Nursing shifts

[Scooby Doo]

Can anyone help with this problem, its for my wife who works at the local
hospital and they want to optimise the staffing levels.

If you need any further questions pls do not hesitate to ask.

Thanks all


Shift patterns
Early (E) - 7.5 hrs
Late (L) - 7.5 hrs
Night (N) - 10 hrs

Each member of staff has two days off per week, 36 days holiday and 10 days
study leave (part time pro rata).

Normal shift numbers would be on a Mon, Wed, Thur Sat & Sun.
Two qualified members of staff and three unqualified staff are required on
the E shift.
Tue & Fri would require three qualified and two unqualified on the E shift.

L shift would require two qualified and two unqualified.
N shift would require two qualified and one unqualified.

Ward has 18 patients, with 4 patients per nurse per shift on average
(excluding night shift).

Current staffing levels are:
9 staff working 37.5 hrs per week
1 staff working 20 hrs
(1 staff on maternity leave at 37.5 hrs per week)
(1 staff currently on sick leave = 37.5 hrs per week)

Unqualified
2 staff on 36 hrs
3 staff on 37.5 hrs
1 staff on 30 hrs
1 staff on 20 hrs

1) How many staff would be required to cover the above criteria?
2) How many beds would need to close for the above criteria to be met?

 

[Vasant Nanavati]

This is a linear programming problem; not an Excel problem. And even if
someone were willing to make a significant time investment to attempt to
solve it, I don't believe that enough information has been provided.

 

[Harlan Grove]

This is a linear programming problem; not an Excel problem. And even
if someone were willing to make a significant time investment to
attempt to solve it, I don't believe that enough information has been
provided.

....

Assigning the shifts might involve linear programming, but I don't think so.
Determining the staffing level can be done directly.
....

So this is one of the consequences of so many blown NHS IT projects?

This totals 25 hours. Days outside the UK have only 24 hours. What are the
actual shift times?

Holidays in addition to the two days off a week (what would be weekends in
other occupations)? And the 10 study days are on top of that? Then there
would be 365 - 2 * 52 - 36 - 10 = 215 work days in most years, so the
equivalent of 43 work weeks.

So who works M W Th Sa Su and who works Tu F ? Does it change each week?
Each month?

What's the rotation of L and N shifts? Do nurses on the N shift work 5 days
a week, so 50 hours, while E and L shift nurses work only 35 hours a week?

So 4.5 nurses on average on the ward.

Ignoring holidays and study days, your available qualified staff work 357.5
hours per week, but you seem to need

2*5*7.5 + 3*2*7.5 + 2*7*7.5 + 2*7*10 = 365 hours staff time.

For the sake of argument, the two unavailable qualified nurses partially
offset the holiday and study day needs of all.

As for unqualified staff, they work 234.5 hours per week, but you seem to
need

3*5*7.5 + 2*5*7.5 + 2*7*7.5 + 2*7*10 = 432.5 hours staff time.

They're the limiting factor, and reflecting holidays (and study days?) means
that there are approximately half the staff needed.

So if your wife's hospital doesn't double the number of unqualified staff,
would that mean that just shy of half the qualified nurses would be
redundant?