Computing Bid Prices for Revenue Management Under Customer Choice Behavior

We consider a choice-based, network revenue management (RM) problem in a setting where heterogeneous customers consider an assortment of products offered by a firm (e.g., different flight times, fare classes, and/or routes). Individual choice decisions are modeled through an ordered list of preferences, and minimal assumptions are made about the statistical properties of this demand sequence. The firm manages the availability of products using a bid-price control strategy, and would like to optimize the control parameters. We formulate a continuous demand and capacity model for this problem that allows for the partial acceptance of requests. The model admits a simple calculation of the sample path gradient of the revenue function. This gradient is then used to construct a stochastic steepest ascent algorithm. We show that the algorithm converges (w.p.1) to a stationary point of the expected revenue function under mild conditions. The procedure is relatively efficient from a computational standpoint, and in our synthetic and real-data experiments performs comparably to or even better than other choice-based methods that are incompatible with the current infrastructure of RM systems. These features make it an interesting candidate to be pursued for real-world applications.