Hostname: page-component-cb9f654ff-mwwwr Total loading time: 0 Render date: 2025-08-27T23:08:16.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Algorithms for a continuous-review (s, S) inventory system

Published online by Cambridge University Press:  14 July 2016

V. Ramaswami
V. Ramaswami*
Affiliation:
Drexel University
*
∗Postal address: Department of Mathematical Sciences, Drexel University, Philadelphia, PA 19104, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The steady-state distribution of the inventory position for a continuous-review (s, S) inventory system is derived in a computationally tractable form. Demands for items in inventory are assumed to form an N-process which is the ‘versatile Markovian point process' introduced by Neuts (1979). The N-process includes the phase-type renewal process, Markov-modulated Poisson process etc., as special cases and is especially useful in modelling a wide variety of qualitative phenomena such as peaked arrivals, interruptions, inhibition or stimulation of arrivals by certain events etc.

Keywords

COMPUTATIONAL PROBABILITYCONTINUOUS-REVIEW INVENTORYN-PROCESSPHASE-TYPE DISTRIBUTIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 461 - 472
Copyright
Copyright © Applied Probability Trust 

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.)

Article purchase

Temporarily unavailable

References

[1] Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123–187.Google Scholar
[2] Feldman, R. M. (1978) A continuous review (s, S) inventory system in a random environment. J. Appl. Prob. 15, 654–659.Google Scholar
[3] Hunter, J. J. (1969) On the moments of Markov renewal processes. Adv. Appl. Prob. 1, 188–210.Google Scholar
[4] Neuts, M. F. (1975) Probability distributions of phase type. In Liber Amicorum Professor Emeritus H. Florin, Department of Mathematics, University of Louvain, 173–206.Google Scholar
[5] Neuts, M. F. (1976) Renewal processes of phase type. Naval Res. Logist. Quart. 25, 445–453.Google Scholar
[6] Neuts, M. F. (1979) A versatile Markovian point process. J. Appl. Prob. 16, 764–779.Google Scholar
[7] Ramaswami, V. (1980) The N/G/1 queue and its detailed analysis. Adv. Appl. Prob. 12, 222–261.Google Scholar
[8] Ramaswami, V. (1978) The N/G/8 queue. Unpublished technical report.Google Scholar
[9] Richards, F. R. (1975) Comments on the distribution of inventory position in a continuous-review (s, S) inventory system. Operat. Res. 23, 366–371.Google Scholar
[10] Sivazlian, B. D. (1974) A continuous-review (s, S) inventory system with arbitrary interarrival distribution between unit demand. Operat. Res. 22, 65–71.Google Scholar
[11] Wachter, P. (1973) Solving Certain Systems of Homogeneous Equations with Special Reference to Markov Chains. , Department of Mathematics, McGill University.Google Scholar