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Navigating Complexity: The Cost Model and Constraints Behind Tail Assignment Optimization


In the second of a series of blogs on Tail Assignment we explore we dive deeper into this subject by taking a closer look at the cost model and constraints behind a Tail Assignment optimization.

In this series of blogs, we explore the dynamics of Tail Assignment. Our first blog “Unlocking Efficiency in Airline Scheduling with Tail Assignment Optimization”  gave an introduction of what tail assignment means and how it can generate significant financial returns for airlines. We also explained that in order to execute this optimization effectively, airlines must take into account a wide range of factors, including costs, constraints, and more. In this blog post, we dive deeper into this subject by taking a closer look at the cost model and constraints behind a Tail Assignment optimization.

Tail Assignment is all about assigning the optimal aircraft (tail number) to each flight, in such a way that the costs are minimized, but also that all planned flights can effectively be flown while complying with all constraints.

We try to model the optimization problem as close as possible to the real-world with following components:

  • A model of the available resources, i.e.
    • Aircraft, taking into account planned maintenance and also outages due to repairs.
    • Crew (Statistics), with the necessary qualifications and other constraints to operate the assigned aircrafts. Note that in tail assignment we will work with anonymous crew members. These statistics will be used to assess high level if there is sufficient crew with the right qualifications for a tail assignment.
  • The flight plan, with indication of
    • Minimum turnaround times per airport and aircraft model
    • Scheduled block time per flight
    • Minimum number of seats required (e.g. based on the number of bookings or a forecast of the number of expected bookings) and the class configuration.
  • cost model, taking into account all different costs, e.g.
    • Fuel Costs
      • Green levies
      • Navigation charges (Overflying fees)
      • Landing fees
      • Ground handling fees
      • Maintenance costs
      • Parking & Towing fees
      • Delay & Cancellation penalty fees
      • …​
    • A sustainability model expressing the amount of emissions and noise generated by the different flights, e.g.
      • NOx emissions: can be modelled per block hour, allowing an optimization run on minimization of these emissions.
      • CO2 emissions
      • Noise pollution
    • The constraints, i.e. a set of rules, which will impact the tail assignment. E.g. specific airport restrictions (on Maximum Takeoff Weight or pollution or noise, airport curfews or restrictions…​)

We try to model the optimization problem as close as possible to the real-world

In order to optimize tail assignments effectively, the best way is to incorporate all the applicable costs and constraints to model the real-world as closely as possible. Airlines can then consider tweaking the weights of these costs to put more emphasis on what they want to see as an ideal result. E.g. if NOx emissions are more important than some hard cash costs, one can tweak the weight of this component in the cost function to steer the optimizer towards a further NOx emission reduction.

The resource availability and flight plan are easy to model, as those are very tangible and the constraints are a set of rules, which are defined by the airline, by the departure or arrival airport, by aircraft manufacturers and by regulators. As such these rules need to be respected and are typically modelled as autonomous, independent conditional checks.

The cost model is therefore the most complex part of the input model (when excluding the actual optimization, which will be the subject of the next blog post). Let us have a deeper look at each individual cost element:

  • Fuel Costs: the fuel cost is expressed in a currency (e.g. EUR) per hour flight. This parameter depends therefore on the fuel consumption and the fuel price, i.e.
    • The fuel consumption (expressed in kg/hour) is dependent on a lot of factors, like the aircraft manufacturer and aircraft model, but also on the flight lengths (as departing and landing take more fuel), the weather and jet stream conditions (e.g. tail wind or not), the airline’s flying policies and procedures, the taxi time, the cargo weight, the amount of fuel filled in the tanks and even the individual aircraft (i.e. different tail numbers of the same aircraft model will have different fuel consumptions, sometimes these difference can be up to 10% between aircrafts of the same model).
    • The fuel price (expressed in currency/ton) will depend on the airport (as different countries, but also airlines might have negotiated different pricings per airport), the amount of fuel filled in the aircraft, the moment of filling (the price fluctuates based on demand, although most airlines will hedge their fuel price) and the type of fuel (e.g. pure jet fuel or combination with SAF, biofuels or synthetic fuels – cfr. new European regulation).
  • Green levies: tax imposed or subsidies granted by the government to compensate the negative impact of flying on the environment (i.e. carbon emissions). This tax or subsidy will depend mainly on the CO2 emission (and thus also on all factors described above in the fuel consumption), but also on the departing and arrival airport and the countries overflown during the flight.
  • Navigation charges (Overflying fees): a fee which pays for all navigation expenses (air traffic control centers) to fly over a country or list of countries. The navigation charge typically depends on the MTOW (Maximum Take Off Weight) of the aircraft, but also on the departure and arrival airport.
  • Landing fees: a fee paid by an aircraft operator to an airport company for landing at a particular airport. The fees are to pay for using the airport’s facilities like terminal facilities, taxiway and runway. The fee will depend again on the airport and on the MTOW of the aircraft, but sometimes also on the time the aircraft lands at the airport. Often this fee is also dependent on the noise and emission (carbon and NOx emissions) generated by the aircraft.
  • Ground handling fees: a fee based on the aircraft type, paid for performing the turnaround of the aircraft (baggage handling, load sheet, passenger handling…​) to the ground handler.
  • Maintenance costs: the cost to properly maintain and repair an aircraft. This maintenance cost will also depend on several factors like the aircraft model, the aircraft utilization (expressed in flight hours per year), the aircraft cycles, the aircraft age…​ Important here is also to consider the MEL list (Minimum Equipment List), describing which pieces of equipment may be allowed to be inoperable along with any procedures while maintaining the aircraft airworthy.
  • Parking & Towing fees: these are fees to be paid by the airline to the airport for parking the aircraft (typically when the plane stays a long time at the airport) and/or towing the aircraft from and to a parking stand. This fee will typically depend on the airport and the MTOW (Maximum Takeoff Weight) of the aircraft.
  • Delay & Cancellation penalty fees: governments impose airlines to pay significant compensations to passengers in case of delays on flights or cancellations of flights. These costs can be a significant part of the overall operational cost structure of an airline, hence the need to calculate a robust schedule, which can avoid, minimize or easily mitigate certain delays or cancellations (e.g. access to a backup aircraft in case of unexpected technical issues).
  • Any other costs considered related to a specific aircraft performing a flight

The interactions of all these different costs on the total cost of the flight plan is untraceable for the human mind.

Obviously modelling all the costs in a perfect way is impossible. As a result, every Tail Optimization will work with simplifications, by excluding certain less relevant costs and/or by calculating a specific cost element based on less variables (often derived from historical data).

It becomes quickly clear that the interactions of all these different costs on the total cost of the flight plan is untraceable for the human mind, let alone one would be able to take into account all the required constraints. The expertise of companies specialized in airline optimizations can help in setting up a model, which closely models the real-world. A powerful computer will then grind through all the possibilities, minimizing the total costs of the model, while complying to the constraints laid out in the model. This allows for quick iterations and emphasis on key topics, while making sure the airline is always operating on its best.

In the next blog post in this series, we will take a closer look at how the optimization (calculation) actually works and the sophisticated algorithms behind that.


Photo by Josh Appel on Unsplash