scispace - formally typeset
Journal ArticleDOI

ALGORITHMS FOR A CONTINUOUS-REVIEW (s, S) INVENTORY SYSTEM

V. Ramaswami
- 01 Jun 1981 - 
- Vol. 18, Iss: 02, pp 461-472
TLDR
In this article, the steady state distribution of the inventory position for a continuous review (s, S) inventory system is derived in a computationally tractable form, where demands for items in inventory are assumed to form an N-process which is the'versatile Markovian point process' introduced by Neuts (1979).
Abstract
The steady-state distribution of the inventory position for a continuousreview (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. COMPUTATIONAL PROBABILITY; CONTINUOUS-REVIEW INVENTORY; N-PROCESS; PHASE-TYPE DISTRIBUTIONS

read more

Citations
More filters
Book

Fundamentals of Matrix-Analytic Methods

Qi-Ming He
TL;DR: This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods, especially useful for engineering analysis and design.
Journal Article

Markovian arrivals in stochastic modelling: a survey and some new results

TL;DR: A comprehensive review on Markovian arrival processes (MAPs) can be found in this article, where the authors provide an overview of the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.
Journal ArticleDOI

Production-inventory systems in stochastic environment and stochastic lead times

TL;DR: This work considers a production-inventory system where the production and demand rates are modulated by a finite state Continuous Time Markov Chain, and derives the distribution of the inventory level, and analyzes the long run holding, backlogging, and ordering cost rate per unit time.
Journal ArticleDOI

The use of phase-type distributions in inventory-control models

TL;DR: This article investigates the use of phase-type distributions to model the demand process and the replenishment leadtimes in the standard reorder-point/order-quantity model of inventory control and finds that the marginal distribution of leadtime demand has a discrete phase- type distribution with the same number of phases.
References
More filters
Journal ArticleDOI

A versatile Markovian point process

TL;DR: In this article, a versatile class of point processes on the real line, which are closely related to finite-state Markov processes, is introduced, and the treatment of existing probability models can be generalized in a systematic manner to arrival processes of the type discussed in this paper.
Journal ArticleDOI

Markov renewal theory

TL;DR: In this paper, the authors consider a stochastic process X(t) (t ≧ 0) taking values in a countable state space, where a particle moves from state to state in such a way that the successive states visited form a Markov chain, and the particle stays in a given state a random amount of time depending on the state it is in as well as on the next state to be visited next.
Journal ArticleDOI

The n/g/1 queue and its detailed analysis

TL;DR: In this paper, a single-server queue whose input is the versatile Markovian point process was discussed, referred to as the N-process, and a unified treatment of many models which were discussed earlier by several authors and which turn out to be special cases.
Journal ArticleDOI

Renewal processes of phase type

TL;DR: In this article, a class of analytically and numerically tractable renewal processes, which generalize the Poisson process, are discussed, when used to describe interarrival or service times in queues.
Journal ArticleDOI

On the moments of markov renewal processes

TL;DR: In this article, the authors derived the asymptotic values of the first passage time distributions in the associated semi-Markov process, generalising the results of Kemeny and Snell [4] obtained for Markov chains.
Related Papers (5)