Help me make an equitable schedule

Factual Questions
1

Can someone help me sort out this problem:

At my job, our work schedules are set every eight weeks.

In those eight weeks, we have to work 4 Saturdays and 2 Sundays.

And 2 of those Saturdays have to be in each of the two four-week sections of those eight weeks, Weeks 1-4 and 5-8.

And the 2 Sundays have to be split between weeks 1-4 and 5-8.

There are five people who are scheduled.

Presuming that no one asks for vacation time, what is the most equitable distribution possible of people getting a consecutive Saturday and Sunday off?

Sunday is the beginning of the work week and Saturday is the end.

My numerous charts I have prepared can’t figure this out.

2

How many can you have working at once?

3

How many people work each day?

4

It’s not that hard to work out, except that with five employees, there seem to be days where there is an extra worker.

I’ve worked out a system where in weeks 1, 4, 5, 8 there are three workers on Saturday. Weeks 2, 3, 6, 7 have two Saturday workers.

Similarly, in the same system, I’ve got two workers on weeks 1 and 4 on Sunday, and one Sunday worker during the other weeks.

With four employees, this works out perfectly. The fifth employees is kind of a monkey wrench.

5

Here’s a visual aid:



	Wkr 1	Wkr 2	Wkr 3	Wkr 4	Wkr 5
	------	------	-------	-------	-------
1	A, U		A	A	U
2		A, U		A	
3	A		U		A
4		A	A	U	A

5	A, U		A	A	U
6		A, U		A	
7	A		U		A
8		A	A	U	A

Saturday = A
Sunday = U

Workers 1 and 2 get four complete weekends weekends off. The other three employees get two complete weekends off.

Maybe we can use this scheme as a start, and work on trading some spots around.

6

We get part-time people to fill in where needed. Normally, there are 3 full-timers on Saturday and 1 or 2 on Sunday.

7

Bob, using full-timers only, I can come up with three employees only half of the time. Can we allow a part-timer to fill in every other Saturday? Otherwise, some of your full-timers will work 5 or more Saturdays in an eight-week period.

8

Um … in the post above, I was adressing strictly Saturday work … in case it wasn’t clear.

Bob indicated that part-timers can work Sundays if needed, so Sundays seem to licked.

9

The primary goal is keeping people to the scheduling guideline. That is a union regulation. The Powers That Be will provide extra help as needed.

10

OK then, Bob, try this:



	Wkr 1	Wkr 2	Wkr 3	Wkr 4	Wkr 5
	------	------	-------	-------	-------
1	A, U		A	A	U
2		A, U		A	
3	A		U		A
4		A	A	U	A

5	U	A	A	 	A,U
6		A		A, U	
7	A		U		A
8	A	U	A	A

This way, over an eight-week period four of your full-timers get three full weekends off, while the fifth gets two full weekends off.

Every eight-week period, rotate the worker who gets the two weekends off (in the chart above, it’s worker 3). Over a period of forty weeks, all five full-timers will get 14 full weekends off.

11

Also, looking at the last chart, no one has to work more than one weekend in an eight-week period. Over a forty-week period, all five full-timers will work only four full weekends.

And for the worker who gets the two-weekends-in-eight-off (wkr 3)? The trade-off is that s/he doesn’t have to work any full weekends during those eight weeks.

12

Thanks.

I hope I can keep everyone happy.