There could be two interpretations of this - Do we want to know (i) the Maximum ZFW for the particular flight, or do we want to know (ii) the calculations based on the MZFW certification, let's call it 'DESIGN' Limitation?
Here are figures for a large existing airplane:
MAX DESIGN WEIGHTS based (TONS)
DESIGN TAKEOFF - 351.5
DESIGN LANDING - 251.2
DESIGN ZFW - 237.7
The above weights must not be exceeded.
Typical DOW^^ - 175.0
^^ DOW - The Operator publishes the Dry Operating Weight. This is the basic/empty weight of the airplane alongwith standard furnishings, crew complement with their luggage, pantry load, etc. - generally any regular load that is not fuel and not payload. DOW is arrived at by calculating the sum of all components of the airplane, as well as actually weighing the airplane.
Example for interpretation (ii) above:
Using MAX DESIGN ZFW
MAX Payload (DESIGN) = 237.7 - 175.0 = 62.7 TONS
MAX DESIGN ZFW, limits Fuel to to 351.5 - 237.7 = 113.8 TONS
The Fuel tank capacity is about 145.0 TONS, so we lose a possible 31.2 TONS of Fuel/about 4hours of flight if we carry MAX DESIGN Payload.
An example of interpretation (i):
Based on Route, forecast winds, weights (!) etc. and available RWY at a particular point in time at a particular airfield, the dispatcher/Pilot calculations yield the following numbers:
RTOW = 342.0 TONS, REGULATED TOW, calculated for actual conditions
MINIMUM FUEL = 119.4 TONS, by calculation under actual conditions
RTOW - MINIMUM FUEL = MAXZFW = 222.6 TONS (= a loss of 15.1TONS)
i.e. only 47.6 TONS OF Payload compared to the MAX 'DESIGN' value of 62.7 TONS.
The Take Off Weight is the sum of the following three weights:
DOW (as described earlier at ^^)
PAYLOAD - The Commercial Dept. are the ones who know how much Payload there is for the flight. We assume, in general, that they always want to load the flight to the fullest.
FUEL - The Dispatcher and Pilot are the ones who calculate how much Fuel is required to despatch the flight.They also calculate the performance limited MaxTOW for the flight (aka Regulated TOW, RTOW).
Take Off Weight, TOW = DOW + Payload + Fuel
When we add Payload to the DOW we get the Zero Fuel Weight:
DOW + Payload = ZFW, this should not exceed the Max DESIGN ZFW Limitation in any eventuality.
Substituting ZFW for DOW + Payload:
TOW = ZFW + FUEL.
As mentioned earlier, the Dispatch and Pilot calculate the Minimum Fuel and the Maximum TOW (RTOW)for the flight. The Pilot may choose to carry more than the Min fuel if the preflight briefing indicates a need for more fuel (marginal weather, last minute technical issues, etc.), last minute issues can also reduce the RTOW (RWY change eg). So the allowable load for the day is:
RTOW - Fuel = Max ZFW for the flight.
This Max ZFW tells the Commercial Load Control office how much Payload can be loaded. This is the answer to interpretation (i).
For interpretation (ii) A "Use Max ZFW" option on the Performance App could be an option for relatively short legs where the fuel requirement is known to be well below any limits and there is an unsatisfied demand for Payload. Such a figure, is, in any case, a fixed figure being the DESIGN MZFW less the DOW:
DESIGN MZFW - DOW = MAX DESIGN PAYLOAD which should never be exceeded, however favorable the Fuel and TOW maybe.
Note that this is a fixed figure save for minor variations of DOW due things like variations in standard crew numbers, fewer galley carts, etc.