Flexible Team Orienteering Problem In Team Orienteering Problem (TOP) we have a graph $G=(V,E)$ and $K$ participants, We are supposed to find $K$ paths with total edge cost less than a threshold while maximising total vertex rewards. The constraint on reward collecting is once a reward has been collected by some participant the it can not be collected again by another participant. e.g. each vertex have only one piece of reward. 



But given a graph like this, and two participants, where $s,t$ are the start and terminating points. I want to have two pieces of reward in $d$ but only one piece of reward in $b$ and $c$.

Does this problem has a name ? Is that proven to be NP-Complete ?
I don't know if it has a name but it's NP-hard. Just take $K=1$, give every edge and vertex weight&nbsp;$1$ and ask if there's a solution with vertex reward&nbsp;$|V|$ and edge cost at most $|V|-1$. This happens if, and only if, there's an $s$&ndash;$t$ Hamiltonian path.  The decision version "Can I get reward at least&nbsp;$R$ with cost at most&nbsp;$C$" is NP-complete.