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A Lagrangian Relaxation Approach to Assigning Aircraft to Routes in Hub and Spoke Networks

Author

Listed:
  • Mark S. Daskin

    (Northwestern University, Evanston, Illinois 60208)

  • Nicholaos D. Panayotopoulos

    (Northwestern University, Evanston, Illinois 60208)

Abstract

The problem of assigning aircraft to routes to maximize profits in a hub and spoke network is formulated as an integer linear programming problem. A Lagrangian relaxation of the problem is outlined together with heuristics for converting the Lagrangian solutions into primal feasible solutions and for improving on the solutions. Computational results from 324 runs spanning a range of problem sizes are reported. The results suggest that the Lagrangian relaxation is effective at providing an upper bound on the profits and the heuristics yield good solutions when the maximum number of aircraft required to fly all routes in the schedule is less than or equal to the number of available aircraft.

Suggested Citation

  • Mark S. Daskin & Nicholaos D. Panayotopoulos, 1989. "A Lagrangian Relaxation Approach to Assigning Aircraft to Routes in Hub and Spoke Networks," Transportation Science, INFORMS, vol. 23(2), pages 91-99, May.
    • Handle: RePEc:inm:ortrsc:v:23:y:1989:i:2:p:91-99
    DOI: 10.1287/trsc.23.2.91
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    Cited by:

    1. Cynthia Barnhart & Amr Farahat & Manoj Lohatepanont, 2009. "Airline Fleet Assignment with Enhanced Revenue Modeling," Operations Research, INFORMS, vol. 57(1), pages 231-244, February.
    2. Brian Rexing & Cynthia Barnhart & Tim Kniker & Ahmad Jarrah & Nirup Krishnamurthy, 2000. "Airline Fleet Assignment with Time Windows," Transportation Science, INFORMS, vol. 34(1), pages 1-20, February.
    3. Kenan, Nabil & Jebali, Aida & Diabat, Ali, 2018. "The integrated aircraft routing problem with optional flights and delay considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 355-375.
    4. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).
    5. Okan Örsan Özener & Melda Örmeci Matoğlu & Güneş Erdoğan & Mohamed Haouari & Hasan Sözer, 2017. "Solving a large-scale integrated fleet assignment and crew pairing problem," Annals of Operations Research, Springer, vol. 253(1), pages 477-500, June.
    6. Ioachim, Irina & Desrosiers, Jacques & Soumis, Francois & Belanger, Nicolas, 1999. "Fleet assignment and routing with schedule synchronization constraints," European Journal of Operational Research, Elsevier, vol. 119(1), pages 75-90, November.
    7. Huang, Sheng-Chen Alex, 1998. "Airline Delay Perturbation Problem Under Minor Disturbance," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt557153vs, Institute of Transportation Studies, UC Berkeley.
    8. Cynthia Barnhart & Timothy S. Kniker & Manoj Lohatepanont, 2002. "Itinerary-Based Airline Fleet Assignment," Transportation Science, INFORMS, vol. 36(2), pages 199-217, May.
    9. Mohamed Haouari & Shengzhi Shao & Hanif D. Sherali, 2013. "A Lifted Compact Formulation for the Daily Aircraft Maintenance Routing Problem," Transportation Science, INFORMS, vol. 47(4), pages 508-525, November.
    10. Hanif D. Sherali & Ebru K. Bish & Xiaomei Zhu, 2005. "Polyhedral Analysis and Algorithms for a Demand-Driven Refleeting Model for Aircraft Assignment," Transportation Science, INFORMS, vol. 39(3), pages 349-366, August.
    11. F M Zeghal & M Haouari & H D Sherali & N Aissaoui, 2011. "Flexible aircraft fleeting and routing at TunisAir," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 368-380, February.
    12. Haouari, Mohamed & Aissaoui, Najla & Mansour, Farah Zeghal, 2009. "Network flow-based approaches for integrated aircraft fleeting and routing," European Journal of Operational Research, Elsevier, vol. 193(2), pages 591-599, March.
    13. Ahmad I. Jarrah & Jon Goodstein & Ram Narasimhan, 2000. "An Efficient Airline Re-Fleeting Model for the Incremental Modification of Planned Fleet Assignments," Transportation Science, INFORMS, vol. 34(4), pages 349-363, November.
    14. Sarac, Abdulkadir & Batta, Rajan & Rump, Christopher M., 2006. "A branch-and-price approach for operational aircraft maintenance routing," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1850-1869, December.
    15. Saravanan Venkatachalam & Suresh Acharya & Kenji Oba & Yoshinari Nakayama, 2020. "Prescriptive Analytics for Swapping Aircraft Assignments at All Nippon Airways," Interfaces, INFORMS, vol. 50(2), pages 99-111, March.
    16. Khaled, Oumaima & Minoux, Michel & Mousseau, Vincent & Michel, Stéphane & Ceugniet, Xavier, 2018. "A compact optimization model for the tail assignment problem," European Journal of Operational Research, Elsevier, vol. 264(2), pages 548-557.

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