## Main Article Content

## Abstract

In this paper we discuss a mathematical model of two parties technology transfer from a leader to a follower. The model is reconstructed via dynamical system approach from a known standard Raz and Assa model and we found some important conclusion which have not been discussed in the original model. The model assumes that in the absence of technology transfer from a leader to a follower, both the leader and the follower have a capability to grow independently with a known upper limit of the development. We obtain a rich mathematical structure of the steady state solution of the model. We discuss a special situation in which the upper limit of the technological development of the follower is higher than that of the leader, but the leader has started earlier than the follower in implementing the technology. In this case we show a paradox stating that the follower is unable to reach its original upper limit of the technological development could appear whenever the transfer rate is sufficiently high. We propose a new model to increase realism so that any technological transfer rate could only has a positive effect in accelerating the rate of growth of the follower in reaching its original upper limit of the development.

## Keywords

## Article Details

*How to Cite*

*Journal of the Indonesian Mathematical Society*,

*22*(1), 37–59. https://doi.org/10.22342/jims.22.1.212.37-59

* * References

- begin{thebibliography}{99}
- bibitem{anggriani2015} Anggriani, N., Lesmana, E., Supriatna, A., Husniah, H., and Yudha, M. (2015), Dynamic analysis of a two products inventory control, {em Jurnal Teknik Industri}, Vol 17(1), pp 17-26 (in Indonesian).
- bibitem{barzakay1971} Bar-Zakay, S.N. (1971), A Technology Transfer Model, {em Technological Forecasting and Social Change} 2, 321-337.
- bibitem{forrester1958} Forrester, J. (1958), Forrester, Jay W. 1958. "Industrial Dynamics--A Major Breakthrough for Decision Makers."
- Harvard Business Review, Vol. 36, No. 4, pp. 37-66. Also appears in revised form as Chapter 2 in the author's Industrial Dynamics 1961 and Chapter 1, pp. 1-29, of Collected Papers 1975; also as Chapter 2, pp. 37-65 in Edward B. Roberts, ed.,Managerial Applications of System Dynamics, 1978, all from Waltham, MA: Pegasus Communications.
- bibitem{goc2002} Goc, M.L. (2002), Development Techniques for International Technology Transfer, Book Review, Westport, CT: Quorum Books, pp 184, ISBN: 1-56720-493-7, {em Technological Forecasting and Social Change}, Vol 70, pp 923-927.
- bibitem{haq1979} Haq, A.K.M.A. (1979), {em A Dynamic and Spatial Model for Measuring Technology Transfer Potentials}, D.Eng. Dissertation, Asian Institute of Technology.
- bibitem{husniah2011} Husniah, H., Pasaribu, U.S., Halim, A.H., and Iskandar, B.P. (2011), Hybrid minimal repair and age replacement policy for two-dimensional warranted products, {em International Journal of Collaborative Enterprise}, Vol 2(4), pp 284-301.
- bibitem{husniah2014} Husniah, H., Pasaribu, U.S., Cakravastia, A., and Iskandar, B.P. (2014), Two-dimensional maintenance contracts for a fleet of dump-trucks used in mining industry, {em Applied Mechanics and Materials}, 660, pp 1026-1031.
- bibitem{husniah2015} Husniah, H., Pasaribu, U.S., and Iskandar, B.P. (2015), Service contracts management with availability improvement and cost reduction, {em ARPN journal of Engineering and Applied Sciences}, Vol 10(1), pp 146-151.
- bibitem{iskandar2014} Iskandar, B.P., Husniah, H., and Pasaribu, U.S. (2014), Maintenance service contracts for equipment sold with two-dimensional warranties, {em Quality Technology and Quantitative Management}, Vol 11, pp 307-333.
- bibitem{jayaraman1998} Jayaraman, V. (1998), {em A Quantitative Model for Measuring Technology Transfer at the Industrial Level – An Application Towards Establishing Technological Cooperation}, PhD. Thesis, School of Quantitative Methods and Business Operations, University of Western Sydney, Nepean.
- bibitem{krengwang2013} Kreng, V.B. and Wang, B.J. (2013), An innovation diffusion of successive generations by system dynamics — An empirical study of Nike Golf Company, {em Technological Forecasting and Social Change}, Vol 80, pp 77-87.
- bibitem{kreyszig1988} Kreyszig, E. (1988), {em Advanced Engineering Mathematics} Sixth Edition, John Wiley & Sons, Newyork.
- bibitem{kwasnicki2013} Kwasnicki, W. (2013), Logistic growth of the global economy and competitiveness of nations, {em Technological Forecasting and Social Change} 80, 50-76.
- bibitem{leeetal2010} Lee A.H.I. Wang W.M., and Lin T.Y. (2010), An Evaluation Framework for Technology Transfer of New Equipment in High Technology Industry, {em Technological Forecasting and Social Change}, Vol 77, pp 135–150.
- bibitem {liu1993} Liu, W.G. (1993), A Quantitative technology transfer model and its application to aircraft engines, {em Technological Forecasting and Social Change} 44, 179-186.
- bibitem{pachamuthu2011} Pachamuthu, S. (2011), {em An Extended Model for Measuring the Technology Transfer Potentials at the Industrial Level}. Ph.D Thesis. Southern Cross University, Australia.
- bibitem{pasaribu2015} Pasaribu, U.S., Husniah, H. and Iskandar, B.P. (2015), A mathematical model for imperfect maintenance contract, {em International Journal of Applied Mathematics and Statistics}, Vol 53(2), pp 20-35.
- bibitem{ramanathan1994} Ramanathan, K. (1994), The polytrophic components of manufacturing technology, {em Technological Forecasting and Social Change} 46, 221-258.
- bibitem{razassa1988} Raz, B. and Assa, I. (1988), A model of "Coupled" Technology Transfer. A Logistic Curve Approach, {em Technological Forecasting and Social Change} 33, 251-265.
- bibitem{razetal1983} Raz, B., Steinberg, G., and Ruina, A. (1983), A Quantitative Model for Technology Transfer and Technological Catch-up – The Case of Developing Countries’, {em Technological Forecasting and Social Change}, Vol 3, pp 251-265.
- bibitem{syarif} Sharif, M.N., and Ramanathan, K. (1982), Polynomial Innovation Diffusion models, {em Technological Forecasting and Social Change}, Vol 21, pp 301-323.
- bibitem{souder1990} Souder, W.E., Nashar, A.S. and Padmanathan, V. (1990), A guide to the best technology transfer practices, {em Journal of Technology Transfer} 15, 1-2.
- bibitem{sukchareonpong1979} Sukchareonpong, P. (1979), {em A Quantitative Model Incorporating Time and a Dynamic Technological Gap for Determining Technology Transfer Potentials}, D.Eng. Dissertation, Asian Institute of Technology.
- bibitem{Tsai2013} Tsai, B.H. (2013), Predicting the diffusion of LCD TVs by incorporating price in the extended Gompertz model, {em Technological Forecasting and Social Change}, Vol 80, pp 106-131.
- bibitem{verhults} Verhults, F. (1989), {em Nonlinear Differential Equations and Dynamical Systems}, Universitex.
- bibitem{vogel1970} Vogel, P.H. (1970), A Basis for Technological Forecasting, {em Technological Forecasting} 1, 313-323.
- end{thebibliography}

#### References

begin{thebibliography}{99}

bibitem{anggriani2015} Anggriani, N., Lesmana, E., Supriatna, A., Husniah, H., and Yudha, M. (2015), Dynamic analysis of a two products inventory control, {em Jurnal Teknik Industri}, Vol 17(1), pp 17-26 (in Indonesian).

bibitem{barzakay1971} Bar-Zakay, S.N. (1971), A Technology Transfer Model, {em Technological Forecasting and Social Change} 2, 321-337.

bibitem{forrester1958} Forrester, J. (1958), Forrester, Jay W. 1958. "Industrial Dynamics--A Major Breakthrough for Decision Makers."

Harvard Business Review, Vol. 36, No. 4, pp. 37-66. Also appears in revised form as Chapter 2 in the author's Industrial Dynamics 1961 and Chapter 1, pp. 1-29, of Collected Papers 1975; also as Chapter 2, pp. 37-65 in Edward B. Roberts, ed.,Managerial Applications of System Dynamics, 1978, all from Waltham, MA: Pegasus Communications.

bibitem{goc2002} Goc, M.L. (2002), Development Techniques for International Technology Transfer, Book Review, Westport, CT: Quorum Books, pp 184, ISBN: 1-56720-493-7, {em Technological Forecasting and Social Change}, Vol 70, pp 923-927.

bibitem{haq1979} Haq, A.K.M.A. (1979), {em A Dynamic and Spatial Model for Measuring Technology Transfer Potentials}, D.Eng. Dissertation, Asian Institute of Technology.

bibitem{husniah2011} Husniah, H., Pasaribu, U.S., Halim, A.H., and Iskandar, B.P. (2011), Hybrid minimal repair and age replacement policy for two-dimensional warranted products, {em International Journal of Collaborative Enterprise}, Vol 2(4), pp 284-301.

bibitem{husniah2014} Husniah, H., Pasaribu, U.S., Cakravastia, A., and Iskandar, B.P. (2014), Two-dimensional maintenance contracts for a fleet of dump-trucks used in mining industry, {em Applied Mechanics and Materials}, 660, pp 1026-1031.

bibitem{husniah2015} Husniah, H., Pasaribu, U.S., and Iskandar, B.P. (2015), Service contracts management with availability improvement and cost reduction, {em ARPN journal of Engineering and Applied Sciences}, Vol 10(1), pp 146-151.

bibitem{iskandar2014} Iskandar, B.P., Husniah, H., and Pasaribu, U.S. (2014), Maintenance service contracts for equipment sold with two-dimensional warranties, {em Quality Technology and Quantitative Management}, Vol 11, pp 307-333.

bibitem{jayaraman1998} Jayaraman, V. (1998), {em A Quantitative Model for Measuring Technology Transfer at the Industrial Level – An Application Towards Establishing Technological Cooperation}, PhD. Thesis, School of Quantitative Methods and Business Operations, University of Western Sydney, Nepean.

bibitem{krengwang2013} Kreng, V.B. and Wang, B.J. (2013), An innovation diffusion of successive generations by system dynamics — An empirical study of Nike Golf Company, {em Technological Forecasting and Social Change}, Vol 80, pp 77-87.

bibitem{kreyszig1988} Kreyszig, E. (1988), {em Advanced Engineering Mathematics} Sixth Edition, John Wiley & Sons, Newyork.

bibitem{kwasnicki2013} Kwasnicki, W. (2013), Logistic growth of the global economy and competitiveness of nations, {em Technological Forecasting and Social Change} 80, 50-76.

bibitem{leeetal2010} Lee A.H.I. Wang W.M., and Lin T.Y. (2010), An Evaluation Framework for Technology Transfer of New Equipment in High Technology Industry, {em Technological Forecasting and Social Change}, Vol 77, pp 135–150.

bibitem {liu1993} Liu, W.G. (1993), A Quantitative technology transfer model and its application to aircraft engines, {em Technological Forecasting and Social Change} 44, 179-186.

bibitem{pachamuthu2011} Pachamuthu, S. (2011), {em An Extended Model for Measuring the Technology Transfer Potentials at the Industrial Level}. Ph.D Thesis. Southern Cross University, Australia.

bibitem{pasaribu2015} Pasaribu, U.S., Husniah, H. and Iskandar, B.P. (2015), A mathematical model for imperfect maintenance contract, {em International Journal of Applied Mathematics and Statistics}, Vol 53(2), pp 20-35.

bibitem{ramanathan1994} Ramanathan, K. (1994), The polytrophic components of manufacturing technology, {em Technological Forecasting and Social Change} 46, 221-258.

bibitem{razassa1988} Raz, B. and Assa, I. (1988), A model of "Coupled" Technology Transfer. A Logistic Curve Approach, {em Technological Forecasting and Social Change} 33, 251-265.

bibitem{razetal1983} Raz, B., Steinberg, G., and Ruina, A. (1983), A Quantitative Model for Technology Transfer and Technological Catch-up – The Case of Developing Countries’, {em Technological Forecasting and Social Change}, Vol 3, pp 251-265.

bibitem{syarif} Sharif, M.N., and Ramanathan, K. (1982), Polynomial Innovation Diffusion models, {em Technological Forecasting and Social Change}, Vol 21, pp 301-323.

bibitem{souder1990} Souder, W.E., Nashar, A.S. and Padmanathan, V. (1990), A guide to the best technology transfer practices, {em Journal of Technology Transfer} 15, 1-2.

bibitem{sukchareonpong1979} Sukchareonpong, P. (1979), {em A Quantitative Model Incorporating Time and a Dynamic Technological Gap for Determining Technology Transfer Potentials}, D.Eng. Dissertation, Asian Institute of Technology.

bibitem{Tsai2013} Tsai, B.H. (2013), Predicting the diffusion of LCD TVs by incorporating price in the extended Gompertz model, {em Technological Forecasting and Social Change}, Vol 80, pp 106-131.

bibitem{verhults} Verhults, F. (1989), {em Nonlinear Differential Equations and Dynamical Systems}, Universitex.

bibitem{vogel1970} Vogel, P.H. (1970), A Basis for Technological Forecasting, {em Technological Forecasting} 1, 313-323.

end{thebibliography}