IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v47y2013i4p508-525.html
   My bibliography  Save this article

A Lifted Compact Formulation for the Daily Aircraft Maintenance Routing Problem

Author

Listed:
  • Mohamed Haouari

    (Department of Mechanical and Industrial Engineering, Qatar University, Doha, Qatar)

  • Shengzhi Shao

    (Grado Department of Industrial and Systems Engineering (0118), Virginia Tech, Blacksburg, Virginia 24061)

  • Hanif D. Sherali

    (Grado Department of Industrial and Systems Engineering (0118), Virginia Tech, Blacksburg, Virginia 24061)

Abstract

Given a set of flights for a specific fleet type, the aircraft routing problem (ARP) determines the flying sequence for each individual aircraft while incorporating specific considerations of minimum turn time, maintenance checks, as well as restrictions on the total accumulated flying time, the total number of takeoffs, and the total number of days between two consecutive maintenances. This stage is significant to airline companies as it directly assigns operational routes and maintenance breaks for each aircraft in service. Most approaches related to the problem adopt set partitioning formulations that include exponentially many variables, which requires the design of specialized column generation or branch-and-price algorithms and codes. In this paper, we present a compact polynomial-sized representation for the ARP, which is then linearized and lifted using the reformulation-linearization technique. In addition, we propose two root-node strategies for further augmenting the model formulation. The resulting formulations remain polynomial in size, and we show that they can be solved very efficiently by commercial software without complicated algorithmic implementations. The numerical experiments demonstrate high-quality solutions and significant savings in computational time.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:4:p:508-525
    DOI: 10.1287/trsc.1120.0433
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1120.0433
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.1120.0433?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Diego Klabjan, 2005. "Large-Scale Models in the Airline Industry," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 163-195, Springer.
    2. Ram Gopalan & Kalyan T. Talluri, 1998. "The Aircraft Maintenance Routing Problem," Operations Research, INFORMS, vol. 46(2), pages 260-271, April.
    3. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    4. Kalyan T. Talluri, 1998. "The Four-Day Aircraft Maintenance Routing Problem," Transportation Science, INFORMS, vol. 32(1), pages 43-53, February.
    5. 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.
    6. Lloyd Clarke & Ellis Johnson & George Nemhauser & Zhongxi Zhu, 1997. "The aircraft rotation problem," Annals of Operations Research, Springer, vol. 69(0), pages 33-46, January.
    7. Hanif D. Sherali & Warren P. Adams & Patrick J. Driscoll, 1998. "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems," Operations Research, INFORMS, vol. 46(3), pages 396-405, June.
    8. Amy Mainville Cohn & Cynthia Barnhart, 2003. "Improving Crew Scheduling by Incorporating Key Maintenance Routing Decisions," Operations Research, INFORMS, vol. 51(3), pages 387-396, June.
    9. 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.
    10. Sherali, Hanif D. & Bish, Ebru K. & Zhu, Xiaomei, 2006. "Airline fleet assignment concepts, models, and algorithms," European Journal of Operational Research, Elsevier, vol. 172(1), pages 1-30, July.
    11. Shan Lan & John-Paul Clarke & Cynthia Barnhart, 2006. "Planning for Robust Airline Operations: Optimizing Aircraft Routings and Flight Departure Times to Minimize Passenger Disruptions," Transportation Science, INFORMS, vol. 40(1), pages 15-28, 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. Guy Desaulniers & Jacques Desrosiers & Yvan Dumas & Marius M. Solomon & François Soumis, 1997. "Daily Aircraft Routing and Scheduling," Management Science, INFORMS, vol. 43(6), pages 841-855, June.
    14. Anne Mercier, 2008. "A Theoretical Comparison of Feasibility Cuts for the Integrated Aircraft-Routing and Crew-Pairing Problem," Transportation Science, INFORMS, vol. 42(1), pages 87-104, February.
    15. Sriram, Chellappan & Haghani, Ali, 2003. "An optimization model for aircraft maintenance scheduling and re-assignment," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(1), pages 29-48, January.
    16. 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.
    17. Diego Klabjan & Ellis L. Johnson & George L. Nemhauser & Eric Gelman & Srini Ramaswamy, 2002. "Airline Crew Scheduling with Time Windows and Plane-Count Constraints," Transportation Science, INFORMS, vol. 36(3), pages 337-348, August.
    18. Thomas A. Feo & Jonathan F. Bard, 1989. "Flight Scheduling and Maintenance Base Planning," Management Science, INFORMS, vol. 35(12), pages 1415-1432, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Max Z. & Ryerson, Megan S., 2019. "Reviewing the DATAS of aviation research data: Diversity, availability, tractability, applicability, and sources," Journal of Air Transport Management, Elsevier, vol. 75(C), pages 111-130.
    2. Shengzhi Shao & Hanif D. Sherali & Mohamed Haouari, 2017. "A Novel Model and Decomposition Approach for the Integrated Airline Fleet Assignment, Aircraft Routing, and Crew Pairing Problem," Transportation Science, INFORMS, vol. 51(1), pages 233-249, February.
    3. Xiao, Fan & Guo, Siqi & Huang, Lin & Huang, Lei & Liang, Zhe, 2022. "Integrated aircraft tail assignment and cargo routing problem with through cargo consideration," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 328-351.
    4. He, Yonghuan & Ma, Hoi-Lam & Park, Woo-Yong & Liu, Shi Qiang & Chung, Sai-Ho, 2023. "Maximizing robustness of aircraft routing with heterogeneous maintenance tasks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    5. De Bruecker, Philippe & Beliën, Jeroen & Van den Bergh, Jorne & Demeulemeester, Erik, 2018. "A three-stage mixed integer programming approach for optimizing the skill mix and training schedules for aircraft maintenance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 439-452.
    6. Zhe Liang & Wanpracha Art Chaovalitwongse, 2013. "A Network-Based Model for the Integrated Weekly Aircraft Maintenance Routing and Fleet Assignment Problem," Transportation Science, INFORMS, vol. 47(4), pages 493-507, November.
    7. Shaukat, Syed & Katscher, Mathias & Wu, Cheng-Lung & Delgado, Felipe & Larrain, Homero, 2020. "Aircraft line maintenance scheduling and optimisation," Journal of Air Transport Management, Elsevier, vol. 89(C).
    8. Safaei, Nima & Jardine, Andrew K.S., 2018. "Aircraft routing with generalized maintenance constraints," Omega, Elsevier, vol. 80(C), pages 111-122.
    9. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).
    10. Ben Ahmed, Mohamed & Zeghal Mansour, Farah & Haouari, Mohamed, 2018. "Robust integrated maintenance aircraft routing and crew pairing," Journal of Air Transport Management, Elsevier, vol. 73(C), pages 15-31.
    11. Maher, Stephen J. & Desaulniers, Guy & Soumis, François, 2018. "The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints," European Journal of Operational Research, Elsevier, vol. 264(2), pages 534-547.
    12. Sanchez, David Torres & Boyacı, Burak & Zografos, Konstantinos G., 2020. "An optimisation framework for airline fleet maintenance scheduling with tail assignment considerations," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 142-164.
    13. Carlos Lagos & Felipe Delgado & Mathias A. Klapp, 2020. "Dynamic Optimization for Airline Maintenance Operations," Transportation Science, INFORMS, vol. 54(4), pages 998-1015, July.
    14. Saltzman, Robert M. & Stern, Helman I., 2022. "The multi-day aircraft maintenance routing problem," Journal of Air Transport Management, Elsevier, vol. 102(C).
    15. Sciau, Jean-Baptiste & Goyon, Agathe & Sarazin, Alexandre & Bascans, Jérémy & Prud’homme, Charles & Lorca, Xavier, 2024. "Using constraint programming to address the operational aircraft line maintenance scheduling problem," Journal of Air Transport Management, Elsevier, vol. 115(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Başdere, Mehmet & Bilge, Ümit, 2014. "Operational aircraft maintenance routing problem with remaining time consideration," European Journal of Operational Research, Elsevier, vol. 235(1), pages 315-328.
    2. 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.
    3. Zhe Liang & Wanpracha Art Chaovalitwongse, 2013. "A Network-Based Model for the Integrated Weekly Aircraft Maintenance Routing and Fleet Assignment Problem," Transportation Science, INFORMS, vol. 47(4), pages 493-507, November.
    4. Zhe Liang & Wanpracha Art Chaovalitwongse & Huei Chuen Huang & Ellis L. Johnson, 2011. "On a New Rotation Tour Network Model for Aircraft Maintenance Routing Problem," Transportation Science, INFORMS, vol. 45(1), pages 109-120, February.
    5. 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.
    6. Hanif D. Sherali & Ki-Hwan Bae & Mohamed Haouari, 2013. "An Integrated Approach for Airline Flight Selection and Timing, Fleet Assignment, and Aircraft Routing," Transportation Science, INFORMS, vol. 47(4), pages 455-476, November.
    7. Liang, Zhe & Feng, Yuan & Zhang, Xiaoning & Wu, Tao & Chaovalitwongse, Wanpracha Art, 2015. "Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 238-259.
    8. Sanchez, David Torres & Boyacı, Burak & Zografos, Konstantinos G., 2020. "An optimisation framework for airline fleet maintenance scheduling with tail assignment considerations," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 142-164.
    9. Parmentier, Axel & Meunier, Frédéric, 2020. "Aircraft routing and crew pairing: Updated algorithms at Air France," Omega, Elsevier, vol. 93(C).
    10. Oliver Faust & Jochen Gönsch & Robert Klein, 2017. "Demand-Oriented Integrated Scheduling for Point-to-Point Airlines," Transportation Science, INFORMS, vol. 51(1), pages 196-213, February.
    11. 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.
    12. Gopalan, Ram, 2014. "The Aircraft Maintenance Base Location Problem," European Journal of Operational Research, Elsevier, vol. 236(2), pages 634-642.
    13. Chunhua Gao & Ellis Johnson & Barry Smith, 2009. "Integrated Airline Fleet and Crew Robust Planning," Transportation Science, INFORMS, vol. 43(1), pages 2-16, February.
    14. Sciau, Jean-Baptiste & Goyon, Agathe & Sarazin, Alexandre & Bascans, Jérémy & Prud’homme, Charles & Lorca, Xavier, 2024. "Using constraint programming to address the operational aircraft line maintenance scheduling problem," Journal of Air Transport Management, Elsevier, vol. 115(C).
    15. 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.
    16. Safaei, Nima & Jardine, Andrew K.S., 2018. "Aircraft routing with generalized maintenance constraints," Omega, Elsevier, vol. 80(C), pages 111-122.
    17. Lacasse-Guay, Eve & Desaulniers, Guy & Soumis, François, 2010. "Aircraft routing under different business processes," Journal of Air Transport Management, Elsevier, vol. 16(5), pages 258-263.
    18. Shengzhi Shao & Hanif D. Sherali & Mohamed Haouari, 2017. "A Novel Model and Decomposition Approach for the Integrated Airline Fleet Assignment, Aircraft Routing, and Crew Pairing Problem," Transportation Science, INFORMS, vol. 51(1), pages 233-249, February.
    19. Valentina Cacchiani & Juan-José Salazar-González, 2017. "Optimal Solutions to a Real-World Integrated Airline Scheduling Problem," Transportation Science, INFORMS, vol. 51(1), pages 250-268, February.
    20. Eltoukhy, Abdelrahman E.E. & Wang, Z.X. & Chan, Felix T.S. & Fu, X., 2019. "Data analytics in managing aircraft routing and maintenance staffing with price competition by a Stackelberg-Nash game model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 143-168.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:47:y:2013:i:4:p:508-525. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.