Sorting data for multiple people given preferences

[phill at GE]

Hi,

I have searched for something I can use to solve my problem but its difficult to know what to look for when you can't envisage the solution.

Bearing in mind I did Mathematics at Uni I should be able to solve this but, hey, it was a few years ago!

Problem
I have ~20 ppl to place in different jobs. They each have 3 main choices (upto 5 in total), but I want to place them in one of their top 3 locations. I would also like somehow to weight the preferences, so not only everyone gets a top3 but overall the av.pick is minimised (i.e. overall people get their 1.3rd choice say)

In a more perfect world, I would also like to rank the person, so I have say 10 ppl I definately want to get top 2, whilst still keeping everyone else in top3. In know this sounds (a) complicated and (b) harsh (!!) but it's faster and fairer than a pick & choose methodology.

Hope this makes sense and sorry if it has been covered elsewhere.

Regards,
Phill

 

[RalphA]

Me, personally, don't quite understand what you need.

Perhaps if, instead of simply describing your problem, you could post a snall example with actual values, show what results you expect, and then explain your problem, based on referring to the data, I might be able to help you.

 

[phill at GE]

Thanks Ralph:

Name - choice 1 2 3
Phill - London BoZ Shannon
Nicola - Paris Dublin Stavanger
Marco - London Paris BoZ
Annie - Dublin Stavanger London
Pavel - Paris London BoZ

Ok so here is a mini example. Each person above has picked 3 choices of where to live (in order of preference).

I would like a tool to pick the combination of locations for people that minimises the average pick.

e.g.
Phill - BoZ, Nicola - Dublin, Marco - London, Annie - Stavanger, Pavel - Paris.
This gives the set an average pick of 1.6 and all are in top 3. If this seems easier to do by hand then just try it for 20 people.

Hope this makes it clear.

Phill

 

[RalphA]

Phil, I don't know how to attack this type of problem in Excel. As an exercize, I entered a list of all the cities, one after the other, did an A-Z sort, then wntered the cities in a row, in alphabetical order. Then, to the left of each person, I wrote the cities of their choice, under the alphabetical listing, with a preceding number 1, 2, or 3. Thus, I obtained:
--------BoZ---Dub---Lon---Par---Sha---Sta
Phil-----2-------------1-------------3
Nicola----------2-------------1------------3
Marco--3-------------1-------2
Annie----------1-----3--------------------3
Pavel--3-------------2-------1

By inspection, and Trial and Error, I arrived at this listing:

Phil---2Boz
Nicola-3Stav
Marco-1Lon
Annie-1Dub
Pavel-1Par

The average pick is (2+3+1+1+1)/5 = 1.6, the same as you obtained with Nicola -2Dub and Annie-2Stav.

It did take a bit of trying for this small group of 5. I can imagine that it would be a long time before I could get my act together with 20 people, and can see that, if a system could be worked out to give the minimum "average pick", it would be great. Except that I have a sneaking feeling it may not be possible to come up with a solution that we can put into a formula or, even, into a series of statements!