Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 81508, 22 pages
On inventory system with random lead time and repeated
Department of Mathematics, Amrita Vishwa Vidyapeetham, Amritapuri, Kollam, Kerala 690 525, India
Received 20 June 2006; Revised 23 September 2006; Accepted 8 October 2006
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.
We consider an inventory system with random lead time and repeated demands of unsatisfied demands from the orbit. Whenever the inventory level falls to the level , an order is placed to bring the level to . The quantity ordered is . 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.