Forecasting needed staff

[Guybrush]

Hi everyone,
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.

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