Optimal Starting Times for End-of-Season Sales and Optimal Stopping Times for Promotional Fares

TLDR

Many industries, such as airlines, hotels, theaters, and seasonal retailers, must sell a fixed inventory over a finite horizon and use price changes to maximize revenue beyond salvage value. The study aims to determine the optimal timing for a single price change from an initial price to a lower or higher second price. The authors model this as a decision problem over a finite horizon with stochastic, price‑sensitive demand. They prove that, under mild conditions, it is optimal to lower (or raise) the price when the remaining time falls below (or exceeds) a threshold that depends on the number of unsold items.

Abstract

Many industries face the problem of selling a fixed stock of items over a finite horizon. These industries include airlines selling seats before planes depart, hotels renting rooms before midnight, theaters selling seats before curtain time, and retailers selling seasonal goods such as air-conditioners or winter coats before the end of the season. Given a fixed number of seats, rooms, or coats, the objective for these industries is to maximize revenues in excess of salvage value. When demand is price sensitive and stochastic, pricing is an effective tool to maximize revenues. In this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price. Under mild conditions, we show that it is optimal to decrease (resp., to increase) the initial price as soon as the time-to-go falls below (resp., above) a time threshold that depends on the number of yet unsold items.