# Solver, Transportation problem with empty runs

1. ## 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.

Best regards

2. ## Re: Solver, Transportation problem with empty runs

I always receive the error, that my system doesn't fulfill the requirements for linearity.
You object function I20 contains the formula "=SUM(I21:I41)" and solver has no problem with a sum formula but I values is the product of the H values and the corresponding G value and the G value uses the ABS function i.e. a smooth nonlinear function.

http://www.solver.com/excel-solver-s...near-functions

Alf

3. ## Re: Solver, Transportation problem with empty runs

Thank you very much for your help!

Regards

4. ## Re: Solver, Transportation problem with empty runs

You are welcome.

I'm not sure I understands you problem. Normally these kind of exercise has a truck making deliveries to a number of locations and the problem is to find in what order the locations should be visited in order to travel the total shortest distance (travelling salesman problem).

Is your problem that you should find the starting point that will give you the shortest empty (return trip) back to the starting point? I.e. if you started at point E then travel through all locations and do you last delivery to point H then you do the final empty travel from H to E.

Alf

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