Hi,

I want to build a model that can transport stuff from (i to j) directly or by stopping over at facility r.

The transportcost (i to r) and (r to j) are cheaper than the direct transport (i to j).

Problems:

Open(r ) is either 0 or all possible r are opened and the amount is divided up evenly

Even if transportcosts are way lower for the extrastop r than without, the model does never choose to move all products past extrastop r. (capacities are more than enough)

(goal is to minimize total cost (fixed cost and transport cost included)

Related Constraints:

- Amount(i,r)+Amount(d,r)<=Demand(i)*OpenRecycling( r) // index (i,d,r)
- sum(i,Amount(i,r))+sum(d,Amount(d,r))<=Capacity(r)* Open( r) //index (r )
- sum(r,Amount(i,r))+sum(r,Amount(d,r))=(Returnrate(i)*(demand(i))) //index (i,r)
- sum(i,Amount(i,d))<=Capacity(d)*open(d) //index(d)
- sum(i,Amount(i,d))=sum(r,Amount(d,r)) //index(d)

Thanks for your help.

I´m more than happy to post my model if that helps

**Best answer by Marcel Hunting**