Modeling innovation adoption incorporating time lag between awareness and adoption process

  • Richie Aggarwal
  • Ompal Singh
  • Adarsh AnandEmail author
  • P. K. Kapur
Original Article


Demand forecasting is an arduous task in today’s competitive world. The changing environment of market structure demands firms to be more cognizant about the customers’ stipulation before the successful introduction of an innovation into the market. Only after being satisfied by the characteristics of the innovation, the potential adopters get positively motivated to buy the product. There is a finite time lag in the adoption process; from the moment potential buyers get information about the innovation and the time they make the actual purchase. Using this fundamental of time lag we have proposed a framework of innovation diffusion where the final purchase is happening in number of stages. Distributed time lag approach methodology has been utilized to capture the time delay between customer’s motivation and its final adoption. In this approach, the contributions of time delay are ascertained as a weighted response measured over a finite interval of past time through appropriate memory kernels. To cater actual adoption process, certain mathematical models with the help of integro-differential equations have been formulated and solved through Laplace transforms. Furthermore, we have validated the model on the real life sales data set.


Laplace transform Innovation diffusion Integro-differential equation Time lag 



The research work presented in this paper is supported by grants to the second and third author from DST, via DST PURSE phase II, India.


  1. Adler L (1986) Time lag in new product development. J Mark 30:17CrossRefGoogle Scholar
  2. Aggrawal D, Agarwal M, Anand A, Aggarwal R (2017) Convolution of awareness in modeling industrial and technological innovation adoption. In: 8th DQM international conference on life cycle science engineering and management, Serbia, pp 143–152Google Scholar
  3. Anand A, Singh O, Agarwal M, Aggarwal R (2014) Modeling adoption process based on awareness and motivation of consumers. In: 2014 3rd international conference on reliability, Infocom Technologies and Optimization (ICRITO) (Trends and Future Directions), pp 1–6Google Scholar
  4. Anand A, Agarwal M, Bansal G, Garmabaki AHS (2016a) Studying product diffusion based on market coverage. J Mark Anal 4(4):135–146CrossRefGoogle Scholar
  5. Anand A, Singh O, Aggarwal R, Aggrawal D (2016b) Diffusion modeling based on customer’s review and product satisfaction. Int J Technol Diffus (IJTD) 7(1):20–31CrossRefGoogle Scholar
  6. Bartholomew J (1967) Stochastic models for social processes. Wiley, HobokenGoogle Scholar
  7. Bass FM (1969) A new product growth model for consumer durables. Manag Sci 15(5):215–224CrossRefzbMATHGoogle Scholar
  8. Coleman JS (1964) Introduction to mathematical sociology. Princeton University Press, PrincetonGoogle Scholar
  9. Cushing JM (1975) An operator equation and bounded solutions of integro-differential systems. SIAM J Math Anal 6(3):433–445MathSciNetCrossRefzbMATHGoogle Scholar
  10. Diamond AM Jr (2005) Measurement, incentives and constraints in Stigler’s economics of science. Eur J Hist Econ Thought 12(4):635–661CrossRefGoogle Scholar
  11. Easingwood C, Mahajan V, Muller E (1981) A nonsymmetric responding logistic model for forecasting technological substitution. Technol Forecast Soc Change 20(3):199–213CrossRefGoogle Scholar
  12. Feder G, Slade R (1984) The acquisition of information and the adoption of new technology. Am J Agric Econ 66(3):312–320CrossRefGoogle Scholar
  13. Floyd A (1968) A methodology for trend forecasting of figures of merit. In: Bright J (ed) Technological forecasting for industry and government: methods and applications, vol 95. Prentice-Hall Inc., Englewood CliffsGoogle Scholar
  14. Garmabaki AS, Kapur PK, Jyotish NP, Ragini KS (2012) The optimal time of new generation product in the market. Commun Depend Qual Manag 15(1):123–137Google Scholar
  15. Kalish S (1985) A new product adoption model with pricing, advertising and uncertainty. Manage Sci 31:1569–1585CrossRefzbMATHGoogle Scholar
  16. Kapur PK, Aggarwal AG, Garmabaki AHS, Singh G (2013) Modelling diffusion of successive generations of technology: a general framework. Int J Oper Res 16(4):465–484MathSciNetCrossRefzbMATHGoogle Scholar
  17. Kapur PK, Aggarwal AG, Garmabaki AH, Tandon A (2015) Multi-generational innovation diffusion modelling: a two dimensional approach. Int J Appl Manag Sci 7(1):1–18CrossRefGoogle Scholar
  18. Karmeshu (1982) Time lag in a diffusion model of information. Math Model 3(2):137–141MathSciNetCrossRefzbMATHGoogle Scholar
  19. Lal VB, Kaicker S (1988) Modeling innovation diffusion with distributed time lag. Technol Forecast Soc Change 34(2):103–113CrossRefGoogle Scholar
  20. Lindner R, Fischer A, Pardey P (1979) The time to adoption. Econ Lett 2(2):187–190CrossRefGoogle Scholar
  21. Mahajan V, Muller E, Kerin AR (1984a) Introduction strategy for new products with positive and negative word-of-mouth. Manag Sci (INFORMS) 30(12):1389–1404CrossRefzbMATHGoogle Scholar
  22. Mahajan V, Muller E, Sharma S (1984b) An empirical comparisons of awareness forecasting models of new product introduction. Mark Sci 3(3):179–197CrossRefGoogle Scholar
  23. Mansfield E (1961) Technical change and the rate of imitation. Econom J Econom Soc 741–766Google Scholar
  24. Rogers EM (2003) Diffusion of innovations, 5th edn. The Free Press, New YorkGoogle Scholar
  25. Sharif MN, Kabir C (1976) A generalized model for forecasting technological substitution. Technol Forecast Soc Change 8(4):353–364CrossRefGoogle Scholar
  26. Skiadas C (1985) Two generalized rational models for forecasting innovation diffusion. Technol Forecast Soc Change 27(1):39–61CrossRefGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  • Richie Aggarwal
    • 1
  • Ompal Singh
    • 1
  • Adarsh Anand
    • 1
    Email author
  • P. K. Kapur
    • 1
    • 2
  1. 1.Department of Operational ResearchUniversity of DelhiDelhiIndia
  2. 2.Centre for Interdisciplinary ResearchAmity UniversityNoidaIndia

Personalised recommendations