Urgent and quick help from logical maths person please!

[CatherineCawoodsbestie]

I am turning to the power of Mumsnet!

i have about an hour to create a 4 week duty rota for 2 different roles. I have a number of full and part time workers who all need to work the most equal number of days possible - full days - as the duty worker.

please can someone help me with the sums, or tell me the formula to do this!

Role 1: 20 days to cover
staff available :
2 FT
1 0.8
1 0.6
1 0.4
1 0.2

role 2 20 days to cover

5 FT
2 0.5

i would be eternally grateful!
thank you

Have you tried Chat-GPT?

Ask pi.ai

Role 1:
Each 0.2 is 1 day.
You have 20 x 0.2 available, so each 0.2 gets a day's duty.

So employees 1 and 2 do 5 days, employee 3 does 4, employee 4 does 3, employee 5 does 2, and employee 6 does 1.

Are you saying that within the roles, they need to spend some time on a certain duty for 20 days between them?

If so, for the easier one, you have 5 x full time and 2 x 0.5, so 6 people equivalent.

20/6 = 3.33 so each FT person would cover 3.33 days and each 0.5 person would cover 1.66. Round to 3.5 and 1.5. This gives 3.5 x 5= 17.5 and 1.5 x 2= 3, total 20.5, so someone can drop 0.5 of a day.

I agree with @Lougle for the first role

That would work if there were part days allowed, but @CatherineCawoodsbestie says that she wants full days.

I think you'd have to use a longer cycle to ensure that every x weeks an employee has one less duty to achieve @123ZYX 's method but keep full days.

For role 1 you essentially have 4 full time employees. So that's 5 days per full time employee

1+2 do 5
0.8 does 4
0.6 does 3
0.4 does 2
0.2 does 1

Role 2 you have 6 full time employees so 3.3 days per full time employee
So full time do 3.5 each and PT do 1.5 each and rotate each 4 weeks who gets the .5 off

@Lougle you're right, I missed that. Double the days over a 40 day period would resolve it. Or for more accuracy, go to 60 days and you don't need to round, it would be FT = 10 days each and PT =5

I agree @123ZYX . A 60 day rota would be easiest.

If you don't want to do that, @CatherineCawoodsbestie, then having FT employee 1 do 4 duties, FT 2-5 do 3 duties, and PT employees do 2 duties over the 20 days would work. Then the next cycle you'd have to have FT employee 2 do the extra duty, then the following cycle FT employee 3, etc.

Do you have annual leave plus sickness to consider? For role 2 I would consider full timers do one day a week each and part timer covers annual leave. With 5 people having 5 weeks each that’s 25 weeks so averages about one every two weeks so is proportional.

Thank you all - you are amazing! All sorted thanks to you lot!

here is a spreadsheet that does it. role 1 works out perfectly, role 2 is harder to sort.

I wish I was this clever with maths and numbers. I really envy this.

@parietal @Lougle and everyone else too: thank you so much. Rota completed successfully. I will definitely use the spreadsheet for the next one. I was getting into a terrible muddle. Mumsnet is great!

Wow. I sometimes think that I'm a pretty smart person until reality comes and hit me hard. I'm impressed!