Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adler L (1986) Time lag in new product development. J Mark 30:17
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 143–152
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 1–6
Anand A, Agarwal M, Bansal G, Garmabaki AHS (2016a) Studying product diffusion based on market coverage. J Mark Anal 4(4):135–146
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):20–31
Bartholomew J (1967) Stochastic models for social processes. Wiley, Hoboken
Bass FM (1969) A new product growth model for consumer durables. Manag Sci 15(5):215–224
Coleman JS (1964) Introduction to mathematical sociology. Princeton University Press, Princeton
Cushing JM (1975) An operator equation and bounded solutions of integro-differential systems. SIAM J Math Anal 6(3):433–445
Diamond AM Jr (2005) Measurement, incentives and constraints in Stigler’s economics of science. Eur J Hist Econ Thought 12(4):635–661
Easingwood C, Mahajan V, Muller E (1981) A nonsymmetric responding logistic model for forecasting technological substitution. Technol Forecast Soc Change 20(3):199–213
Feder G, Slade R (1984) The acquisition of information and the adoption of new technology. Am J Agric Econ 66(3):312–320
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 Cliffs
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):123–137
https://www.statista.com/statistics/263393/global-pc-shipments-since-1st-quarter-2009-by-vendor/. Accessed on 29th Nov 2018
https://www.statista.com/statistics/271490/quarterly-global-smartphone-shipments-by-vendor/. Accessed on 28th Nov 2018
Kalish S (1985) A new product adoption model with pricing, advertising and uncertainty. Manage Sci 31:1569–1585
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):465–484
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):1–18
Karmeshu (1982) Time lag in a diffusion model of information. Math Model 3(2):137–141
Lal VB, Kaicker S (1988) Modeling innovation diffusion with distributed time lag. Technol Forecast Soc Change 34(2):103–113
Lindner R, Fischer A, Pardey P (1979) The time to adoption. Econ Lett 2(2):187–190
Mahajan V, Muller E, Kerin AR (1984a) Introduction strategy for new products with positive and negative word-of-mouth. Manag Sci (INFORMS) 30(12):1389–1404
Mahajan V, Muller E, Sharma S (1984b) An empirical comparisons of awareness forecasting models of new product introduction. Mark Sci 3(3):179–197
Mansfield E (1961) Technical change and the rate of imitation. Econom J Econom Soc 741–766
Rogers EM (2003) Diffusion of innovations, 5th edn. The Free Press, New York
Sharif MN, Kabir C (1976) A generalized model for forecasting technological substitution. Technol Forecast Soc Change 8(4):353–364
Skiadas C (1985) Two generalized rational models for forecasting innovation diffusion. Technol Forecast Soc Change 27(1):39–61
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aggarwal, R., Singh, O., Anand, A. et al. Modeling innovation adoption incorporating time lag between awareness and adoption process. Int J Syst Assur Eng Manag 10, 83–90 (2019). https://doi.org/10.1007/s13198-018-00756-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-018-00756-8