Help with rota

etymon

Hi all
I have been tasked with doing the work on-call rota for the nest 6 months and I'm a bit lost.

There are 182 days to cover between 12 people. Normally we would just do a rolling rota and keep repeating the 12 names until it was covered.

However, 10 people have an equal share of days, 1 person has 0.8 share and 1 person has 0.4 share.

Can anyone help me figure out

1. how many days total each person should get out of 182
2. at what point to insert the 0.8 and 0.4 people in the rolling rota to space out their calls evenly

A couple of us have been trying to figure this out with no luck!!

Yakuza

There's no way to match those number of people in those proportions exactly, if you're working in full day shifts (I'm assuming there's one person per shift and they work a full day).

If you give one of the people with a full share 17 days, the other 9 with a full share 16 days, the person with an 0.8 share 14 days and the person with the 0.4 share 7 days (half the previous person's number), you'll end up with 17 + 9 * 16 + 14 + 7 or 182 days. In my opinion, that's close enough for practical purposes.

As for rostering them, list out Person01-10 16 times. After all but the first and the last Person10, insert Person11, after every 2nd Person11, insert Person12. Right at the end, put the person who's getting the 17th day (Call them Person01). That would evenly space out everyone. I've attached it below.

I've done this in the spirit of solving a linear programming problem, I take no responsibility for how this works out in real life!

(Working in half day blocks, it's possible to have the 10 people working the exact same amount of time by giving the 10 people 32.5 half days, and the other two 26 and 13 half days respectively but that's more an exercise in mathematical purity rather than practicality)

etymon

Amazing! Many many thanks.