Abstract
Vertical flight planning concerns assigning optimal cruise altitude and speed to each trajectory-composing segment, such that the fuel consumption is minimized, and the arrival time constraints are satisfied. The previous work that assigns continuous speed to each segment leads to prohibitively long computation time. In this work, we propose a mixed integer linear programming model that assigns discrete speed. In particular, an all-but-one speed discretization scheme is found to scale well with problem size with only negligible objective deviation from using continuous speed. Extensive experiments with real-world instances have shown the practical effectiveness and feasibility of the proposed speed discretization approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aktürk, M.S., Atamtürk, A., Gürel, S.: Aircraft rescheduling with cruise speed control. Operations Research 62(4), 829–845 (2014)
Altus, S.: Flight planning - the forgotten field in airline operations. presented at AGIFORS Airline Operations (2007). http://www.agifors.org/studygrp/opsctl/2007/
Beale, E.L.M., Tomlin, J.A.: Global Optimization Using Special Ordered Sets. Mathematical Programming 10, 52–69 (1976)
Ben-Tal, A., Nemirovski, A.: On Polyhedral Approximations of the Second-Order Cone. Mathematics of Operations Research 26(2), 193–205 (2001)
Blanco, M., Hoang, N.D.: Personal communication on segment fuel estimation in Erlangen, Germany, April 21, 2015
Cook, A., Tanner, G., Williams, V., Meise, G.: Dynamic cost indexing-managing airline delay costs. Journal of Air Transport Management 15(1), 26–35 (2009)
Dantzig, G.B.: On the significance of solving linear programming problems with some integer variables. Econometrica 28(1), 30–44 (1960)
Glineur, F.: Computational Experiments with a Linear Approximation of Second-Order Cone Optimization. Tech. rep., Image Technical Report 0001, Faculté Polytechnique de Mons, Belgium (2000)
Liden, S.: Optimum cruise profiles in the presence of winds. In: Proceedings of IEEE/AIAA 11th Digital Avionics Systems Conference, pp. 254–261. IEEE (1992)
Lovegren, J.A., Hansman, R.J.: Estimation of potential aircraft fuel burn reduction in cruise via speed and altitude optimization strategies. Tech. rep., ICAT-2011-03, MIT International Center for Air Transportation (2011)
Markowitz, H.M., Manne, A.S.: On the solution of discrete programming problems. Econometrica 25(1), 84–110 (1957)
Ng, H.K., Sridhar, B., Grabbe, S.: Optimizing aircraft trajectories with multiple cruise altitudes in the presence of winds. Journal of Aerospace Information Systems 11(1), 35–47 (2014)
IVAO: IFR cruise altitude or flight level. http://ivao.aero/training/documentation/books/SPP_ADC_IFR_Cruise_Altitude.pdf
Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Mathematical Programming 103(2, Ser. B), 225–249 (2005)
Vielma, J.P., Nemhauser, G.L.: Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 199–213. Springer, Heidelberg (2008)
Wilson, D.: Polyhedral Methods for Piecewise-Linear Functions. Ph.D. thesis, University of Kentucky (1998)
Yuan, Z., Amaya Moreno, L., Maolaaisha, A., Fügenschuh, A., Kaier, A., Schlobach, S.: Mixed integer second-order cone programming for the horizontal and vertical free-flight planning problem. Tech. rep., AMOS#21, Applied Mathematical Optimization Series, Helmut Schmidt University, Hamburg, Germany (2015)
Yuan, Z., Fügenschuh, A., Kaier, A., Schlobach, S.: Variable speed in vertical flight planning. In: Operations Research Proceedings. 6 pages. Springer (2014, to appear)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Yuan, Z., Moreno, L.A., Fügenschuh, A., Kaier, A., Schlobach, S. (2015). Discrete Speed in Vertical Flight Planning. In: Corman, F., Voß, S., Negenborn, R. (eds) Computational Logistics. ICCL 2015. Lecture Notes in Computer Science(), vol 9335. Springer, Cham. https://doi.org/10.1007/978-3-319-24264-4_50
Download citation
DOI: https://doi.org/10.1007/978-3-319-24264-4_50
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24263-7
Online ISBN: 978-3-319-24264-4
eBook Packages: Computer ScienceComputer Science (R0)