Let's say we own a small company flying 10 airplanes (A32X/B73X/A220/E-Jet) in high density low cost environment. Leaving all other costs outside the equation, What would be the minimum flight crew members per ac needed to make this hypothetical company profitable? Let's assume we want to keep flying our fleet as much as possible (...say aircraft utilization of 8 hours).
There is a world of "it depends" involved here, but as a bare minimum starting point:
To get high utilization of each aircraft, you'll need to fly it longer than one crew can stay on duty. So each day you'll need at least two crews: one to start in the morning and fly until early afternoon, and then another crew to fly from then until the airplane is done at the end of the day. So each day, nominally, four pilots touch the airplane. (Yes, there are times you can use just one crew for the whole day - start in California at 0800L and end 10 hours later in New York at 2100L - and times you'll end up with a third crew... flying three 5-hour legs would require that, but let's use two crews/day as an average.)
A 3-day trip is pretty common for domestic crews. Long-haul international gets longer trips, but with augmented or double crews, so use the short-haul case to keep things simple. So each week, an airplane has crews A and B for the first 3 days (an AM crew and a PM crew), crews C and D for the next 3 days, and there's one day left. If everybody works a 3-on, 3-off schedule, those 4 crews can man that aircraft all month long with a total of 8 pilots.
But even in an ideal case, that's not enough pilots.
First, you need reserve coverage, so that when stuff goes sideways, there are pilots on call who can fill in the gaps: weather causes a crew to time out, or somebody gets sick, or whatever else happens that you need another pilot. Depending on the operation, reserve coverage can be 10 to 20%, or sometimes higher. FedEx and UPS, as I understand it, have very high reserve coverage ratios because of the nature of their operation, but that's not what the OP posits, so let's say 20% coverage. Now 8/aircraft is up to about 9.6 pilots / aircraft.
Also, 3-on/3-off can get tiring, and may push crews up against limits on block hours and FDP (see FAR Part 117 for US limits on such things), and something closer to 3-on/4-off is probably more common.
Beyond that, some number of pilots just aren't available in a given week: an individual may have recurrent training, or be on vacation. At a startup, there won't be a great number of pilots out on long-term medical, but as the operation grows that happens. Likewise, nobody probably has much vacation in the first few years of a new company, but training is required. And since pilots can not fly with a head cold or other "minor" illnesses that an office worker can work through, there are inevitably some number of sick calls.
All of that adds up to something in the vicinity of 11-13 pilots per aircraft for a lean operation, and somewhat more than that as things get more complex and more mature.
There are ways to reduce that number, like "we don't fly on Tuesday or Thursday" and "we don't overnight crews away from the hub" -- both of which can be done; I don't have hard numbers for how much that reduces the ratio.
But as a general ballpark, 11-13 pilots per aircraft is a good starting point.
If you're searching for optimization opportunities for the flight attendants, the FAA has multiple requirements and guidelines for flight attendants. (I found the requirements of the FAA first and clear to understand, that's why I explained them)
Crew Amount Requirements
To operate an aircraft the amount of crew is dependent on seat capacity:
- 19-50 Passengers require: one flight attendant
- 51-100 Passengers: two flight attendants
- over 100 Passengers: two flight attendants plus one attendant each for every unit (or part of unit) of 50 Passengers.
So e.g. for a full economy class A320 with 195 Passengers you are required to have four flight attendants on board.
To calculate your needs of personnel, you also have to take the minimum required rest period into account.
- normal duty of up to 14 hours: 10 consecutive hours rest [(2) and (3)]
- long duty between 14 to 16 hours: 12 consecutive hours rest plus one additional flight attendant over minimum requirement [(4)]
- very long duty between 16 and 18 hours: 12 consecutive hours rest plus two additional flight attendants over minimum requirement [(5)]
- extremely long duty between 18 and 20 hours: 12 consecutive hours rest plus three additional flight attendants over minimum requirement [(6)]
There are further additions under subsections (7)-(9).
With this information, you should be able to calculate your needs.