During the model review meeting today with our client I was asked the question if we can do the optimization the other way. My understanding that optimization works in such a way that given an objective function and all the constraints it gives us the optimal solution if any. However, by "the other way" I'm referring to the scenario that our client mentioned that, given the objective and let the model tells me what we need to achieve that objective. For example, given the budget, raw material, capacity and other information optimization can give us the production mix which maximize the profit. "The other way" in this context would be, our objective is X amount of $ profit and the client wants to find out what the potential and ideally optimal solutions in terms of budget, material, capacity, and so forth would be. Certainly, we can and we should prioritize all these factors and assign penalty when these constraints are violated or relaxed.
I'm still relatively new to this area so any comments, suggestions or direction would be appreciated.
Thanks in advance