Hello! I am going to conduct a study on the application of Vehicle Routing Problem in real world. However, I am struggling with how I construct my networks. I would like to ask on how to define the edges/arcs/links between the vertices.
For example, what should the edge between cityA and cityB represent? Most literatures use travel times which is based on road distances from cityA to cityB. However, there are a lot of paths from cityA to cityB. The way to address this is to use the shortest path from cityA to city B. Are there any alternatives to address this issue? What should the edge between two vertices represent?
You might be better off trying some of the tool(s) that are already available...
like this one
https://developers.arcgis.com/python/guide/part7-vehicle-routing-problem/
and, with an example like the next one
https://developers.arcgis.com/python/guide/base64-images/part7_vehicle_routing_problem-g659e66d9-9c8e-24d1-db02-9c229bf421cb.png
https://developers.arcgis.com/python/guide/base64-images/part7_vehicle_routing_problem-g55b3dbdf-ef27-20e1-e2c1-023f760e69a4.png
Good luck
Please see this paper and the references that it contains:
A.N. Letchford, S.D. Nasiri & A. Oukil (2014) Pricing routines for vehicle routing with time windows on road networks. Comput. Oper. Res., 51, 331–337.
You can use the real distance or travel time of the best path that link each pair of cities. Usually, travel times are calculated based on the real distance and an assumed vehicle average velocity.
You always need to calculate the Cost-Matrix between all the cities (nodes) as instance data. To make this possible recommend OSRM or Vallhalla or any proprietary solution like ArcGIS Desktop Network Analyst
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