Journal of Optimization Theory and Applications

, Volume 170, Issue 3, pp 993–1008 | Cite as

Manufacturing High-Tech Products Subject to Rapid Obsolescence



We formulate a production problem in high-tech industry as a free-final-time optimal control problem. The instance with linear production cost is equivalent to a problem proposed by Pangburn and Sundaresan. The instance with quadratic production cost allows us to find a solution which is closer to what is seen in the real world. In the latter instance, the optimal production rate is strictly decreasing in a neighborhood of the final time.


Production Capacity Optimal control Free final time 

Mathematics Subject Classification

91B38 90B30 49N90 


  1. 1.
    Bulow, J.I.: An economic theory of planned obsolescence. Q. J. Econ. 101(4), 729–749 (1986)CrossRefGoogle Scholar
  2. 2.
    Pangburn, M.S., Sundaresan, S.: Capacity decisions for high-tech products with obsolescence. Eur. J. Oper. Res. 197, 102–111 (2009)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bass, F.M.: A new product growth model for consumer durables. Manag. Sci. 15(5), 216–227 (1969)CrossRefMATHGoogle Scholar
  4. 4.
    Bass, F.M.: The relationship between diffusion rates, experience curves, and demand elasticities for consumer durable technological innovations. J. Bus. 53(3), S51–S67 (1980)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ho, T.H., Savin, S., Terwiesch, S.: Managing demand and sales dynamics in new product diffusion under supply constraint. Manag. Sci. 48(2), 187–206 (2002)CrossRefMATHGoogle Scholar
  6. 6.
    Varian, H.R.: Microeconomic Analysis. Norton, New York (1992)Google Scholar
  7. 7.
    Chung, W., Talluri, S., Narasimhan, R.: Price markdown scheme in a multi-echelon supply chain in a high-tech industry. Eur. J. Oper. Res. 215(3), 581–589 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Van Mieghem, J.A.: Capacity management, investment, and hedging: review and recent developments. Manuf. Serv. Oper. Manag. 5, 269–302 (2003)Google Scholar
  9. 9.
    Erkoc, M., Wu, S.D.: Managing high-tech capacity expansion via reservation contracts. Prod. Oper. Manag. 14(2), 232–251 (2005)CrossRefGoogle Scholar
  10. 10.
    Seierstad, A., Sydsæter, K.: Optimal Control Theory with Economic Applications. North-Holland, Amsterdam (1987)MATHGoogle Scholar
  11. 11.
    Chiang, A.C.: Elements of Dynamic Optimization. McGraw Hill, Singapore (1992)Google Scholar
  12. 12.
    Dockner, E., Jørgensen, S., Long, N.V., Sorger, G.: Differential Games in Economics and Management Science. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  13. 13.
    Johnson, C.D., Gibson, J.E.: Singular solutions in problems of optimal control. IEEE Trans. Autom. Control AC-8, 4–15 (1963)Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PadovaPaduaItaly

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