pgrouting
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Linear Referencing System (LRS)
In a GRASS GIS presentation I found the following slide about "Linear Referencing System (LRS)":
Slide 13: https://www.grassbook.org/wp-content/uploads/presentations/MitOSGeoDataFOSS4G9.pdf
This looks like a suitable problem for pgRouting, and it might be a good initial solution eventually for some VRP optimizer.
https://grasswiki.osgeo.org/wiki/Linear_Reference_System