Skip to main content

Solution of a Product Substitution Problem Using Stochastic Programming

  • Chapter
Probabilistic Constrained Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 49))

Abstract

Stochastic programming models of optical fiber production planning are presented. The purpose is to set the optimal fiber manufacturing goals while accounting for the uncertainty primarily in the yield and secondly in the demand. The model is solved for the case when the data follows a multivariate discrete distribution, and also for the case of a multivariate normal distribution, which is used to approximate the discrete data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beale, E. M. L. 1955. On Minimizing a Convex Function Subject to Linear Inequalities. J. Royal Statist. Soc, Ser. £17, 173–184.

    MathSciNet  MATH  Google Scholar 

  2. Bitran G. R. and T-Y. Leong. 1989. Deterministic Approximations to Co-Production Problems with Service Constraints. Working Paper #3071–89-MS, MIT Sloan School of Management.

    Google Scholar 

  3. Charnes, A., W. W. Cooper, and G. H. Symonds. 1958. Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil Production. Management Science 4, 235–263.

    Article  Google Scholar 

  4. Dantzig, G. B. 1955. Linear Programming under Uncertainty. Management Science 1, 197–206.

    Article  MathSciNet  MATH  Google Scholar 

  5. Deák, I. 1988. Multidimensional Integration and Stochastic Programming. In Numerical Techniques for Stochastic Optimization, Yu. Ermoliev and R. J-B Wets (eds.). Springer-Verlag, New York.

    Google Scholar 

  6. Dupagová, J., A. Gaivoronski, Z. Kos, and T. Szántai. 1991. Stochastic Programming in Water Management: A Case Study and a Comparison of Solution Techniques. European Journal of Operational Research 52, 28–44.

    Article  Google Scholar 

  7. Flegal, W. M., E. A. Haney, R. S. Elliott, J. T. Kamino, and D. N. Ernst. 1986. Making Single-Mode Preforms by the MCVD Process. AT&T Technical Journal 65, 56–61.

    Google Scholar 

  8. Gassmann, H. 1988. Conditional Probability and Conditional Expectation of a Random Vector. In Numerical Techniques for Stochastic Optimization, Yu. Ermoliev and R. J-B Wets (eds.). Springer-Verlag, New York.

    Google Scholar 

  9. IMSL. 1987. IMSL Math/Library User’s Manual, IMSL, Houston, Texas.

    Google Scholar 

  10. Jablonowski, D. P., U. C. Paek, and L. S. Watkins. 1987. Optical Fiber Manufacturing Techniques. AT&T Technical Journal 66, 33–44.

    Google Scholar 

  11. Maros, I. 1990. MILP Linear Programming Optimizer for Personal Computers under DOS. Institut für Angewandte Mathematik, Technische Universität Braunschweig.

    Google Scholar 

  12. Maros, I. and A. Prékopa. 1990. MIPROB, A Computer Code to Solve Probabilistic Constrained Stochastic Programming Problems with Discrete Random Variables. Manuscript.

    Google Scholar 

  13. Miller, B. L. and H. M. Wagner. 1965. Chance Constrained Programming with Joint Constraints. Operations Research 13, 930–945.

    Article  MATH  Google Scholar 

  14. Murr, M. R. 1992. Some Stochastic Problems in Fiber Production. Ph.D. Dissertation, Rutgers University, New Brunswick, New Jersey.

    Google Scholar 

  15. Prékopa, A. 1970. On Probabilistic Constrained Programming. In Proceedings of the Princeton Symposium on Mathematical Programming (1967), H. Kuhn (ed.). Princeton University Press, Princeton, 113–138.

    Google Scholar 

  16. Prékopa, A. 1971. Logarithmic Concave Measures with Application to Stochastic Programming. Acta Sci. Math. (Szeged) 32, 301–316.

    MathSciNet  MATH  Google Scholar 

  17. Prékopa, A. 1973. On Logarithmic Concave Measures and Functions. Acta Sci. Math. (Szeged) 34, 335–343.

    MathSciNet  MATH  Google Scholar 

  18. Prékopa, A. 1980. Logarithmically Concave Measures and Related Topics. In Stochastic Programming. Proceedings of the 1974 Oxford International Conference, M. Dempster (ed.). Academic Press, London, 63–82.

    Google Scholar 

  19. Prékopa, A. 1990. Dual Method for the Solution of a One-Stage Stochastic Programming Problem with Random RHS Obeying a Discrete Probability Distribution. ZOR 34, 441–461.

    MATH  Google Scholar 

  20. Prékopa, A. 1995. Stochastic Programming. Kluwer Scientific Publishers. Dordrecht, The Netherlands.

    Google Scholar 

  21. Prékopa, A. and W. Li. 1995. Solution of and Bounding in a Linearly Constrained Optimization Problem with Convex, Polyhedral Objective Function. Mathematical Programming 70, 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  22. Prékopa, A. and T. Szántai. 1978. Flood Control Reservoir System Design Using Stochastic Programming. Mathematical Programming Study 9, 138–151.

    Article  Google Scholar 

  23. Prékopa, A., B. Vizvári, and T. Badics. 1996. Programming under Probabilistic Constraints with Discrete Random Variables. RUTCOR Research Report 10–96.

    Google Scholar 

  24. Sen, S. 1992. Relaxations for Probabilistically Constrained Programs with Discrete Random Variables. Operations Research Letters 11, 81–86.

    Article  MathSciNet  MATH  Google Scholar 

  25. Szántai, T. 1988. A Computer Code for Solution of Probabilistic-constrained Stochastic Programming Problems. In Numerical Techniques for Stochastic Optimization, Yu. Ermoliev and R. J-B Wets (eds.). Springer-Verlag, New York.

    Google Scholar 

  26. Wets, R. J-B. 1983. Solving Stochastic Programs with Simple Recourse. Stochastics 10, 219–242.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Murr, M.R., Prékopa, A. (2000). Solution of a Product Substitution Problem Using Stochastic Programming. In: Uryasev, S.P. (eds) Probabilistic Constrained Optimization. Nonconvex Optimization and Its Applications, vol 49. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3150-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3150-7_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4840-3

  • Online ISBN: 978-1-4757-3150-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics