I'm struggling with this problem which seems easy, but somehow I'm not getting it to work properly.
Lets say we have a production process which converts inputs into outputs which are being transported to several regions. My model (see attachment for a toy example which gives the same results) makes use of a variable (between 0 and 1) which allocates the use of the different types of inputs, technology and the area to which the products are being transported. However, somehow the model always transports both products ("product" and "waste") to the same area, which might not be the most cost-efficient option. In the attached example the costs would be lowest when the product is transported to Area 2 and the waste to Area 1, but when the model is forced to do this it says it is infeasible, so there should be some inconsistency somewhere. The listing file doesn't seem to give any clues where to look.
I tried adding the "Output" set to the allocation variable, but then only waste (and no product) is being produced and transported to area 1, as only the transport of waste to Area 1 has a positive impact on the objective value (negative transportation costs).
Does anyone have a clue how to solve this?
Problems with modeling
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