An Analysis of Bid-Price Controls for Network Revenue Management

TLDR

Bid‑price controls are increasingly popular for inventory sales in revenue management, yet their theoretical foundations and optimality remain poorly understood. The authors use a general demand‑process model to show that bid‑price control is not generally optimal, analyze its failure modes, and study the properties of asymptotically optimal bid prices. Bid‑price control sets threshold prices for each resource and sells a product only when the fare exceeds the sum of the relevant threshold prices. When capacities and sales volumes are large, correctly chosen bid‑price controls are asymptotically optimal; the authors also provide analytical revenue upper bounds and show that asymptotically optimal bid prices are time‑constant, possibly non‑unique, even under nonstationary demand.

Abstract

Bid-prices are becoming an increasingly popular method for controlling the sale of inventory in revenue management applications. In this form of control, threshold—or “bid”—prices are set for the resources or units of inventory (seats on flight legs, hotel rooms on specific dates, etc.) and a product (a seat in a fare class on an itinerary or room for a sequence of dates) is sold only if the offered fare exceeds the sum of the threshold prices of all the resources needed to supply the product. This approach is appealing on intuitive and practical grounds, but the theory underlying it is not well developed. Moreover, the extent to which bid-price controls represent optimal or near optimal policies is not well understood. Using a general model of the demand process, we show that bid-price control is not optimal in general and analyze why bid-price schemes can fail to produce correct accept/deny decisions. However, we prove that when leg capacities and sales volumes are large, bid-price controls are asymptotically optimal, provided the right bid prices are used. We also provide analytical upper bounds on the optimal revenue. In addition, we analyze properties of the asymptotically optimal bid prices. For example, we show they are constant over time, even when demand is nonstationary, and that they may not be unique.