At 16:37 22/08/2016 +0200, Wiebe van der Worp wrote:
There is a group of ~100 people (n). In 5 time slots they visit 5
rooms in groups of ~20 people (n/5). The composition of the groups
should be as different as possible for each time slot. One person
may not visit a room more than once.
I'm guessing your "about" 20 is because of the "about 100"; do you
actually need all groups to be exactly n/5? I also get the general
idea of "as different as possible", of course - but I think you'd
need to define this more precisely if you need to balance this
requirement against other constraints.
Suppose Column A contains id's, say 1..100. Col. B contains first
time slot room numbers: =INT(RAND()*5+1).
That will put everyone into a group, but by no means produce equal
C, D and E contain room numbers for time slot 2, 3 and 4. F contains
time slot 5, for row 1: =15-SUM(B1:E1). Does anyone have a
suggestion for C1, D1 and E1?
I think this is deceptive: the last grouping is easy only if you have
already come up with a reliable algorithm for the intervening columns!
What you need here is a shuffling process. You can see it as
shuffling your hundred people and then dividing them into five
groups, but that makes ensuring that each person visits all five
rooms problematic. And I'm guessing that this is your principal
criterion. Better, then, to see the problem as shuffling the rooms
that each person is to visit.
Here's an idea:
o In G1, enter =RAND() and fill this across and down to populate
G1:K100 with random numbers. (You can hide this range or put it away
on another sheet if you prefer.)
o In B1, enter =RANK(G1;$G1:$K1) and fill this across and down to fill B1:F100.
This will ensure that each person visits each room exactly once, but
the groups sizes will vary from exactly n/5. You could use COUNTIF()
to list the sizes of the twenty-five groups and determine the range
of sizes using MIN() and MAX(). Then you could use Recalculate Hard
(Ctrl+Shift+F9) repeatedly to regenerate the random numbers until you
were happy with the group sizes.
This problem may be of the sort that would be much easier to solve
through programming that via a spreadsheet.
I trust this helps.
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