Modeling fair air traffic assignment in the vicinity of airports

Aircraft noise is recognized as a serious environmental concern and creates significant political problems. This paper presents a new mathematical model to deal with the aircraft noise in the vicinity of airports. The problem to be solved is defined as an assignment of aircraft operations over the routes in order to minimize the total annoyance to citizens at the same time as respecting a fairness scheme. A social-welfare perspective on the noise distribution problem is taken, in contrast to more traditional acoustics-based approaches. Starting from the so-called -fairness Social Welfare Function (SWF) used for maximization problems, we have defined a new -fairness function for minimization problems. We show that this function has similar properties to the maximization -fairness SWF. Analytic results (optimal air traffic assignment, bounds for the Price of Fairness) are provided for the basic case i.e. when routes do not intersect. For more complex cases, when routes cross each others, we show, using a case study (the Brussels Airports case), that modern solvers are able to solve the problem to optimality for realistic scenarios. The model can be used as a decision support tool for a Central Decision Maker (CDM) to allocate flight operations (take-off and landing) over the routes and establish policies in the vicinity of the airport. The paper also provides insights into understanding the relationship between efficiency and fairness.