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A Lagrangian relaxation approach for network inventory control of stochastic revenue management with perishable commodities

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  • H Jiang

    (University of Cambridge)

Abstract

Airline seat inventory control is the allocation of seats in the same cabin to different fare classes such that the total revenue is maximized. Seat allocation can be modelled as dynamic stochastic programs, which are computationally intractable in network settings. Deterministic and probabilistic mathematical programming models are therefore used to approximate dynamic stochastic programs. The probabilistic model, which is the focus of this paper, has a nonlinear objective function, which makes the solution of large-scale practical instances with off-the-shelf solvers prohibitively time consuming. In this paper, we propose a Lagrangian relaxation (LR) method for solving the probabilistic model by exploring the fact that LR problems are decomposable. We show that the solutions of the LR problems admit a simple analytical expression which can be resolved directly. Both the booking limit policy and the bid-price policy can be implemented using this method. Numerical simulations demonstrate the effectiveness of the proposed method.

Suggested Citation

  • H Jiang, 2008. "A Lagrangian relaxation approach for network inventory control of stochastic revenue management with perishable commodities," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 372-380, March.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:3:d:10.1057_palgrave.jors.2602359
    DOI: 10.1057/palgrave.jors.2602359
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    References listed on IDEAS

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    1. S. L. Brumelle & J. I. McGill, 1993. "Airline Seat Allocation with Multiple Nested Fare Classes," Operations Research, INFORMS, vol. 41(1), pages 127-137, February.
    2. Dimitris Bertsimas & Ioana Popescu, 2003. "Revenue Management in a Dynamic Network Environment," Transportation Science, INFORMS, vol. 37(3), pages 257-277, August.
    3. Fred Glover & Randy Glover & Joe Lorenzo & Claude McMillan, 1982. "The Passenger-Mix Problem in the Scheduled Airlines," Interfaces, INFORMS, vol. 12(3), pages 73-80, June.
    4. Peter P. Belobaba, 1989. "OR Practice—Application of a Probabilistic Decision Model to Airline Seat Inventory Control," Operations Research, INFORMS, vol. 37(2), pages 183-197, April.
    5. A. Ciancimino & G. Inzerillo & S. Lucidi & L. Palagi, 1999. "A Mathematical Programming Approach for the Solution of the Railway Yield Management Problem," Transportation Science, INFORMS, vol. 33(2), pages 168-181, May.
    6. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    7. de Boer, Sanne V. & Freling, Richard & Piersma, Nanda, 2002. "Mathematical programming for network revenue management revisited," European Journal of Operational Research, Elsevier, vol. 137(1), pages 72-92, February.
    8. Kalyan Talluri & Garrett van Ryzin, 1999. "A Randomized Linear Programming Method for Computing Network Bid Prices," Transportation Science, INFORMS, vol. 33(2), pages 207-216, May.
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    Cited by:

    1. Yoon, Moon Gil & Lee, Hwi Young & Song, Yoon Sook, 2012. "Linear approximation approach for a stochastic seat allocation problem with cancellation & refund policy in airlines," Journal of Air Transport Management, Elsevier, vol. 23(C), pages 41-46.
    2. Andreea Popescu & Earl Barnes & Ellis Johnson & Pinar Keskinocak, 2013. "Bid Prices When Demand Is a Mix of Individual and Batch Bookings," Transportation Science, INFORMS, vol. 47(2), pages 198-213, May.

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