IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v505y2018icp512-522.html
   My bibliography  Save this article

Discount pricing in word-of-mouth marketing: An optimal control approach

Author

Listed:
  • Li, Pengdeng
  • Yang, Xiaofan
  • Wu, Yingbo
  • He, Weiyi
  • Zhao, Pengpeng

Abstract

This paper addresses the discount pricing in word-of-mouth (WOM) marketing. First, a dynamic model capturing WOM spreading processes is suggested. Second, the problem of finding an optimal discount strategy boils down to an optimal control problem. Third, the existence of an optimal control for the control problem is proved, and an optimality system for finding an optimal control is presented. Thereby, the dynamic discount strategy associated with the optimal control is recommended. Some examples of the optimal control are given. Finally, the influence of different factors on the optimal expected net profit is examined.

Suggested Citation

  • Li, Pengdeng & Yang, Xiaofan & Wu, Yingbo & He, Weiyi & Zhao, Pengpeng, 2018. "Discount pricing in word-of-mouth marketing: An optimal control approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 512-522.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:512-522
    DOI: 10.1016/j.physa.2018.03.062
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118303923
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.03.062?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    3. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    4. James P. Monahan, 1984. "A Quantity Discount Pricing Model to Increase Vendor Profits," Management Science, INFORMS, vol. 30(6), pages 720-726, June.
    5. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
    6. Ming Chen & Zhi-Long Chen, 2015. "Recent Developments in Dynamic Pricing Research: Multiple Products, Competition, and Limited Demand Information," Production and Operations Management, Production and Operations Management Society, vol. 24(5), pages 704-731, May.
    7. Xia, Cheng-yi & Wang, Zhen & Sanz, Joaquin & Meloni, Sandro & Moreno, Yamir, 2013. "Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1577-1585.
    8. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    9. Li, Pengdeng & Yang, Xiaofan & Yang, Lu-Xing & Xiong, Qingyu & Wu, Yingbo & Tang, Yuan Yan, 2018. "The modeling and analysis of the word-of-mouth marketing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 1-16.
    10. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    11. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
    12. Adam J. Mersereau & Dan Zhang, 2012. "Markdown Pricing with Unknown Fraction of Strategic Customers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 355-370, July.
    13. Yang, Lu-Xing & Draief, Moez & Yang, Xiaofan, 2016. "The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 403-415.
    14. Zhang, Tianrui & Yang, Lu-Xing & Yang, Xiaofan & Wu, Yingbo & Tang, Yuan Yan, 2017. "Dynamic malware containment under an epidemic model with alert," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 249-260.
    15. Linhe Zhu & Hongyong Zhao, 2017. "Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(10), pages 2064-2078, July.
    16. Hau L. Lee & Meir J. Rosenblatt, 1986. "A Generalized Quantity Discount Pricing Model to Increase Supplier's Profits," Management Science, INFORMS, vol. 32(9), pages 1177-1185, September.
    17. Amiya K. Chakravarty & G. E. Martin, 1989. "Discount pricing policies for inventories subject to declining demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 89-102, February.
    18. Chen, Duanbing & Lü, Linyuan & Shang, Ming-Sheng & Zhang, Yi-Cheng & Zhou, Tao, 2012. "Identifying influential nodes in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1777-1787.
    19. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    20. repec:inm:ormnsc:v:30:y:1984:i:12:p:1524-1539(2 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Fang & Huang, Yao-Huei & Li, Jun, 2019. "Alternative solution algorithm for winner determination problem with quantity discount of transportation service procurement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guillermo Gallego & Michael Z. F. Li & Yan Liu, 2020. "Dynamic Nonlinear Pricing of Inventories over Finite Sales Horizons," Operations Research, INFORMS, vol. 68(3), pages 655-670, May.
    2. Muzaffer Buyruk & Ertan Güner, 2022. "Personalization in airline revenue management: an overview and future outlook," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(2), pages 129-139, April.
    3. Yiwei Chen & Vivek F. Farias, 2013. "Simple Policies for Dynamic Pricing with Imperfect Forecasts," Operations Research, INFORMS, vol. 61(3), pages 612-624, June.
    4. Sabri Çelik & Alp Muharremoglu & Sergei Savin, 2009. "Revenue Management with Costly Price Adjustments," Operations Research, INFORMS, vol. 57(5), pages 1206-1219, October.
    5. Dasu, Sriram & Tong, Chunyang, 2010. "Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes," European Journal of Operational Research, Elsevier, vol. 204(3), pages 662-671, August.
    6. Peter Seele & Claus Dierksmeier & Reto Hofstetter & Mario D. Schultz, 2021. "Mapping the Ethicality of Algorithmic Pricing: A Review of Dynamic and Personalized Pricing," Journal of Business Ethics, Springer, vol. 170(4), pages 697-719, May.
    7. Netessine, Serguei, 2006. "Dynamic pricing of inventory/capacity with infrequent price changes," European Journal of Operational Research, Elsevier, vol. 174(1), pages 553-580, October.
    8. Tamer Boyacı & Özalp Özer, 2010. "Information Acquisition for Capacity Planning via Pricing and Advance Selling: When to Stop and Act?," Operations Research, INFORMS, vol. 58(5), pages 1328-1349, October.
    9. Kyle Y. Lin, 2004. "A sequential dynamic pricing model and its applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 501-521, June.
    10. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2021. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Dynamic Games and Applications, Springer, vol. 11(3), pages 463-490, September.
    11. Yalç{i}n Akçay & Harihara Prasad Natarajan & Susan H. Xu, 2010. "Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice," Management Science, INFORMS, vol. 56(8), pages 1345-1361, August.
    12. Zhou, Yong-Wu & Lin, Xiaogang & Zhong, Yuanguang & Xie, Wei, 2019. "Contract selection for a multi-service sharing platform with self-scheduling capacity," Omega, Elsevier, vol. 86(C), pages 198-217.
    13. Cenying Yang & Yihao Feng & Andrew Whinston, 2022. "Dynamic Pricing and Information Disclosure for Fresh Produce: An Artificial Intelligence Approach," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 155-171, January.
    14. Mochen Yang & Gediminas Adomavicius & Alok Gupta, 2019. "Efficient Computational Strategies for Dynamic Inventory Liquidation," Information Systems Research, INFORMS, vol. 30(2), pages 595-615, June.
    15. Doan, Xuan Vinh & Lei, Xiao & Shen, Siqian, 2020. "Pricing of reusable resources under ambiguous distributions of demand and service time with emerging applications," European Journal of Operational Research, Elsevier, vol. 282(1), pages 235-251.
    16. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    17. Gökgür, Burak & Karabatı, Selçuk, 2019. "Dynamic and targeted bundle pricing of two independently valued products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 184-198.
    18. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    19. Dasci, A. & Karakul, M., 2009. "Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly," European Journal of Operational Research, Elsevier, vol. 197(3), pages 945-968, September.
    20. Yuri Levin & Jeff McGill & Mikhail Nediak, 2008. "Risk in Revenue Management and Dynamic Pricing," Operations Research, INFORMS, vol. 56(2), pages 326-343, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:512-522. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.