# Airline NLP Module 1: Base Case

You can navigate to the Airline NLP example starting in the directory in which Analytica is installed: `Example Models/Optimizer Examples/Airline NLP.ana`

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The goal is to determine optimum ticket fare and the number of planes to operate such that the airline can achieve the highest profit possible.

Decisions are **Fare** and the **Number of Planes**. Since this is an NLP, the values we use to define these decisions will be used as initial guesses in the optimization. **Fare** will be a continuous variable with lower and upper bounds. **Number of Planes** will be an Integer value with lower and upper bounds.

Decision Fare := 200 Domain of Fare := Continuous(100, 400) Decision Number_of_Planes := 3 Domain of Number_of_Planes := Integer(1, 5)

First, we assume a base level of demand in passenger-trips per year assuming a base fare of $200 per trip.

`Variable Base_Demand := 400k`

Actual demand will vary by price according to market demand elasticity.

`Variable Elasticity := 3`

`Variable Demand := Base_Demand*(Fare/200)^(-Elasticity)`

Each plane holds 200 passengers. We assume each plane makes two trips per day, 360 days per year.

`Variable Seats_per_plane := 200`

`Variable Annual_Capacity := Number_of_Planes*Seats_per_Plane*360*2`

Annual seats sold is limited either by capacity or by passenger demand.

`Variable Seats_Sold := Min([Demand, Annual_Capacity])`

We assume annual fixed cost per plane and variable cost per passenger.

`Variable Fixed_cost := 15M`

`Variable Var_cost := 30`

The objective, **Profit**, is the difference between revenue and cost.

`Objective Profit := Seats_sold*(Fare - Var_cost) - Number_of_Planes*Fixed_cost`

Finally, we create the optimization node and solution quantities.

Variable Opt := DefineOptimization( Decisions: Number_of_Planes, Fare Maximize: Profit) Decision Optimal_Fare := OptSolution(Opt, Fare) Decision Optimal_Planes := OptSolution(Opt, Number_of_Planes) Objective Optimal_Profit := OptObjective(Opt) Variable Opt_Status := OptStatusText(Opt)

The solution yields an optimal fare of $195 with three planes in service.

## See Also

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