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Optimal Slot Scheduling for Long-Term Flight Planning


Project team leaders: Prof. Dr. Andreas Brieden, Prof. Dr. Peter Gritzmann, Matthias Hähre, Dipl.-Ing. Gunter Heinrich, Dr. Michael Ritter
Co-operation partners Fraport AG Frankfurt Airport Services Worldwide, Frankfurt
Project Period 2003 - 2008


Over the last decades, civil air traffic has seen a tremendous increase both in terms of air transport movements and in passenger numbers. With these developments, airports around the world are increasingly facing the problem of insufficient capacity to serve all requests from airlines. Building new runways, parking positions and terminal buildings is impossible in many cases due to space restrictions, and even if additional capacities can be built, this is often a lengthy process. To allocate the limited capacity to the increasing demands of airlines, a system of allocation so-called slots, i.e. landing and take-off privileges at some specific time, is used. The number of slots available for an airport at any given time of day depends on many different factors such as air and ground control capacities, the runway system, the terminal capacities or noise regulation policies.

In this project, a comprehensive mathematical model of the slot allocation system was developed. Based on this model, a detailed analysis of favorable and less favorable allocation structures was devised that enables coordination authorities to recognize potentially limiting schedules ahead of their implementation. In addition, an optimization algorithm was implemented that produces an optimal schedule that accounts for both the airlines' demands and the available slot capacities and helps to fully utilize an airport's limited resources.

Related student theses and projects

Supervised Dissertations

Completed Theses and Projects

  • Thomas Fischer - Schnelle Algorithmen in der Flugplanung (Diploma Thesis, 2012)
  • Michael Winkler - Randomisierte Algorithmen für die Slotplanung (Diploma Thesis, 2009)
  • Michael Öllinger - Kombinatorische Designs, lokale Strukturbedingungen und Bewertungsfunktionen (Diploma Thesis, 2009)
  • Thomas Müller - Ein Java-Framework für ein Optimierungsproblem (Project, 2007)

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.