Stochastic Inventory Model with Reworks

Abstract

In most of the inventory models, a single stock is considered from where items are served for the customers. In this paper, two stocks are considered. One is for fresh items and another is for returned items. The model is more appropriate where warranties are provided for a fixed time duration. Moreover, inventory which are kept to the stock may not have finite shelf-life is also considered here such as milk, meat, vegetables, radioactive materials, volatile liquids. In this current model, we considered the inventory is decayed in a constant rate θ. It is assumed that inventory level for both the fresh and returned items are pre-determined. When inventory level reaches at s, a replenishment takes place with parameter ϒ The demands that arrive for fresh items and returned items follow Poisson process with parameter λ & δ respectively. Service will be provided with Poisson process for returned items with parameter μ. The joint probability distribution for inventory level of returned items and for fresh items is obtained in the steady state analysis. Some systems characteristics of the model are derived and the results are illustrated with the help of numerical examples.

The Chittagong Univ. J. Sci. 40(1) : 59-74, 2018