Solver is not solving

I think those kind of problems should be solved with Evolutionary algorithm. Also, under options unhook the box that says ignore integer contstraints.

I did some changes to the layout and your formulas, I have no clue if that makes a difference.

With the sheet setup as it should, Solver runs but it cannot find a solution within the constraints if you start with all zeroes.
What I did was loosen up the constraints a bit ( 2 OR 1 products a day instead of just 2) and then I reduced the number of options (maximum 3 instead of 4). Solver then found a solution within the constraints. Starting from that solution I increased maximum back to 4 and started and it found a pretty good solution. Oh yeah, I also increased the number of iterations by a factor of 10, I have no idea what that even means, I'm only guessing.
Note that I put all equal looking days next to each other to make it look good.

Before I could make Solver cooperate I considered writing a post saying this would be faster to do manually. That might still be true but it's more fun trying to manipulate Solver than trying to manipulate the numbers.

Just a small manual adjustment on the previous result. I think this is as good as it gets.

Optimal.JPG

I don't think a "always fast and correct" solution to this problem exists. It's like the travelling salesman problem or similar. http://en.wikipedia.org/wiki/Travell...lesman_problem
http://en.wikipedia.org/wiki/Cutting_stock_problem

There are numerous problems like this, scheduling problems, cut-length-to-minimize-waste problem (pipe or board or whatever).

Maybe it is possible to write a algorithm that is better than Solver if it's made for just this problem but I don't think it will be correct every time either.

If the problem is small enough I guess it would be possible to loop through all combinations possible but I am not up to writing that algorithm. Also I think you would have to leave your computer running for a long time.

Edit: Solver themselves confirm that the evolutionary solver is reasonably good at finding "a solution" but not finding the best solution. http://www.solver.com/content/basic-...ing-conditions

well i tried it again but this time i picked 10 values from the 24 and summed them so i knew there was a definite answer
so i set solver to find the sum of those 10 which i know exists and it still failed miserably. i even tried rounding everything as -ve numbers often cannot be stored correctly still no joy