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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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    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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