A state dependent M/M/1 queue: A production-inventory model
type: Item
instance of: scholarly article
title: A state dependent M/M/1 queue: A production-inventory model
zbMATH Open document ID: 0687.90042
DOI: 10.1016/0893-9659(88)90083-3
author: Zeev Schuss
author: Charles Tier
author: Charles Knessl
author: B. J. Matkowsky
published in: Applied Mathematics Letters
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with a model of production and inventory control. The model incorporates a continuous-level production rate with a base-stock level inventory policy subject to fluctuating demand. The inventory level at time t is denoted by Y(t) and the base stock level by M. The quantity of interest here is \(U(t)=M-Y(t)\). The authors compute the stationary density of U(t) including the facility utilization and the mean time for U(t) to reach or exceed a given value. They analyze the production busy period of the facility, they compute the mean length of a production period and the mean time for a production busy period to end, given the current value of U(t). Finally, they compute the integral of U(t) during a busy period, and the distribution of the minimum inventory level.
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90B05
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 4126984
zbMATH Keywords: continuous-level production rate
zbMATH Keywords: fluctuating demand
zbMATH Keywords: production busy period
zbMATH Keywords: mean length
reviewed by: Monique Bertrand
MaRDI profile type: Publication
full work available at URL: 0893-9659(88)90083-3
OpenAlex ID: W2075957724
cites work: Operating Characteristics of a Simple Production, Inventory-Control Model
cites work: Q3970132
cites work: Q5725179
cites work: Q3938929
cites work: Q4134686
cites work: Asymptotic Analysis of a State-Dependent $M/G/1$ Queueing System
description: scientific article; zbMATH DE number 4126984