It is used in many, many ways.
Planning routes and aircraft deployment. The airline will want to maximise the number of routes that it can serve with the minimum number of aircraft. This will also require careful management of service schedules. The aircraft must be in a location where it can have a proper service. Otherwise you end up flying it empty and empty flights cost money!
The airlines needs to manage plane loading. Also, the load and distance will impact of the amount of fuel that is required. Too much fuel and the airline is wasting fuel carrying the extra weight of the fuel; too little fuel and - you don't really want to think about that!
Dynamic pricing of airline tickets. Leaving aside complications arising from competitors' prices, what are the best pricing policies? Cheaper seats so that more seats are occupied or more expensive one so that revenue per seat is higher. Do you stick with one set of prices or keep changing it as the demand fluctuates? Are you better modelling passenger behaviour?
Pay for air crew, ground staff, their training and other payments. Is it better to have low staff costs even if it means high staff turnover or higher staff costs but labour stability and - maybe - loyalty.
All these considerations will need some mathematical input. And these are only a few that I could think of off the top of my head.
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