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Math Help - Scheduling

  1. #1
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    Scheduling

    Alright, here's a hard one.
    Say I have 7 employees.
    Four different jobs: A, B, C & D.
    Is it possible to create a repeating weekly rotation that allows the following criteria:

    1. 1 employee every week on job A.
    2. 1 employee every week on job B.
    3. 1 employee every TWO weeks on job C. (Must be consecutive weeks)
    4. The remaining 4 employees weekly on job D.

    Is this even possible to create being PRECISELY and PERFECTLY fair?
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  2. #2
    Senior Member TriKri's Avatar
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    Can you please specify the conditions a little bit more clearly; does 1 employee every week on job A mean that one employee will do job A all week long or does he have to do it one time that week? What do you mean with a rotating schedule; does the job share (percentage of A, B, C and D) have to be equal to all employees or does it mean that every one has to do the jobs in the same order and equally much?
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  3. #3
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    Quote Originally Posted by TriKri View Post
    Can you please specify the conditions a little bit more clearly; does 1 employee every week on job A mean that one employee will do job A all week long or does he have to do it one time that week? What do you mean with a rotating schedule; does the job share (percentage of A, B, C and D) have to be equal to all employees or does it mean that every one has to do the jobs in the same order and equally much?
    Sorry about that. Yes, it's a week long assignment. The employees would not necessarily do the job in the same order, but that's okay. All employees should do job A, job B, and job C once in a rotation, but the rest of the employees default to job D, so they will be doing it multiple times. Hope I made myself a little clearer. Sorry I'm so confusing.
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  4. #4
    Super Member Deadstar's Avatar
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    Vague question is vague.
    Does C need to be done for 2 weeks or one week on one week off?

    Employees are numbered 1-7

    \begin{array}{c|c|c|c|c|c|c|c|c}<br />
\textrm{Week} & A & B & C & D & D & D & D & \textrm{extra } D \\<br />
1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & - \\<br />
2 & 7 & 1 & - & 3 & 4 & 5 & 6 & 2 \\<br />
3 & 6 & 7 & 1  & 2 & 3 & 4 & 5 & - \\<br />
4 & 5 & 6 & - & 1 & 2 & 3 & 4 & 7 \\<br />
5 & 4 & 5 & 6  & 7 & 1 & 2 & 3 & - \\<br />
6 & 3 & 4 & - & 6 & 7 & 1 & 2 & 5 \\<br />
7 & 2 & 3 & 4  & 5 & 6 & 7 & 1 & - \\<br />
\end{array}
    \begin{array}{c|c|c|c|c|c|c|c|c}<br />
\textrm{Week} & A & B & C & D & D & D & D & \textrm{extra } D \\<br />
8 & 1 & 2 & - & 4 & 5 & 6 & 7 & 3 \\<br />
9 & 7 & 1 & 2  & 3 & 4 & 5 & 6 & - \\<br />
10 & 6 & 7 & - & 2 & 3 & 4 & 5 & 1 \\<br />
11 & 5 & 6 & 7  & 1 & 2 & 3 & 4 & - \\<br />
12 & 4 & 5 & - & 7 & 1 & 2 & 3 & 6 \\<br />
13 & 3 & 4 & 5  & 6 & 7 & 1 & 2 & - \\<br />
14 & 2 & 3 & - & 5 & 6 & 7 & 1 & 4 \\<br />
\end{array}

    Basically if you 'shift' along one letter each week unless you are shifting to C and it had been done the previous week in which case you go to the 'extra D' column then next week resume normal pattern (i.e, you're on B, next week you move to C but it had been done the week before so go to 'extra D' then the week after go to the first D column.)
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  5. #5
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    Great! Thank you!
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