On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> inventory system with random lead time and repeated
demands

Ushakumari, P. V.

doi:https://doi.org/10.1155/JAMSA/2006/81508

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 081508 | https://doi.org/10.1155/JAMSA/2006/81508

On (s,S) inventory system with random lead time and repeated demands

P. V. Ushakumari¹

Received20 Jun 2006

Revised23 Sept 2006

Accepted08 Oct 2006

Published04 Jan 2007

Abstract

We consider an (s,S) inventory system with random lead time and repeated demands of unsatisfied demands from the orbit. Whenever the inventory level falls to the level s, an order is placed to bring the level to S. The quantity ordered is M=S−s. Demands to the system are served immediately if there is a positive inventory. Otherwise it will go to a pool of unsatisfied customers called orbit. After a random amount of time, that demand is retried for service. We assume a Markovian setup for the time between consecutive arrivals, replenishments, and retrials. We obtained the condition for ergodicity of the system, steady state system size probabilities, expected length of the busy period of the system, expected inventory level, expected number of customers waiting in the orbit, expected waiting times, and so forth. A control problem is studied and some numerical illusrtations are provided.

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Copyright

Copyright © 2006 P. V. Ushakumari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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