NDLI: Stochastic decomposition in production inventory with service time (abstract only)

Content Provider	ACM Digital Library
Author	Krishnamoorthy, A. Narayanan, Viswanath C.
Abstract	We study an (s, S) inventory system with positive service time (for an overview of the work reported so far in inventory with positive service time one may refer to Krishnamoorthy, Lakshmi and Manikandan: A survey on inventory models with positive service time, OPSEARCH, DOI 10.1007/s12597-010-0032-z). This leads to a queue of demands being formed. The process of demand arrival constitutes a Poisson process. The duration of each service is exponentially distributed. Our model is a supply chain where items are added to the inventory through a production process. This starts each time the inventory level goes down to s and continues to be on until inventory level reaches S with the time required to add one unit of the item into the inventory when the production is on, are independent, identically distributed exponential random variables. Further all distributions involved in this paper are assumed to be mutually independent. We assume that no customer joins the queue when the inventory level is 0. This assumption leads us to an explicit product form solution for the steady state probability vector, using a simple approach. This is despite the fact that there is a strong correlation between lead time (the time required to add an item into the inventory) and the number of customers joining the queue during the lead time (except when the inventory level is zero during which time no customer joins the queue). The technique is to combine the steady state probability vector of the classical M/M/1 queue and that of the production inventory system where each service requires negligible time and no backlogs are allowed. Using a similar technique, the expected length of a production cycle is also obtained explicitly. The optimality of the highest inventory level S and the production switching on level s has been studied using a cost function constructed using the steady state system performance measures. Since we have obtained explicit expressions for these measures, analytic expressions have been derived for the optimal values of S and s. To show that our method can be applied to other similar problems, we analyze in detail a variant of the above problem (discussed in Schwarz M, Sauer. C, Daduna, H., Kulik, R and Szekli, R: M/M/1 Queueing systems with inventory, Queueing Systems, 54,55-78, 2006). For that model, we assume that in a production run, production occurs only once in a cycle and the amount produced is sufficient to take the inventory level back to S. A brief discussion on the application of our method to inventory system with lead time for replenishment has also been provided.
Starting Page	28
Ending Page	28
Page Count	1
File Format	PDF
ISSN	01635999
DOI	10.1145/2185395.2185415
Journal	ACM SIGMETRICS Performance Evaluation Review (PERV)
Volume Number	39
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Hardware and Architecture Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The impact of dampening demand variability in a production/inventory system with multiple retailers (abstract only)

The algorithmization of mathematics:the story of stochastic models (abstract only)

A fluid introduction to brownian motion & stochastic integration (abstract only)

Bilateral matrix-exponential distributions (abstract only)

Two-dimensional fluid queues with temporary assistance (abstract only)

Majorization and Extremal PH-Distributions (abstract only)

Moment distributions of phase-type (abstract only)

Product-form distributions and network algorithms (abstract only)

Synthesis of local-rule processes:successes and challenges (abstract only)

Stochastic decomposition in production inventory with service time (abstract only)

Similar Documents

The impact of dampening demand variability in a production/inventory system with multiple retailers (abstract only)

The algorithmization of mathematics:the story of stochastic models (abstract only)

A fluid introduction to brownian motion & stochastic integration (abstract only)

Bilateral matrix-exponential distributions (abstract only)

Two-dimensional fluid queues with temporary assistance (abstract only)

Majorization and Extremal PH-Distributions (abstract only)

Moment distributions of phase-type (abstract only)

Product-form distributions and network algorithms (abstract only)

Synthesis of local-rule processes:successes and challenges (abstract only)

Stochastic decomposition in production inventory with service time (abstract only)