Optimize allocation based on preferences

[speachman89]

Hi all,

I think fundamentally this query should be straightforward but I just can't quite work it through so I thought I'd serve it up to some greater minds than mine. I have reduced the size of data against which I am trying to apply this logic for the purpose of explanation as I presume any solution should be easily scalable.

So, in this example I have 15 students and 15 courses, and each student has given preferences 1 - 15. Clearly some options will be more popular than others. I therefore want to find a solution to optimize this allocation. To my mind, if we assume 15 points are awarded to someone who gets their top preference, and 1 point to someone who gets their bottom preference, the optimum solution would be the allocation that achieves the highest possible score overall based of preferences provided (i.e. if all got their top preference (which won't be possible) the total score would be 15 x 15 =225)

In reality there will be 15 preferences against more than 15 courses so I would assume these courses not "preferenced" would be allocated zero points. There will also be more than 15 students in total. It would be useful if any solution could bear this in mind.

I have uploaded an image of some sample data and would be grateful to anyone that could help me solve this challenge. The column of random numbers 1 - 15 can be generated =SORTBY(SEQUENCE(15),RANDARRAY(15)).

Thanks in advance!

 

[KRice]

Welcome to the board! What are the constraints on your problem? For example, is there a minimum class size and a maximum class size? Do these sizes vary for different courses? Must each student sign up for some required number of classes?