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Dynamic Bid Prices in Revenue Management

Graduate School of Business, University of Chicago, Chicago, Illinois 60637
dan.adelman{at}chicagogsb.edu

We formally derive the standard deterministic linear program (LP) for bid-price control by making an affine functional approximation to the optimal dynamic programming value function. This affine functional approximation gives rise to a new LP that yields tighter bounds than the standard LP. Whereas the standard LP computes static bid prices, our LP computes a time trajectory of bid prices. We show that there exist dynamic bid prices, optimal for the LP, that are individually monotone with respect to time. We provide a column generation procedure for solving the LP within a desired optimality tolerance, and present numerical results on computational and economic performance.

Subject classifications: revenue management; pricing; network; bid prices; dynamic programming/optimal control; applications; approximate.
History: Received July 2005; revision received June 2006; accepted June 2006.

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