Optimizer key concepts: Airline Example

Analytica Optimizer GuideOptimizer key concepts: Airline Example

The Airline Non-Linear Program (NLP) Example demonstrates a set of key concepts that Analytica Optimizer modelers should be familiar with. Although it includes some topics that apply only to NLP models, each module includes content that is relevant to all optimization types.

Sections

• Concepts Covered in the Airline NLP Example
• NLP Characteristics
• Airline NLP Module 1: Base Case
• Using parametric analysis: Airline NLP Module 2
• Optimizing with Uncertainty
• Improving Computational Efficiency of NLPs
• Module 5: Time as an Extrinsic index
• Identifying the Source of an Extrinsic Index
• Module 6: Time as an Intrinsic Index
• Module 7: Embedding an NLP in a Dynamic Loop
• Controlling Engine Selection and Settings

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

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)^(-Elacticity)

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)

Optimizing with ArraysOptimizer key concepts: Airline ExampleOptimizer Attribute Reference