IDEAS home Printed from https://ideas.repec.org/a/inm/orisre/v34y2023i2p409-422.html
   My bibliography  Save this article

Estimating Life Cycle Sales of Technology Products with Frequent Repeat Purchases: A Fractional Calculus-Based Approach

Author

Listed:
  • Aslan Lotfi

    (Robins School of Business, University of Richmond, Richmond, Virginia 23173)

  • Zhengrui Jiang

    (Business School, Nanjing University, Nanjing, Jiangsu 210093, China)

  • Ali Lotfi

    (Ivey Business School, Western University, London, Ontario N6G 0N1, Canada)

  • Dipak C. Jain

    (China Europe International Business School, Pudong, Shanghai 201206, P.R. of China)

Abstract

Accurately predicting the sales trajectory of a product in its life cycle is critically important for firms’ medium- and long-term planning. Because classic product-diffusion models such as the Bass model consider only initial product purchases, they are ill-fitted for sales prediction for today’s technology products with a shorter life cycle and frequent repeat purchases or subscription renewals. Despite the long tradition of product diffusion research, there exists no viable model option when repeat purchases constitute a large proportion of product sales. The present study introduces a new sales growth model, termed the generalized diffusion model with repeat purchases (GDMR), to fill this void. The GDMR formulates the growth rate of sales using a noninteger-order integral equation rather than the integer-order differential equation typically adopted in existing diffusion models. The GDMR is parsimonious and easy to implement. Empirical results show that the GDMR fits sales data with varying proportions of repeat purchases quite well, making it suitable for predicting sales of a wide variety of products. In addition, the GDMR can be extended to incorporate marketing mix variables, thus enhancing its applicability in business decision making. Furthermore, using both real and simulated data, we show that the GDMR can reliably recover a product’s adoption trend using only sales data, thus cementing its theoretical validity and empirical effectiveness. Finally, we show that the GDMR is superior to generic time series and machine learning models in predicting future product sales.

Suggested Citation

  • Aslan Lotfi & Zhengrui Jiang & Ali Lotfi & Dipak C. Jain, 2023. "Estimating Life Cycle Sales of Technology Products with Frequent Repeat Purchases: A Fractional Calculus-Based Approach," Information Systems Research, INFORMS, vol. 34(2), pages 409-422, June.
  • Handle: RePEc:inm:orisre:v:34:y:2023:i:2:p:409-422
    DOI: 10.1287/isre.2022.1131
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/isre.2022.1131
    Download Restriction: no

    File URL: https://libkey.io/10.1287/isre.2022.1131?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
    ---><---

    References listed on IDEAS

    as
    1. John A. Norton & Frank M. Bass, 1987. "A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products," Management Science, INFORMS, vol. 33(9), pages 1069-1086, September.
    2. Zhiling Guo & Jianqing Chen, 2018. "Multigeneration Product Diffusion in the Presence of Strategic Consumers," Information Systems Research, INFORMS, vol. 29(1), pages 206-224, March.
    3. Qing Hu & Carol Saunders & Mary Gebelt, 1997. "Research Report: Diffusion of Information Systems Outsourcing: A Reevaluation of Influence Sources," Information Systems Research, INFORMS, vol. 8(3), pages 288-301, September.
    4. Trichy V. Krishnan & Frank M. Bass & Dipak C. Jain, 1999. "Optimal Pricing Strategy for New Products," Management Science, INFORMS, vol. 45(12), pages 1650-1663, December.
    5. Wagner A. Kamakura & Siva K. Balasubramanian, 1987. "Long‐term forecasting with innovation diffusion models: The impact of replacement purchases," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 6(1), pages 1-19.
    6. Il-Horn Hann & Byungwan Koh & Marius F. Niculescu, 2016. "The Double-Edged Sword of Backward Compatibility: The Adoption of Multigenerational Platforms in the Presence of Intergenerational Services," Information Systems Research, INFORMS, vol. 27(1), pages 112-130, March.
    7. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    8. Chul-Yong Lee & Sung-Yoon Huh, 2017. "Technology Forecasting Using a Diffusion Model Incorporating Replacement Purchases," Sustainability, MDPI, vol. 9(6), pages 1-14, June.
    9. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    10. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Economic interpretation of fractional derivatives," Papers 1712.09575, arXiv.org.
    11. Gary L. Lilien & Ambar G. Rao & Shlomo Kalish, 1981. "Bayesian Estimation and Control of Detailing Effort in a Repeat Purchase Diffusion Environment," Management Science, INFORMS, vol. 27(5), pages 493-506, May.
    12. Vijay Gurbaxani & Haim Mendelson, 1990. "An Integrative Model of Information Systems Spending Growth," Information Systems Research, INFORMS, vol. 1(1), pages 23-46, March.
    13. Ambar G. Rao & Masataka Yamada, 1988. "Forecasting with a Repeat Purchase Diffusion Model," Management Science, INFORMS, vol. 34(6), pages 734-752, June.
    14. Joe A. Dodson, Jr. & Eitan Muller, 1978. "Models of New Product Diffusion Through Advertising and Word-of-Mouth," Management Science, INFORMS, vol. 24(15), pages 1568-1578, November.
    15. Marius F. Niculescu & Seungjin Whang, 2012. "Research Note ---Codiffusion of Wireless Voice and Data Services: An Empirical Analysis of the Japanese Mobile Telecommunications Market," Information Systems Research, INFORMS, vol. 23(1), pages 260-279, March.
    16. Zhengrui Jiang & Dipak C. Jain, 2012. "A Generalized Norton-Bass Model for Multigeneration Diffusion," Management Science, INFORMS, vol. 58(10), pages 1887-1897, October.
    17. Lawrence Loh & N. Venkatraman, 1992. "Diffusion of Information Technology Outsourcing: Influence Sources and the Kodak Effect," Information Systems Research, INFORMS, vol. 3(4), pages 334-358, December.
    18. Baesens, Bart & Viaene, Stijn & Van den Poel, Dirk & Vanthienen, Jan & Dedene, Guido, 2002. "Bayesian neural network learning for repeat purchase modelling in direct marketing," European Journal of Operational Research, Elsevier, vol. 138(1), pages 191-211, April.
    Full references (including those not matched with items on IDEAS)

    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. Chul-Yong Lee & Sung-Yoon Huh, 2017. "Technology Forecasting Using a Diffusion Model Incorporating Replacement Purchases," Sustainability, MDPI, vol. 9(6), pages 1-14, June.
    2. Bayrak, Busra & Guray, Busra & Uzunlar, Nilsu & Nadar, Emre, 2024. "Diffusion control in closed-loop supply chains: Successive product generations," International Journal of Production Economics, Elsevier, vol. 268(C).
    3. Ruiz-Conde, Enar & Wieringa, Jaap E. & Leeflang, Peter S.H., 2014. "Competitive diffusion of new prescription drugs: The role of pharmaceutical marketing investment," Technological Forecasting and Social Change, Elsevier, vol. 88(C), pages 49-63.
    4. Guo, Xuezhen, 2014. "A novel Bass-type model for product life cycle quantification using aggregate market data," International Journal of Production Economics, Elsevier, vol. 158(C), pages 208-216.
    5. Singhal, Shakshi & Anand, Adarsh & Singh, Ompal, 2020. "Studying dynamic market size-based adoption modeling & product diffusion under stochastic environment," Technological Forecasting and Social Change, Elsevier, vol. 161(C).
    6. Bo Tan & Zhiguo Zhu & Pan Jiang & Xiening Wang, 2023. "Modeling Multi-Generation Product Diffusion in the Context of Dual-Brand Competition and Sustainable Improvement," Sustainability, MDPI, vol. 15(17), pages 1-22, August.
    7. Ghobadi, Somayeh Najafi- & Bagherinejad, Jafar & Taleizadeh, Ata Allah, 2021. "A two-generation new product model by considering forward-looking customers: Dynamic pricing and advertising optimization," Journal of Retailing and Consumer Services, Elsevier, vol. 63(C).
    8. Shi, Xiaohui & Chumnumpan, Pattarin, 2019. "Modelling market dynamics of multi-brand and multi-generational products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 199-210.
    9. Samuel Sale, R. & Mesak, Hani I. & Inman, R. Anthony, 2017. "A dynamic marketing-operations interface model of new product updates," European Journal of Operational Research, Elsevier, vol. 257(1), pages 233-242.
    10. Lim, Hyungsoo & Jun, Duk Bin & Hamoudia, Mohsen, 2019. "A choice-based diffusion model for multi-generation and multi-country data," Technological Forecasting and Social Change, Elsevier, vol. 147(C), pages 163-173.
    11. Krishnan, Trichy V. & Feng, Shanfei & Jain, Dipak C., 2023. "Peak sales time prediction in new product sales: Can a product manager rely on it?," Journal of Business Research, Elsevier, vol. 165(C).
    12. Brito, Thiago Luis Felipe & Islam, Towhidul & Stettler, Marc & Mouette, Dominique & Meade, Nigel & Moutinho dos Santos, Edmilson, 2019. "Transitions between technological generations of alternative fuel vehicles in Brazil," Energy Policy, Elsevier, vol. 134(C).
    13. Orbach Yair & Fruchter Gila E., 2010. "A Utility-Based Diffusion Model Applied to the Digital Camera Case," Review of Marketing Science, De Gruyter, vol. 8(1), pages 1-28, June.
    14. Michelle M.H. Şeref & Janice E. Carrillo & Arda Yenipazarli, 2016. "Multi-generation pricing and timing decisions in new product development," International Journal of Production Research, Taylor & Francis Journals, vol. 54(7), pages 1919-1937, April.
    15. Hongmin Li, 2020. "Optimal Pricing Under Diffusion-Choice Models," Operations Research, INFORMS, vol. 68(1), pages 115-133, January.
    16. Herbert Dawid & Reinhold Decker & Thomas Hermann & Hermann Jahnke & Wilhelm Klat & Rolf König & Christian Stummer, 2017. "Management science in the era of smart consumer products: challenges and research perspectives," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 203-230, March.
    17. M. Berk Ataman & Carl F. Mela & Harald J. van Heerde, 2008. "Building Brands," Marketing Science, INFORMS, vol. 27(6), pages 1036-1054, 11-12.
    18. Chumnumpan, Pattarin & Shi, Xiaohui, 2019. "Understanding new products’ market performance using Google Trends," Australasian marketing journal, Elsevier, vol. 27(2), pages 91-103.
    19. Kim, Namwoon & Srivastava, Rajendra K. & Han, Jin K., 2001. "Consumer decision-making in a multi-generational choice set context," Journal of Business Research, Elsevier, vol. 53(3), pages 123-136, September.
    20. Zhengrui Jiang & Dipak C. Jain, 2012. "A Generalized Norton-Bass Model for Multigeneration Diffusion," Management Science, INFORMS, vol. 58(10), pages 1887-1897, October.

    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:inm:orisre:v:34:y:2023:i:2:p:409-422. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.