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Optimal dynamic pricing problem considering patient and impatient customers’ purchasing behaviour

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  • Ping Cao
  • Mengmeng Fan
  • Ke Liu

Abstract

We divide customers into two types according to their purchasing behaviour: one is impatient and the other is patient. An impatient customer will be immediately lost if his reservation price of the product is below the current price, while a patient customer will wait until the price drops below his reservation price and buy one item. The seller’s objective is to maximise his expected discounted overall revenue by dynamically pricing. We prove that the optimal pricing policy has a control limit structure, examine the impact of the proportion parameter on the seller’s expected discounted overall revenue and show that the limiting behaviour of the optimal pricing policy when there are little patient customers is the same as the optimal static pricing policy. We also show that the seller will make more profit if he partially knows the number of waiting customers by providing subscription service to customers. A set of numerical results illustrates the value of dynamic pricing and information with respect to problem parameters such as the arriving probability and the subscription probability.

Suggested Citation

  • Ping Cao & Mengmeng Fan & Ke Liu, 2015. "Optimal dynamic pricing problem considering patient and impatient customers’ purchasing behaviour," International Journal of Production Research, Taylor & Francis Journals, vol. 53(22), pages 6719-6735, November.
    • Handle: RePEc:taf:tprsxx:v:53:y:2015:i:22:p:6719-6735
    DOI: 10.1080/00207543.2015.1056320
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    Cited by:

    1. Lin, Xuxun & Wang, Haiyan, 2022. "Dynamic pricing for online information services considering service duration and quality level," Omega, Elsevier, vol. 109(C).
    2. Li, Zonghuo & Yang, Wensheng & Jin, Hyun Seung & Wang, Di, 2021. "Omnichannel retailing operations with coupon promotions," Journal of Retailing and Consumer Services, Elsevier, vol. 58(C).
    3. Hu, Man & Liu, Xue-Xin & Jia, Fu, 2024. "Optimal Emergency Order Policy for Supply Disruptions in the Semiconductor Industry," International Journal of Production Economics, Elsevier, vol. 272(C).
    4. Silva, Ana Teresa & Moro, Sérgio & Rita, Paulo & Cortez, Paulo, 2018. "Unveiling the features of successful eBay smartphone sellers," Journal of Retailing and Consumer Services, Elsevier, vol. 43(C), pages 311-324.
    5. Mozhu Wang & Jianming Yao, 2023. "A reliable location design of unmanned vending machines based on customer satisfaction," Electronic Commerce Research, Springer, vol. 23(1), pages 541-575, March.

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