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Key insight, loading cargo into an airplane is a problem similar to loading the family car for a vacation.
Also similar to a less complex problem of loading a container (on a truck), or a ship full of containers.
We optimize total revenue for the carrier, with constraints for safety (weight, # passengers, % distance coverage of fuel > 100%)
Passengers: Family vacation has parents and kids in car. They each need room for snacks, games, clothes and pillows, and personal space.
They each have a weight and volume, and need extra room to cross legs, move a bit, sleep, lean, etc. Constraint: don't squeeze them too much, or they fight.
Luggage. For a 1-week beach trip, they each were allowed one carry-on to fit in the trunk/hatch back.
Gasoline: Filled it up every time, but was that smart?
I could have brought a trailer or put stuff in a roof carrier, but did not.
We did check the vehicle weight limit. Most cars allows x,xxx pounds of extra weight, and we had to get an SUV for this trip.
I once packed a U-Haul truck for a daughter to move across country. Standard boxes were easy. I could fill every cubic inch of space with the right sized boxes.
Those boxes were stable too...did not move during the long, bumpy ride.
Each box had a weight limit, or it got too heavy and crushed things under it. Every box had to stack.
Constraint: Heavy items like furniture went on the bottom (but was limited to the first level of cargo, not very many of them).
The problem was odd-shaped and odd-sized items, and fragile items. We broke furniture during this trip, as it was not packed well. Save time and money on packing, but lost it in breakage (constraint)
We had odd-shaped and odd-sized items that we just propped here and there. They moved during the drive, and we had to leave empty space for them.
A trucking container (whether on a ship or not), has other attributes. Total Weight, Total Height, and probably a balance aspect.
Also has materials warnings (what is in the cargo) that determines how it is transported. Flamable is an example. Explosive, e.g., Lithiuim batteries, another.
Fuel, in an airplane the fuel has 2 main attributes: Weight vs. total capacity and distance to travel. Optimization here too.
Extra people and stuff needed for the ride:
In an airplane, we have employees, snack carts, and safety equipment (e.g., the rafts).
On our car trip, we have a spare tire, safety kit, food, water and blankets. All take up room. No extra people thank goodness (2 drivers).
Are all legs of a flight the same?:
In the case of our 2018 trip, we rented a very large SUV, and filled it to maximum capacity with people and stuff on the way out.
By the way back, we had used up alot of stuff, so we have a bit extra room. However, we bought keepsakes, and they offset the food we ate.
For an aircraft, maybe each leg/flight is the same...but not summer vacations.
So, we create an optimization problem just like the summer vacation car ride
May 2, 2019: Jeffrey Cohen
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