Vehicle routing on road networks: How good is Euclidean approximation?

Fast upper and lower bounds for a large‐scale real‐world arc routing problem

“…Figure 1(b) shows the corresponding digraph G ′ , before we remove any arcs from A 2 . We see that the arc (12,11) is in A 2 , yet both of its nodes are in the same R-component. So, this arc will be removed from G ′ .…”

“…The costs are also indicated on the links. Suppose that the first two phases have produced a giant tour which traverses the required links in the order (1, 2), (3,4), (8,9), (9,10), (13,12), (12,11). Figure 1(b) shows the corresponding digraph G ′ , before we remove any arcs from A 2 .…”

“…Figure 1(g) represents the sparsified version of G ′ , which only contains required arcs and deadheading arcs corresponding to edges in the reduced MST. One can check that links (4, 7), (7,12) and (11,8) form the minimum cost amount of extra deadheading needed to make all nodes balanced. Figure 1(h) shows the new giant tour in G. It can be checked that the new giant tour costs 3 less than the old one.…”

The Carbon Footprint of Airport Ground Access as Part of an Outbound Holiday Trip

“…Specifically, this study considers that all tourists travelled from the centroid of their NUTS3 to the airport instead of their actual residence, and we used data regarding the straight-line distances multiplied by a factor of 1.3 separating airports and centroids instead of data of the real distances travelled by tourists. Despite this being an approximate figure that has been widely used [45], the distances travelled to access airports could be improved. The mode split for airport access was mainly taken from a report of the German Aerospace Centre and the European Commission [47] that provided information for German airport access in 2008, but results could be improved by obtaining detailed information for each airport.…”

“…They have been used for setting the distance between the origin airport and the Canary Islands. However, with the aim of considering actual road distances instead of Euclidean distances, we have followed the recommendations based on previous studies [45] that state that multiplying Euclidean distances by 1.3 is a good approximation to estimate actual travel distances in route networks. Therefore, distances in Table 3 display an estimation of actual average distances travelled by German tourists when going to the airport to fly to the Canary Islands.…”