== Abstract ==

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 class of strategies has been proposed to reduce contrail formation in the United States airspace. A 3D grid based on weather data is built and the cruising altitude level of aircraft is adjusted to avoid the persistent contrail potential area with the consideration to fuel-eciency. In this paper, the authors introduce a contrail avoidance strategy on 3D grid by considering additional operationally feasible constraints from an air trac controllers aspect. First, shifting too many aircraft to the same cruising level will make the miles-in-trail at this level smaller than the safety separation threshold. Furthermore, the high density of aircraft at one cruising level may exceed the manageable workload for the trac controller. Therefore, in our new model we restrict the number of total aircraft at each level. Second, the aircraft count variation for successive intervals can not be too drastic since the workload to manage climbing/descending aircraft is much larger than managing cruising aircraft. The contrail reduction problem is formulated as integer programming and the problem is shown to have the property of total unimodularity. Solving the corresponding relaxed linear programming with the simplex method provides an optimal and integral solution to the problem. Simulation results are provided to illustrate the methodology.

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== Original document ==

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The different versions of the original document can be found in:

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* [http://www.aviationsystemsdivision.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf http://www.aviationsystemsdivision.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf]

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* [http://arc.aiaa.org/doi/pdf/10.2514/6.2012-4754 http://arc.aiaa.org/doi/pdf/10.2514/6.2012-4754],

: [http://dx.doi.org/10.2514/6.2012-4754 http://dx.doi.org/10.2514/6.2012-4754]

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* [http://www.aere.iastate.edu/~pwei/proceedings/gnc12.pdf http://www.aere.iastate.edu/~pwei/proceedings/gnc12.pdf],

: [https://aviationsystemsdivision.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf https://aviationsystemsdivision.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf],

: [https://www.aviationsystems.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf https://www.aviationsystems.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf],

: [https://ntrs.nasa.gov/search.jsp?R=20120016837 https://ntrs.nasa.gov/search.jsp?R=20120016837],

: [https://www.aere.iastate.edu/~pwei/proceedings/gnc12.pdf https://www.aere.iastate.edu/~pwei/proceedings/gnc12.pdf],

: [https://repository.exst.jaxa.jp/dspace/handle/a-is/240029 https://repository.exst.jaxa.jp/dspace/handle/a-is/240029],

: [http://www.aviationsystems.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf http://www.aviationsystems.arc.nasa.gov/publications/2012/AIAA-2012-4754.pdf],

: [https://trid.trb.org/view.aspx?id=1247627 https://trid.trb.org/view.aspx?id=1247627],

: [https://academic.microsoft.com/#/detail/2164382049 https://academic.microsoft.com/#/detail/2164382049]

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