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Two-dimensional cargo overbooking models

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  • Luo, Sirong
  • Çakany?ld?r?m, Metin
  • Kasilingam, Raja G.

Abstract

This paper introduces two-dimensional (weight and volume) overbooking problems arising mainly in the cargo revenue management, and compares them with one-dimensional problems. It considers capacity spoilage and cargo offloading costs, and minimizes their sum. For one-dimensional problems, it shows that the optimal overbooking limit does not change with the magnitude of the booking requests. In two-dimensional problems, the overbooking limit is replaced by a curve. The curve, along with the volume and weight axes, encircles the acceptance region. The booking requests are accepted if they fall within this region. We present Curve (Cab) and Rectangle (Rab) models. The boundary of the acceptance region in the Cab (resp. Rab) model is a curve (resp. rectangle). The optimal curve for the Cab model is shown to be unique and continuous. Moreover, it can be obtained by solving a series of simple equations. Finding the optimal rectangle for the Rab model is more challenging, so we propose an approximate rectangle. The approximate rectangle is a limiting solution in the sense that it converges to the optimal rectangle as the booking requests increase. The approximate rectangle is numerically shown to yield costs that are very close to the optimal costs.

Suggested Citation

  • Luo, Sirong & Çakany?ld?r?m, Metin & Kasilingam, Raja G., 2009. "Two-dimensional cargo overbooking models," European Journal of Operational Research, Elsevier, vol. 197(3), pages 862-883, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:3:p:862-883
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    References listed on IDEAS

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    Cited by:

    1. Tatsiana Levina & Yuri Levin & Jeff McGill & Mikhail Nediak, 2011. "Network Cargo Capacity Management," Operations Research, INFORMS, vol. 59(4), pages 1008-1023, August.
    2. Yingjie Lan & Michael O. Ball & Itir Z. Karaesmen, 2011. "Regret in Overbooking and Fare-Class Allocation for Single Leg," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 194-208, December.
    3. Yuri Levin & Mikhail Nediak & Huseyin Topaloglu, 2012. "Cargo Capacity Management with Allotments and Spot Market Demand," Operations Research, INFORMS, vol. 60(2), pages 351-365, April.
    4. He, Wen, 2019. "Impact of capacity flexibility on the use of booking limits," European Journal of Operational Research, Elsevier, vol. 274(1), pages 199-213.
    5. Michael F. Gorman & John-Paul Clarke & Amir Hossein Gharehgozli & Michael Hewitt & René de Koster & Debjit Roy, 2014. "State of the Practice: A Review of the Application of OR/MS in Freight Transportation," Interfaces, INFORMS, vol. 44(6), pages 535-554, December.
    6. Amaruchkul, Kannapha & Sae-Lim, Patipan, 2011. "Airline overbooking models with misspecification," Journal of Air Transport Management, Elsevier, vol. 17(2), pages 143-147.
    7. Dalalah, Doraid & Ojiako, Udechukwu & Chipulu, Maxwell, 2020. "Voluntary overbooking in commercial airline reservations," Journal of Air Transport Management, Elsevier, vol. 86(C).
    8. Masato Wada & Felipe Delgado & Bernardo K. Pagnoncelli, 2017. "A risk averse approach to the capacity allocation problem in the airline cargo industry," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 643-651, June.
    9. Delgado, Felipe & Trincado, Ricardo & Pagnoncelli, Bernardo K., 2019. "A multistage stochastic programming model for the network air cargo allocation under capacity uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 292-307.
    10. Han, Dong Ling & Tang, Loon Ching & Huang, Huei Chuen, 2010. "A Markov model for single-leg air cargo revenue management under a bid-price policy," European Journal of Operational Research, Elsevier, vol. 200(3), pages 800-811, February.
    11. Moussawi-Haidar, Lama, 2014. "Optimal solution for a cargo revenue management problem with allotment and spot arrivals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 173-191.

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