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

Jul 2011
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.


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