IJPAM: Volume 32, No. 1 (2006)

A PERISHABLE INVENTORY SYSTEM WITH SERVICE
FACILITIES AND BATCH MARKOVIAN DEMANDS

B. Sivakumar$^1$, C. Elango$^2$, G. Arivarignan$^3$
$^{1,3}$Department of Applied Mathematics and Statistics
Madurai Kamaraj University
Madurai, 21, INDIA
$^1$e-mail: sivabkumar@yahoo.com
$^3$e-mail: arivarignan@yahoo.com
$^2$Department of Mathematical Sciences
Cardamom Planters' Association College
Bodinayakanur, INDIA
e-mail: cellaelango@yahoo.com


Abstract.This article considers a continuous review $(s,~S)$ inventory system at a service facility in which the waiting hall for customers is of fixed size. We assume batch arrivals of customers. The time points of arrivals of each batch is assumed to form a Poisson process and the number of customers in each batch is a random variable. Each customer undergoes a random time of service at the end of which he/she is issued their order. The service time follows a state-dependent negative exponential distribution. The items of inventory are perishable in nature with exponential life time. It is also assumed that lead time for the reorders is assumed to be distributed as exponential independent of the service time distribution. The joint probability distribution of the number of customers in the system and the inventory level is obtained in both transient and steady state cases. The measures of system performance in the steady state are derived. The results are illustrated with numerical examples.

Received: July 7, 2006

AMS Subject Classification: 90B05, 60J27

Key Words and Phrases: continuous review inventory system, perishable item, Markov process, service facilities, bulk arrival

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 1