Forecasting Neeed Staff

Hi everyone,
I'm not sure where to post this, but I have a problem that i think might require the help of a Statistics student or Statistician (depending on how hard this might be). I need help finding the optimum number of employees to have on staff considering the following situation. IF there is a better place to post this, please let me know.

We'll use one example with smaller staff numbers. Imagine that you have waiters on a ship that serve on rotations. When a waiter gets hired he signs a contract that says he'll work 210 days in a row, after that he rotates out and gets 155 days off. When he leaves obviously someone takes his place.

Now lets say there are only 17 open positions, they always need to be filled, but

because each waiter gets time off after 210 days we need another waiter o fill that open

position.

Here's how it's being calculated now...

we'll call it the 'Current Method' or (CM).


Current method
==============
155/210 = .74

so 17 * (1 + (.6)) = 29.58 people on staff


The problem is they are usually off on how much they actually need. I believe the problem is that 29.58 represents the most optimum number we need IF the position start dates are distributed evenly throughout the year.

Sounds nice but, the problem is a scenario like this example. If all 17 working waiters have the same start date, they will have the same end date. So at the end of 210 days, you will need an additional 17 waiters to fill every position. For a total of 34 waiters on the payroll (the 17 that started and 17 to replace them when they went on leave).

Of course the above example is a worst case scenario. So we have 34 for a worst scenario and 27.2 best case scenario.

I'm wondering whether the number we should be using is between 27.2 and 34. Is there a better way to calculate this numbers using a different method? Should we somehow take into account the start and end dates? And if so how do we integrate it?

Guy

Those are crazy numbers. You don't need a statistician. You need a map.

For your small staff of 17 at a time, you can do it with only 25, but this must necessarily include 5 down days for #24 and only 85 days of work for #25. This is simply the minimum possible, as 17*365/255 = 24.333333. It is not a coincidence that 85/255 = 0.333333. #24 must sit out five days only due to scheduling so those account for nothing. There remain 17*365 = 6,205 days of work to be covered. If we are whacking at them 255 days at a time, that's 24.333333 whacks. The absolute minimum.

Warning, this assumes not one single staff member EVER gets ill or falls off the deck or needs a vacation to marry or bury his pet rabbit. Of course, there are five days when #24 is not working and could fill in. Also, there are 255 - 85 = 170 days where #25 could fill in. Not quite so obvious is that those 85 days that #25 is on are NOT contiguous. #25 has a very strange schedule.

Scheduling may be a matter of simply starting one employee every 255/17 = 15 days. This seems a little odd if you are just starting up, but if you run cruises and replace employees, over the course of time, this is a rational assumption.