On Policies for Single-leg Revenue Management with Limited Demand Information
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In this paper we study the single-leg revenue management problem, with no information given about the demand trajectory over time. The competitive ratio for this problem has been established by Ball and Queyranne (2009) under the assumption of independent demand, i.e., demand for higher fare classes does not spill over to lower fare classes. We extend their results to general demand models to account for the buying-down phenomenon, by incorporating the price-skimming technique from Eren and Maglaras (2010). That is, we derive state-dependent price-skimming policies, which stochastically increase their price distributions as the inventory level decreases, in a way that yields the best-possible competitive ratio. Furthermore, our policies have the benefit that they can be easily adapted to exploit available demand information, such as the personal characteristics of an incoming online customer, while maintaining the competitive ratio guarantee. A key technical ingredient in our paper is a new `valuation tracking' subroutine, which tracks the possible values for the optimum, and follows the most inventory-conservative control which maintains the desired competitive ratio.
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