# I need help finding a formula to calculate minimum staff for a given 24 hour period...

1. ## I need help finding a formula to calculate minimum staff for a given 24 hour period...

Ok, I am not asking for someone to outright solve this for me, but if anyone has any ideas to steer me in the right direction, it would be greatly appreciated. I am racking my brain to come up with a good formula that will allow me to plug the constraints into solver, but none are coming to mind that actually make any sense or get me any valid results. Again, all I am looking for is a formula that will help me calculate this. Here is my scenario:

"A hospital emergency room is open 24 hours a day. Nurses report for duty at 1 a.m., 5 a.m., 9 a.m., 1 p.m., 5 p.m. or 9 p.m. and each works an 8-hour shift. Nurses are paid the same, regardless of the shift they work. The following table shows the minimum number of nurses needed during the six periods into which the day is divided. How should the hospital schedule the nurses so that the total staff required for one day's operation is minimized?"

Shift...Time..............Nurses
1.......1-5 a.m..........4
2.......5-9 a.m..........13
3.......9 a.m.-1 p.m...17
4.......1-5 p.m..........10
5.......5-9 p.m..........12
6.......9 p.m.-1 a.m....5

2. ## Re: I need help finding a formula to calculate minimum staff for a given 24 hour period...

Hi -

I can't think of a formula that would do this. However, I set up a simple matrix in the attached spreadsheet that shows you need 33 nurses to cover all shifts at the minimum levels you specified. There will be some time periods that you will have extra nurses. You can move those extra people around, but you still end up at 33. Right now I have the extras split between 5-9 am and 9 pm - 1 am. If you could get a 5 nurses to work a half shift you could reduce staff by 2.5 full time equivalents and exactly meet your need. Otherwise, you would have to cut the number of nurses needed on a couple of the shifts. I think working it out more or less graphically is the best approach.

Hope this helps.

3. ## Re: I need help finding a formula to calculate minimum staff for a given 24 hour period...

Perhaps a setup like this for solver?

Alf

4. ## Re: I need help finding a formula to calculate minimum staff for a given 24 hour period...

I'll give that a try. I need a formula and honestly can't figure out a good one for this. But I'll get back to you when I try it out. Thanks.

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