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Determining the optimal solution to VRP is [[NP-hard]],<ref name=toth>{{cite book |editor=Toth, P. |editor2=Vigo, D. |title=The Vehicle Routing Problem |volume=9 |series=Monographs on Discrete Mathematics and Applications |year=2002 |publisher=Society for Industrial and Applied Mathematics |___location=Philadelphia |isbn=0-89871-579-2}}</ref> so the size of problems that can be optimally solved using [[mathematical programming]] or [[combinatorial optimization]] may be limited. Therefore, commercial solvers tend to use [[Heuristic|heuristics]] due to the size and frequency of real world VRPs they need to solve.
VRP has many direct applications in industry. Vendors of VRP routing tools often claim that they can offer cost savings of 5%–30%.<ref name="Springer Verlag">{{cite book |url=https://books.google.com/books?id=UMI5GzcNd8wC&q=%22vendors+of+routing+tools%22 |title=Geometric Modelling, Numerical Simulation, and Optimization:: Applied Mathematics at SINTEF |date=2007 |publisher=Springer Verlag |isbn=978-3-540-68783-2 |editor=Geir Hasle |___location=Berlin |pages=397–398 |editor2=Knut-Andreas Lie |editor3=Ewald Quak}}</ref>
== Setting up the problem ==
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