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This is an optimization / minimum flow problem. For this directed graph, I would like all vertices to be visited exactly once, but this graph can exist multiple disjoint paths, and each path has constraints on its total cost. The goal of this problem is to minimize the total cost of all disjoint paths.

I only know how to find Dijkstra shortest path, and I am not sure if similar principle can be applied. Please help me out and share your thoughts on this.

Thank you so much!

Corrine
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    Please give an example of a graph that illustrates the range of cases you need to handle. I'm not at all certain what the graph and constraints include. – Prune Jan 17 '19 at 23:09

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It sounds to me you are describing a vehicle routing problem, where each route is constrained e.g. by the vehicle capacity or maximum travel time. Have a look at https://en.wikipedia.org/wiki/Vehicle_routing_problem.

Magnus Åhlander
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  • Thank you for the response! It's actually driver scheduling problem with some variations: each driver has to go to customer and come back to the hub directly. I am not sure if vehicle routing problem still apply, but I will give it a try! – Corrine Jan 18 '19 at 18:40
  • How about, in your case, re-defining the duration between two customers as the duration between the first customer and the hub + the duration between the hub and the second customer? – Magnus Åhlander Jan 18 '19 at 22:16