Rotating Shift Schedule - More Complex than it sounds [Please Help]

Hi everyone,

__INTRO (Skip if you want just the math)__

This is my first post, so please forgive me if this is in the wrong forum or place but I have come to find this quite a mathematics problem and one which I'm battling to wrap my brain around and thought that maybe a mathematics forum would enjoy the exercise as well. I find this problem quite interesting even if I don't have a solution, so maybe someone here can help

__Problem (Just the Math)__

the problem is that we have got a seven day work week with 24 hours a day when someone needs to be on shift. Shifts take place during the following times:

Morning - 07:00 --> 13:00

Afternoon - 13:00 --> 21:00

Night - 21:00 --> 07:00

Each of these shifts have to be covered every day of the month in such a way that it repeats itself. The constraints on the shift rotation are as follows:

Each staff member must:

- Have at least 2 days off between cycles
- Work Equal amounts of time
- Be as close to 50 hour work week's as possible
- Only a single staff member per shift
- You only have four staff to do this with
- It would be nice if staff could establish sleeping patterns during this

Using the above mentioned details, how would the month of August look with this schedule? Draw a calender showing who is on which shift when.

**Conclusion**

I find this problem interesting but so far beyond my ability to solve. It is for a friend of mine who's boss is trying to get her to figure this out but also isn't having any luck. Please help if you can.

Thanks in advance