# Help me make an equitable schedule **URL:** \ **Category:** Factual Questions\ **Created:** [July 24, 2003, 6:41pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686 "2003-07-24T18:41:44Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [July 24, 2003, 6:41pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/1 "2003-07-24T18:41:44Z")
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. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 6:51pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/2 "2003-07-24T18:51:34Z")
How many can you have working at once? ---
**Author:** ![DeVena](https://avatars.discourse-cdn.com/v4/letter/d/dec6dc/32.png) [@DeVena](https://boards.straightdope.com/u/DeVena)\ **Post date:** [July 24, 2003, 6:59pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/3 "2003-07-24T18:59:02Z")
How many people work each day? ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 7:04pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/4 "2003-07-24T19:04:04Z")
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. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 7:11pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/5 "2003-07-24T19:11:46Z")
Here’s a visual aid: ```auto 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. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [July 24, 2003, 7:46pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/6 "2003-07-24T19:46:33Z")
We get part-time people to fill in where needed. Normally, there are 3 full-timers on Saturday and 1 or 2 on Sunday. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 8:32pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/7 "2003-07-24T20:32:59Z")
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. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 8:35pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/8 "2003-07-24T20:35:13Z")
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. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [July 24, 2003, 8:43pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/9 "2003-07-24T20:43:04Z")
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. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 9:11pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/10 "2003-07-24T21:11:37Z")
OK then, Bob, try this: ```auto 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. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [July 24, 2003, 9:16pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/11 "2003-07-24T21:16:06Z")
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. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [July 24, 2003, 9:30pm UTC](https://boards.straightdope.com/t/help-me-make-an-equitable-schedule/190686/12 "2003-07-24T21:30:31Z")
Thanks. I hope I can keep everyone happy.