Skip to main content
SpringerLink
Log in

The infinite time horizon dynamic pricing problem with multi-unit demand

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

This paper studies a dynamic pricing problem for a monopolist selling multiple identical items to potential buyers arriving over time, where the time horizon is infinite, the goods are imperishable and the buyers’ arrival follows a renewal process. Each potential buyer has some private information about his purchasing will, and this private information is unknown to the seller and therefore characterized as a random variable in this paper. Thus, the buyers may have multi-unit demand. Meanwhile, the seller needs to determine the optimal posted price such that his expected discounted revenue is maximized. This problem is formulated as a stochastic dynamic programming in this paper and then how to obtain the solution is explored. A numerical study shows that the optimal posted price performs better than that of optimal fixed price, and this advantage becomes obvious as the interest rate and/or the number of initial items increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chatwin R.E.: Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices. Eur. J. Oper. Res. 125(1), 149–174 (2000)

    Article  MATH  Google Scholar 

  2. Elmaghraby W., Keskinocak P.: Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions. Manag. Sci. 49(10), 1287–1309 (2003)

    Article  MATH  Google Scholar 

  3. Bitran G., Caldentey R.: An overview of pricing models for revenue management. Manuf. Serv. Oper. Manag. 5(3), 203–229 (2003)

    Article  Google Scholar 

  4. Monahan G.E., Petruzzi N.C., Zhao W.: The dynamic pricing problem from a newsvendor’s perspective. Manuf. Serv. Oper. Manag. 6(1), 73–91 (2004)

    Article  Google Scholar 

  5. Chou F.-S., Parlar M.: Optimal control of a revenue management system with dynamic pricing facing linear demand. Optim. Control Appl. Methods. 27(6), 323–347 (2006)

    Article  MathSciNet  Google Scholar 

  6. Das Varma G., Vettas N.: Optimal dynamic pricing with inventories. Econ. Lett. 72(3), 335–340 (2001)

    Article  MATH  Google Scholar 

  7. Gallien J.: Dynamic mechanism design for online commerce. Oper. Res. 54(2), 291–310 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Systems Engineering, Tianjin University, Tianjin, 300072, China

    Cheng Wang, Wansheng Tang & Ruiqing Zhao

  2. Institute of Industrial Engineering, Zhejiang University of Technology, Hangzhou, 310014, China

    Cheng Wang

Authors
  1. Cheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wansheng Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruiqing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wansheng Tang.

Additional information

This work was supported partially by the Natural Science Foundation of China under Grant No. 71071106 and 70971092, Natural Science Foundation of Zhejiang University of Technology (2011XY006), supported partially by Program for Changjiang Scholars and Innovative Research Team in University No. IRT1028, and supported partially by Program for New Century Excellent Talents in Universities of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, C., Tang, W. & Zhao, R. The infinite time horizon dynamic pricing problem with multi-unit demand. Optim Lett 7, 1125–1138 (2013). https://doi.org/10.1007/s11590-012-0487-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-012-0487-3

Keywords

Search

Navigation