Skip to main content
SpringerLink
Log in

Dynamic Network Inventory Control Model with Interval Nonstationary Demand Uncertainty

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

We consider a dynamic inventory control system described by a network model with an interval assigned nonstationary demand. We assume that unknown demand may take any value within the interval, which bounds depend on time. In terms of Kaucher interval arithmetic, we derive necessary and sufficient conditions for the existence of a feasible feedback control and sufficient conditions for the existence of an optimal feedback control strategy. We obtain an optimal feasible storage level and estimate the rate of the system convergence to this level. Then we develop the algorithm of finding the optimal control strategy. These results are applied to an example.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Alefeld and J. Herzberger, Introduction to Interval Computation (Academic Press, New York, 1983).

    Google Scholar 

  2. F. Blanchini, F. Rinaldi and W. Ukovich, A network design problem for a distribution system with uncertain demands, SIAM J. Optim. 7(2) (1997) 560–578.

    Google Scholar 

  3. F. Blanchini, F. Rinaldi and W. Ukovich, Least inventory control of multistorage systems with non-stochastic unknown demand, IEEE Trans. Robotics Automat. 13(5) (1997) 633–645.

    Google Scholar 

  4. V.V. Dombrovsky and E.V. Chausova, Dynamic network inventory control system with interval uncertainty of demand, Comput. Technol. 6(2) (2001) 271–274 (in Russian).

    Google Scholar 

  5. F. Glover, D. Klingman and N.V. Phillips, Network Models in Optimization and Their Applications in Practice (Wiley, New York, 1992).

    Google Scholar 

  6. G. Hadley and T. Whitin, Analysis of Inventory System (Prentice-Hall, Englewood Cliffs, NJ, 1963).

    Google Scholar 

  7. E. Kaucher, Interval analysis in the extended interval space \(\mathbb{I}\mathbb{R}\), Computing Supplement 2 (1980) 33–49.

    Google Scholar 

  8. R.B. Kearfott, M.T. Nakao, A. Neumaier, S.M. Rump, S.P. Shary and P. Hentenryck, Standardized notation in interval analysis, Reliable Computing, to appear.

  9. V.A. Lototsky and A.S. Mandelm, Inventory Control Models and Techniques (Nauka, Moscow, 1991).

    Google Scholar 

  10. S.E. Loveski and I.I. Melamed, Dynamic flows in networks, Automat. Remote Control 11 (1987) 7–29.

    Google Scholar 

  11. R.E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, PA, 1979).

    Google Scholar 

  12. S.P. Shary, Algebraic approach to “outer” problem for interval linear systems, Comput. Technol. 3(2) (1998) 67–114 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tomsk State University, 36 Lenina Street, 634050, Tomsk, Russia

    Elena V. Chausova

Authors
  1. Elena V. Chausova
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chausova, E.V. Dynamic Network Inventory Control Model with Interval Nonstationary Demand Uncertainty. Numerical Algorithms 37, 71–84 (2004). https://doi.org/10.1023/B:NUMA.0000049457.89377.12

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NUMA.0000049457.89377.12

Search

Navigation