**Author(s): ** Rami Atar |

Martin I. Reiman**Journal: ** Stochastic Systems ISSN 1946-5238

**Volume: ** 2;

**Issue: ** 2;

**Start page: ** 232;

**Date: ** 2012;

Original page**Keywords: ** Revenue management |

dynamic pricing |

the Gallego and Van Ryzin model |

fluid optimization problem |

diffusion control problem |

asymptotic optimality |

Brownian bridge |

bridge policy**ABSTRACT**

A dynamic pricing problem that arises in are venue management context is considered, involving several resources and several demand classes, each of which uses a particular subset of the resources. The arrival rates of demand are determined by prices, which can be dynamically controlled. When a demand arrives, it pays the posted price for its class and consumes a quantity of each resource commensurate with its class. The time horizon is finite: at time

*T*the demands cease, and a terminal reward (possibly negative) is received that depends on the unsold capacity of each resource. The problem is to choose a dynamic pricing policy to maximize the expected total reward.When viewed in diffusion scale, the problem gives rise to a diffusion control problem whose solution is a Brownian bridge on the time interval [0,

*T*]. We prove diffusion-scale asymptotic optimality ofa dynamic pricing policy that mimics the behavior of the Brownian bridge.The 'target point' of the Brownian bridge is obtained as the solution of a finite dimensional optimization problem whose structure depends on the terminal reward. We show that, in an airline revenue management problem with no-shows and overbooking, under a realistic assumption on the resource usage of the classes, this finite dimensional optimization problem reduces to a set of newsvendor problems, one for each resource.

## You may be interested in: