What is State Variable

Acquiring and purchasing fuel represents a significant part of operating and managing expenses for an airline, so commercial airline companies are implementing strategies for minimizing costs of fuel for their flight routes. A nonlinear mathematical model for the airline refueling problem is presented to minimize the total cost in a flight route problem. The model is enhanced to include possible discounts in fuel prices, which are performed by adding dummy variables and some restrictive constraints, or by fitting a suitable function that relates prices to the purchased amounts. The obtained fuel plan explains exactly the amounts of fuel to be purchased from each airport in the route. A case study is introduced for a certain flight rotation in a domestic US air aviation company. The mathematical model including stepped discounted fuel prices is formulated, and the results show that introducing the discounted fuel prices dramatically change the strategy of fuel purchase amounts in the aircraft flight problem.