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

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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 Unpublished technical report.Google Scholar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