## Open Tours in VRP

Problems with modeling
User
Posts: 2
Joined: 10 months ago

### Open Tours in VRP

Hello @all,

I'm playing with the VRP model of Prof. Helber at the moment. I have problems figuring out how to change the closed tours to open ones:

Equations:
objectFunction..
ZFW =e= sum((i,j,m),c(i,j)*x(i,j,m));
Kapazitaetsrestriktion(m)..
sum(i, w(i)*y(i,m)) =l= b;
OrtErreichen(i,m)..
sum(j, x(i,j,m)) =e= y(i,m);
OrtVerlassen(j,m)..
sum(i, x(i,j,m)) =e= y(j,m);
OrtZuTour(i)\$(ord(i)>=2)..
sum(m, y(i,m)) =e= 1;
KeineKurzzyklen(i,j)\$((ord(i)>=2) and (ord(j)>=2) and
(ord(i)<>ord(j)))..
z(i)-z(j)+ card(i)*sum(m, x(i,j,m)) =l= card(i)-1;
KeinSelbstanfahren(i,m)..
x(i,i,m) =e= 0;

If i see it wright, in this scenario in equation OrtErreichen, j has to be > 1, so that the starting point of the tour doesn't need to be approached?

Thanks a lot guys!

User
Posts: 2
Joined: 10 months ago

### Re: Open Tours in VRP

...or is there any example of written GAMS compatible code for a Open Tours Vehicle routing problem or school bus routing problem? I usually can find just standard closed ones...