Stochastic Inventory Models with Reworks

Abstract

In most of the inventory models, a single stock is considered where items are served for the customers.
In this paper, two stocks are considered for efficient stock management, One is for fresh items and another is for returned items.
Two models are considered here, first model is developed for non-perishable items where the second one is for perishable items.
The models are more appropriate where warranties are provided for a fixed time duration after sale for fresh items. Moreover,
inventories whose are kept in the stock may not have finite shelf-life that are also considered here in model-II such as milk, meat,
vegetables, radioactive materials, volatile liquids. In model-II, we have considered that the inventory decay in a constant rate
$\theta $. It is assumed that inventory level for both the fresh and returned items are pre-determined. When inventory level
reaches at re-order point s, a replenishment takes place with parameter $\gamma $. The demands that arrive for fresh items and
returned items follow Poisson process with parameter $\lambda $ $\&$ $\delta $ respectively. Service will be provided with
Poisson process for returned items with parameter $\mu$. The joint probability distribution for inventory level of returned
items and for fresh items are obtained in the steady state analysis. Some systems characteristics of two models are derived here
and the results are illustrated with the help of numerical examples.