their destinations.
Most competitive hub location models use a sequential location approach, in
which an existing company (the leader) serves the demand flow in a region, and a
new company (the follower) wants to enter the market and will attempt to capture
the maximum possible demand and thus, maximize its market share. Marianov et al.
(
1999
) introduce competitive hub location models in which the follower wants to
locate a set of hub nodes so as to maximize the captured demand flow. In the first
proposed model it is assumed that demand is fully captured when the flow cost
does not exceed the current competitor's cost. The second model considers a more
realistic version in which a stepwise linear function is used to model the proportion
of demand captured depending on the new flow cost as compared to the competitor's
cost. In both models, at most one path is used to route flow between each O/D pair.
Wagner (
2008b
) points out that if the new company is assumed to capture demand
flow when its flow cost is equal to the current competitor's cost, then the optimal
solution is always to locate a hub node in each location where the leader has one,
making the new company to capture all demand. Therefore, the author suggests
modifying the definition of the problem so that demand is captured by the follower
if and only if the new cost is strictly smaller than the competitor's cost. Eiselt
and Marianov (
2009
) provide an extension to the models presented in Marianov
et al. (
1999
), in which each competitor can have more than one path between O/D
pairs. The proportion of flow that is captured on a particular path is modeled with
a gravity-like attraction function that does not only depend on the flow cost but
also on the travel time. Gelareh et al. (
2010
) present a competitive model arising
in liner shipping networks, where a new liner service provider wants to design a
hub network to maximize its market share, using an stepwise attraction function
