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Multilayer network design with design connectivity: arc a in layer l is supported by the path made of arcs cand d in layer l, and arc b in layer l is supported by the path made of arcs e, f, and d
Contexts in source publication
Context 1
... first type of coupling requirements and constraints, design connectivity, means that an arc opened in a given layer requires some arcs to be opened in another layer. An illustration is given in Figure 1, where arcs a and b in layer l are supported, respectively, by paths (c, d ) and (e, f, emphd) in layer l. Therefore, l is supported by l, and l is supporting l . ...
Context 2
... design-capacity constraint of arc b in supporting layer l limits the number of selected arcs in supported layer l for which arc b is the supporting arc. To illustrate, let the design-capacity of arc d in layer l in Figure 1 be equal to 1, which implies that at most one of the arcs a or bin layer l may be opened in a feasible solution. To further illustrate, a design-capacity constraint is defined for each potential service in the integrated freight rail service network design problem, limiting the number of selected blocks for the service may carry, i.e., for which it may be the supporting service. ...
Context 3
... simplest such constraint arises when the flow on arc b is equal to the summation of the flows on all arcs for which b is a supporting arc. In Figure 1, for example, the flow on arc d would be equal to the summation of the flows on arcs a and b. Note that, with this particular type of flow-connectivity requirements, when only one layer has commodities to route, the flows on other layers can be deduced from the flows on that single layer. ...
Context 4
... B al l be the set of arcs in layer l supported by arc a ∈ A l . For example, in Figure 1, this set for arc 4 in layer l is {1, 2}. Let D l bl be the set of arcs in layer l supporting arc b ∈ A l . ...
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