I might be beating myself up over nothing here, but I am trying to pin down the difference between a model that optimises a set of decisions and one that prioritises them; this is specifically concerning linear optimisation problems.
The example I have in my head is of the optimisation problem involving filling a bag with gems of different sizes and values. The bag only has a finite volume, and so you need to choose the combination of gems that maximises the value.
One option is to take rank the gems in terms of value per unit size and then take the highest-ranked stones until you don’t have any more room, but you might waste space. In my head, this is a prioritisation, not an optimisation.
However, a combination of lower-ranked stones might fill the space perfectly, resulting in an overall higher value. This would be an example of what I would consider an optimisation.
Is this difference important in practice? Is there a better way to actually explain the difference between them?
Final question, if all the rocks are the same size, is there a difference between prioritisation and optimisation anymore? The results of either would be the same, but are the methods of getting there still distinct?
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Thank you in advanced!
In: 3
Just FYI OP, what you’re describing is the [Knapsack Problem](https://en.wikipedia.org/wiki/Knapsack_problem), as well as the *Fractional* Knapsack Problem.
There are algorithms (a set of steps and decisions you can make) that will always get you the optimal choice (for maximizing value).
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