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Double optimal stopping times and dynamic pricing problem: description of the mathematical model

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  • Anna Karpowicz
  • Krzysztof Szajowski

Abstract

In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm’s objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, hotels renting rooms before midnight and theaters selling seats before curtain time that become worthless if not sold by a specific time. 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 double price changes from a given initial price to given lower or higher prices. Under mild conditions, it is shown that it is optimal to decrease the initial price as soon as the time-to-go falls below a time threshold and increase the price if time-to-go is longer than adequate time threshold. These thresholds depend on the number of yet unsold items. Copyright Springer-Verlag 2007

Suggested Citation

  • Anna Karpowicz & Krzysztof Szajowski, 2007. "Double optimal stopping times and dynamic pricing problem: description of the mathematical model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 235-253, October.
  • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:235-253
    DOI: 10.1007/s00186-006-0132-y
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    References listed on IDEAS

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