Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T20:33:49.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous production/inventory model with analogy to certain queueing and dam models

Published online by Cambridge University Press:  01 July 2016

David Perry  and
Benny Levikson
David Perry*
Affiliation:
Haifa University
Benny Levikson
Affiliation:
Haifa University
*
∗Currently visiting the Department of Management Science, University of Waterloo, Ontario, Canada N2L 3G1.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider two storage/production systems in which items are produced continuously over time with fixed rate. In the first system items have infinite lifetime, while in the second system the lifetime of the items are finite and fixed. The inventory level distributions and other important functionals associated with these storage systems are derived. This derivation is accomplished by an analogy existing between the storage systems and certain queueing systems and a finite dam model. Optimization problems connected with these systems are also considered.

Keywords

STORAGE/PRODUCTION MODELVIRTUAL WAITING TIMEELAPSED WAITING TIMEQUEUEING SYSTEM WITH IMPATIENT CUSTOMERSFINITE DAM
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 123 - 141
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Postal address for both authors: Dept. of Statistics, Haifa University, Mt. Carmel, Haifa 31999, Israel.

References

1. Cohen, J. W. (1982) The Single Server Queue, revised edn. North-Holland, Amsterdam.Google Scholar
2. Daley, D. J. (1964) Single server queueing systems with uniform limited queueing times, J. Austral. Math. Soc. 4, 489–505.CrossRefGoogle Scholar
3. De Kok, A. G., Tijms, H. C. and Van Der Duyn Schouten, F. A. (1984) Approximations for the single product production-inventory model with compound Poisson demand and service level constrains. Adv. Appl. Prob. 16, 378–401.Google Scholar
4. Heyman, D. P. and Sobel, M. J. (1982) Stochastic Models in Operations Research, Volume I, Stochastic Processes and Operating Characteristics. McGraw-Hill, New York.Google Scholar
5. Karlin, S. and Taylor, H. (1975). A First Course on Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar
6. Kaspi, H. and Perry, D. (1983) Inventory systems of perishable commodities. Adv. Appl. Prob. 15, 674–685.Google Scholar
7. Kaspi, H. and Perry, D. (1984) Inventory systems for perishable commodities with renewal input and Poisson output. Adv. Appl. Prob. 16, 402–421.Google Scholar
8. Nahmias, S. (1982) Perishable inventory theory: A review. Operat. Res. 30, 680–708.CrossRefGoogle ScholarPubMed
9. Prabhu, N. U. (1980) Stochastic Storage Process. Springer-Verlag, New York.Google Scholar
10. Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
11. Tijms, H. C. (1986) Stochastic Modelling and Analysis; A Computational Approach. Wiley, Chichester.Google Scholar