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Dynamic Stochastic Optimization Models for Air Traffic Flow Management

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  • Mukherjee, Avijit

Abstract

This dissertation presents dynamic stochastic optimization models for Air Traffic Flow Management (ATFM) that enables decisions to adapt to new information on evolving capacities of National Airspace System (NAS) resources. Uncertainty is represented by a set of capacity scenarios, each depicting a particular time-varying capacity profile of NAS resources. We use the concept of a scenario tree in which multiple scenarios are possible initially. Scenarios are eliminated as possibilities in a succession of branching points, until the specific scenario that will be realized on a particular day is known. Thus the scenario tree branching provides updated information on evolving scenarios, and allows ATFM decisions to be re-addressed and revised. First, we propose a dynamic stochastic model for a single airport ground holding problem (SAGHP) that can be used for planning Ground Delay Programs (GDPs) when there is uncertainty about future airport arrival capacities. Ground delays of non-departed flights can be revised based on updated information from scenario tree branching. The problem is formulated so that a wide range of objective functions, including non-linear delay cost functions and functions that reflect equity concerns can be optimized. Furthermore, the model improves on existing practice by ensuring efficient use of available capacity without necessarily exempting long-haul flights. Following this, we present a methodology and optimization models that can be used for decentralized decision making by individual airlines in the GDP planning process, using the solutions from the stochastic dynamic SAGHP. Airlines are allowed to perform cancellations, and re-allocate slots to remaining flights by substitutions. We also present an optimization model that can be used by the FAA, after the airlines perform cancellation and substitutions, to re-utilize vacant arrival slots that are created due to cancellations. Finally, we present three stochastic integer programming models for managing inbound air traffic flow of an airport, when there is adverse weather impacting the arrival capacity of the airport along with its arrival fixes. These are the first models, for optimizing ATFM decisions, which address uncertainty of future capacities of multiple NAS resources.

Suggested Citation

  • Mukherjee, Avijit, 2004. "Dynamic Stochastic Optimization Models for Air Traffic Flow Management," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2vk8w6nc, Institute of Transportation Studies, UC Berkeley.
  • Handle: RePEc:cdl:itsrrp:qt2vk8w6nc
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    References listed on IDEAS

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    1. Octavio Richetta & Amedeo R. Odoni, 1993. "Solving Optimally the Static Ground-Holding Policy Problem in Air Traffic Control," Transportation Science, INFORMS, vol. 27(3), pages 228-238, August.
    2. Lisa Navazio & Giorgio Romanin-Jacur, 1998. "The Multiple Connections Multi-Airport Ground Holding Problem: Models and Algorithms," Transportation Science, INFORMS, vol. 32(3), pages 268-276, August.
    3. Mostafa Terrab & Amedeo R. Odoni, 1993. "Strategic Flow Management for Air Traffic Control," Operations Research, INFORMS, vol. 41(1), pages 138-152, February.
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    5. Michael O. Ball & Robert Hoffman & Amedeo R. Odoni & Ryan Rifkin, 2003. "A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem," Operations Research, INFORMS, vol. 51(1), pages 167-171, February.
    6. Richetta, Octavio & Odoni, Amedeo R., 1994. "Dynamic solution to the ground-holding problem in air traffic control," Transportation Research Part A: Policy and Practice, Elsevier, vol. 28(3), pages 167-185, May.
    7. Dimitris Bertsimas & Sarah Stock Patterson, 2000. "The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach," Transportation Science, INFORMS, vol. 34(3), pages 239-255, August.
    8. Robert Hoffman & Michael O. Ball, 2000. "A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints," Operations Research, INFORMS, vol. 48(4), pages 578-590, August.
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    Cited by:

    1. Liu, Pei-chen Barry & Hansen, Mark & Mukherjee, Avijit, 2008. "Scenario-based air traffic flow management: From theory to practice," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 685-702, August.
    2. Weigang, Li & de Souza, Bueno Borges & Crespo, Antonio Marcio Ferreira & Alves, Daniela Pereira, 2008. "Decision support system in tactical air traffic flow management for air traffic flow controllers," Journal of Air Transport Management, Elsevier, vol. 14(6), pages 329-336.
    3. Mukherjee, Avijit & Hansen, Mark, 2009. "A dynamic rerouting model for air traffic flow management," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 159-171, January.

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