A Linear Programming Approach to the Development of Contrail Reduction Strategies Satisfying Operationally Feasible Constraints

A 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.