Mattias Grönkvist, author of a dissertation on the subject, describes the difficulty in concrete terms:
“If ten plans have just landed at an airport, you have to have a schedule that says in what order the planes should take off-and where they are heading. This is determined by numerous conditions. For example, not all types of airplanes are allowed to land at all airports, and the planes have to have sufficiently large fuel tanks to complete each trip. Everything has to be done as efficiently and economically as possible, with sufficient safety.”
The problem is usually called the Tail Assignment Problem-named after the planes’ so-called tail numbers. In other words, it’s a matter of determining what sequence of flightsroutes-each individual airplane is going to fly. The routes must be constructed in such a way as to provide for sufficient maintenance of every plane and to fulfill a number of regulations. Sometimes it is moreover desirable for the routes created to be optimized in some particular way, such as being minimally affected by delays.
For relatively large airlines the Tail Assignment Problem is highly complex. For instance, from an airline’s hub airport there are an enormous number of routes to choose among. Computer programs are deployed to get a handle on all the different conditions. These programs are based on mathematical models.
One of the aims of Mattias Grönkvist’s work was to come to grips with a couple of the drawbacks of the models most commonly used by airlines today:
“Often, not all necessary regulations are addressed, which means that the routes created are difficult to use without extra manual intervention.”
“Most models can only be optimized in regard to a certain predetermined criterion.”
“Traditional models are often used for only a certain type of planning scenario.”
Mattias Grönkvist has combined two ways of solving these problems, on the one hand, using strictly mathematical methods and, on the other, using methods from computer science that have to do with conditional programming. The idea has been mooted before but can now be executed in practice, partly thanks to the explosive growth in the power of computers in recent years.
“My solution is more generally applicable than its predecessors, and it is designed to be used in a greater part of the planning process. I believe this type of combined methodology will be further developed and become more and more common in the future,” says Mattias Grönkvist.
His method has already been put to use in a commercial product that is used by two airlines. The work was carried out as part of a project together with Carmen Systems AB, which develops and markets programs for solving various logistical and planning problems. In the aviation industry the company has previously worked mostly with timetabling of personnel.
The dissertation is titled: The Tail Assignment Problem