Hi i am looking at a special type of the VRP where the vehicle isn't restricted by the capacity, but can at most visit a given number of costumers $Q$ in a single route. As I see it, it can be be reprecented as a CVRP where the demand for each location is equal to 1 and the capacity of the vehicle is a number $Q$.
My assumption is that the number of routes needed $M$ is equal to, where $N$ is the total number of costumers:
$M = ceil \left(\frac{N}{Q} \right)$
Is this assumtion true, I have not found any litterature on this topic, and can not myself come up with a proof to the statement... Hope you guys can help.
Yes, you can model it as demand $1$ and capacity $Q$. If $M$ is the number of vehicles, then the total capacity is $M Q$, and this must cover the total demand $N$, so $M Q\ge N$, which implies that $M\ge N/Q$. Because $M$ is integer, you can strengthen the lower bound to $M\ge\lceil N/Q\rceil$. Whether this lower bound is attainable depends on the underlying graph.