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Fig. 12.2
Structure of a cycle-star ( a ), star-star ( b ), tree-star ( c ), and line-star ( d ) hub network
Klincewicz ( 1998 )andYamanetal.( 2007 ) consider multi-stop access paths that
may visit more than one O/D nodes on the way to a hub node. Nagi and Salhi ( 1998 ),
Camargo et al. ( 2013 ), Rodríguez-Martín et al. ( 2014 ), and Rieck et al. ( 2014 ) study
problems in which collection and distribution tours have to be designed. Thomadsen
and Larsen ( 2007 ) and Saboury et al. ( 2013 ) describe HLPs in which both the
backbone and access networks are fully interconnected. Figure 12.3 shows some
examples of various access network structures.
12.4.2
Modeling Flow Costs
The assumption of flow-independent discounted costs (Assumption 3) is most
appropriate in applications where hub arcs are associated with faster transportation
modes. However, this can be an oversimplification in applications where the costs
represent the economies of scale due to the bundling of flows on the hub arcs.
For instance, this assumption could lead to solution networks where hub arcs send
considerable less flow than access arcs, yet the flow cost is only discounted on the
hub arcs. It may also happen that the amount of flow that is actually routed on each
hub arc is quite variable, yet the same discount factor is always applied. For these
 
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