It seems to me that the aim of the app is more to help the manager assign the shifts than it is to store them. After all historical copies can be dealt with by printing out the week's roster and the future is not likely to be more than four weeks.
I would sit down and ask myself what information would be needed to decide who goes when: for example has Frank worked more than 30 hours in the last week? When was Jane's last shift? Does Bob do mornings?
It will probably also be helpful to create a big overview screen that shows all the shifts currently assigned, and where staff are needed.
Interesting problem. I think once you have the problem nailed the storage method will suggest itself...
--tidiness is the memory loss of environmental mnemonics
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