Skip to main content

A Dual of a Dynamic Inventory Control Model: The Deterministic and the Stochastic Case

  • Chapter
Duality in Stochastic Linear and Dynamic Programming

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 274))

  • 171 Accesses

Abstract

In this chapter we study a simple multistage production-inventory control model. Two cases are considered: first it is assumed that the demands are deterministic, and after that the demands are supposed to be random variables.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. D.P. Bertsekas, S.E. Shreve (1978). Stochastic Optimal Control; the Discrete Time Case, Academic Press, New York-San Francisco-London.

    Google Scholar 

  2. L. Breiman (1968). Probability, Addison-Wesley, Reading Ma.

    Google Scholar 

  3. W.H. Cunningham (1976). A network simplex method. Math. Programming 11, 105–116.

    Article  Google Scholar 

  4. G.B. Dantzig (1963). Linear Programming and Extensions, Princeton University Press, Princeton NJ.

    Google Scholar 

  5. M.J. Eisner, P. Olsen (1975). Duality for stochastic programming interpreted as L.P. in Lp-space. SIAM J. Appl. Math. 28, 779–792.

    Article  Google Scholar 

  6. W.K. Klein Haneveld (1977). Markovian Inventory Control Models, Report Institute of Econometrics OR 7702, University of Groningen, Groningen.

    Google Scholar 

  7. W.K. Klein Haneveld (1978). Markovian Inventory Control Models — Improvements, Extensions, Report Department of Mathematics, University of Kentucky, Lexington Ky.

    Google Scholar 

  8. W.K. Klein Haneveld (1978). Dual Inventory Control Models, Report Department of Mathematics, University of Kentucky, Lexington Ky.

    Google Scholar 

  9. W.K. Klein Haneveld (1980). A dual of a dynamic inventory control model: the deterministic and stochastic case. P. Kall, A. Prekopa (eds.). Recent Results in Stochastic Programming, Lecture notes in economic and mathematical systems 179, Springer, Berlin-Heidelberg-New York.

    Google Scholar 

  10. P. Olsen (1976). When is a multistage stochastic programming problem well-defined? SIAM J. Control 14, 518–527.

    Article  Google Scholar 

  11. C. Van de Panne (1976). Linear Programming and Related Techniques, second edition, North Holland, Amsterdam.

    Google Scholar 

  12. J. Ponstein (1983). Applying some modern developments to choosing your own Lagrange multipliers. SIAM Rev. 25, 183–199.

    Article  Google Scholar 

  13. R.T. Rockafellar (1970). Convex Analysis, Princeton University Press, Princeton NJ.

    Google Scholar 

  14. R.T. Rockafellar (1974). Conjugate Duality and Optimization, SIAM, Philadelphia Pa.

    Book  Google Scholar 

  15. R.T. Rockafellar, R.J.-B. Wets (1976). Nonanticipativity and L1-martingales in stochastic optimization problems. Math. Programming Study 6, 160–189.

    Google Scholar 

  16. R.T. Rockafellar, R.J.-B. Wets (1978). The optimal recourse problem in discrete time: L1-multipliers for inequality constraints. SIAM J. Control 16, 16–36.

    Article  Google Scholar 

  17. R.T. Rockafellar, R.J.-B. Wets (1983). Deterministic and stochastic optimization problems of Bolza type in discrete time. Stochastics 10, 273–312.

    Article  Google Scholar 

  18. S.E. Shreve (1977). Dynamic Programming in Complete Separable Spaces, Ph.D. dissertation, University of Illinois, Urbana Ill.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Klein Haneveld, W.K. (1986). A Dual of a Dynamic Inventory Control Model: The Deterministic and the Stochastic Case. In: Duality in Stochastic Linear and Dynamic Programming. Lecture Notes in Economics and Mathematical Systems, vol 274. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51697-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-51697-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16793-8

  • Online ISBN: 978-3-642-51697-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics