I can give you the base of calculation we use:
One employee will have:
28 days vacation per year
9 off days a month, resulting in 108 off days a year
go to training twice a year totaling in 2 x 8 days equal 16 days off
go to special training as Dangerous goods, EPR etc for 4 days
and finally have 8 days off which are in Switzerland the "legal off days" as Christmas, New Year etc.
This results in a total per crewmember of 164 days per year off from flight duty or in other words : 201 days on flight duty per crewmember.
Now it is a simple calculation, as we need at least two crews per aircraft it will be 2 x 365 : 201 = 3,63 Crews per plane
This 3,63 is a mathematic minimum and I can assure you, this airline will sit on the ground relatively fast. I never would go below 4,5 better 5 crew. The bigger the fleet, the more we can lower this figure.
The reason is, we need to cover slot delays, technical delays, sickness etc. which will always affect the actual flight duty and finally result in the need for another crew.
So I would say on short range 5 crews for one aircraft, if you are up to 3 aircraft you might go back to 4,5. This is for sure very much variable also of the kind of OPS. A charter airline which has it's business seasonwise can plan the vacation and training of the crews different from what a scheduled needs to.
The other story is the long range OPS. This is very much demanding crews and as mentioned in my previous post, we can easily see a figure of 10. Long range planning is very complex. Additionally to the usual FDR's (Flight Duty Regulations) we need to consider penalties for change in time zones, east - west rotations, night flights, longer off periods etc. Here we can't take any formula just as I showed it on the short haul. It is very much dependable from the network and if the crews fly nothing then long range (MD11, B747, B777, A346) or if it's a kind of mixed duty on short and long as on some A330 or 757/767 operations. If you can mix it with short range, again the factor will come down which is for sure in the operators favor.