Solver, Transportation problem with empty runs

Hi all

I'm working on a transportation problem where the total distance made by empty runs shall be minimized. There are 8 construction locations {A;B;...;H} and the distances between these locations are given. The total demand and supply of each location has to stay the same.

When I try to run the solver I always receive the error, that my system doesn't fulfill the requirements for linearity. Basically, I think that I'm on the right track, but I have no idea what to change. My approach is to compare every single arc like A->B and B->A in order to calculate the empty runs and multiply them by the distance.

Maybe you have some advises?

Best regards