Skip to main content
SpringerLink
Log in

Stochastic theory of inventory control

  • Related Directions in Queuing Theory
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The main results of the probabilistic analysis of the stationary modes in the singleitem and multi-item probabilistic models of optimal control were surveyed. Principles of construction of multidimensional recurrent schemes of calculation of complex probabilistic distributions by their generating functions were presented and illustrated by an example. Some of the results were published for the first time.

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. Adelson, R.M., Compound Poisson Distributions, Oper. Res. Quarterly, 1966, vol. 17, pp. 73–75.

    Article  Google Scholar 

  2. Archibald, B. and Silver, E., (s, S) Policies under Continuous Review and Discrete Compound Poisson Demand, Manag. Sci., 1978, vol. 24, pp. 899–909.

    Article  MATH  Google Scholar 

  3. Arrow, K.J., Karlin, S., and Scarf, H., Studies in the Mathematical Theory of Inventory and Production, Stanford: Stanford Univ. Press, 1958.

    MATH  Google Scholar 

  4. Dvoretzky, A., Kiefer, J., and Wolfovitz, J., On the Optimal Character of (s, S) Policy in Inventory Theory, Econometrica, 1953, vol. 21, pp. 586–596.

    Article  MATH  MathSciNet  Google Scholar 

  5. Federgruen, A., Groenevelt, H., and Tijms, H., Coordinated Replenishments in a Multi-item Inventory System with Compound Poisson Demands and Constant Lead Times, Manag. Sci., 1984, vol. 30, pp. 344–357.

    Article  MATH  Google Scholar 

  6. Friend, J.K., Stock Control with Random Opportunities for Replenishments, Oper. Res. Quart., 1960, vol. 11, no. 3, pp. 130–136.

    Article  Google Scholar 

  7. Johnson, E., Optimality and Computation of (δ, S) Policies in the Multi-item Infinite Horizon Inventory Problem, Manag. Sci., 1967, vol. 13, no. 7, pp. 475–491.

    Article  Google Scholar 

  8. Silver, E.A., Chung-Mei Ho, and Deemer, R.L., Cost-minimizing Inventory Control of Items Having a Special Type of Erratic Demand Pattern, INFOR, 1971, vol. 9, no. 3, pp. 198–219.

    Google Scholar 

  9. Hadley, G. and Whitin, T.M., Analysis of Inventory Systems, Englewood Cliffs: Prentice Hall, 1968. Translated under the title Analiz sistem upravleniya zapasami, Moscow: Nauka, 1969.

    Google Scholar 

  10. Rubal’skii, G.B., On the Stock Level at a Store with Lead Time, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1972, no. 1, pp. 63–68.

  11. Rubal’skii, G.B., Calculation of the Optimal Parameters in a Problem of Inventory Control, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1972, no. 2, pp. 8–12.

  12. Rubal’skii, G.B., Control of Multi-item Stock, Standarty i Kachestvo, 1972, no. 6, pp. 81–90.

  13. Rubal’skii, G.B., Policies of Optimal Control of the Multi-item Stock under Lead Times, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1972, no. 5, pp. 41–46.

  14. Rubal’skii, G.B., Inventory Control under Random Opportunities of Replenishment, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1974, no. 4, pp. 54–61.

  15. Rubal’skii, G.B., Upravlenie zapasami pri sluchainom sprose (modeli s nepreryvnym vremenem) (Inventory Control under Random Demand (Continuous-time Models)), Moscow: Sovetskoe Radio, 1977.

    Google Scholar 

  16. Rubal’skii, G.B., On Calculation of the Stationary Optimal Modes in the Inventory Control Models with Poisson Flow of Random-size Orders, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1984, no. 3, pp. 68–77.

  17. Rubal’skii, G.B., Simple Optimization Algorithm for the Inventory Control Models with Purely Random Opportunities of Replenishment, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1985, no. 4, pp. 75–80.

  18. Rubal’skii, G.B., Strategy of Multiple-size Deliveries in Inventory Control Models, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1986, no. 1, pp. 37–45.

  19. Rubal’skii, G.B., Inventory Control Model with Random Lead Time under Periodic Opportunities of Replenishment, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1986, no. 6, pp. 95–104.

Download references

Author information

Authors and Affiliations

  1. Russian State Social University, Moscow, Russia

    G. B. Rubal’skii

Authors
  1. G. B. Rubal’skii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © G.B. Rubal’skii, 2009, published in Avtomatika i Telemekhanika, 2009, No. 12, pp. 175–186.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rubal’skii, G.B. Stochastic theory of inventory control. Autom Remote Control 70, 2098–2108 (2009). https://doi.org/10.1134/S0005117909120169

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117909120169

Keywords

Search

Navigation