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Revenue management with general stochastic price sensitive demand

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We extend classic, static two-fare class revenue management models to account for demand sensitivity to price, and optimize pricing decisions. We first characterize the sensitivity of the optimal protection level with respect to price in a standard revenue management setting. We then simultaneously optimize price and capacity allocation decisions for the high-end segment, and characterize the uniqueness of the optimal solution. We find that firms with larger capacity should expect lower revenue rates, set higher protection levels, and lower highend prices in a monopolistic environment. We explore several models, with or without demand and resource substitution. Our results hold under general models of stochastic price-dependent demand. A unifying condition for our results is the monotonicity of the elasticity of the rate of lost sales, a concept introduced by Kocabiykoglu and Popescu (2007). Several heuristics for coordinating pricing and allocation decisions are proposed, leading to bounds on expected revenues. Numerical experiments indicate that jointly optimizing the price and protection level for high fare customers leads to significant profit benefits over a hierarchical decision process.

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