`ISRN Applied MathematicsVolume 2011, Article ID 657464, 16 pageshttp://dx.doi.org/10.5402/2011/657464`
Research Article

## A Deterministic Inventory Model of Deteriorating Items with Two Rates of Production, Shortages, and Variable Production Cycle

1Department of Mathematics, Maharaja Manindra Chandra College, Kolkata 700003, India
2Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711103, India

Received 9 March 2011; Accepted 19 April 2011

Academic Editors: S. Cho and D. Spinello

Copyright © 2011 Jhuma Bhowmick and G. P. Samanta. 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.

#### Abstract

A Continuous production control inventory model is developed for a deteriorating item having shortages and variable production cycle. It is assumed that the production rate is changed to another at a time when the inventory level reaches a prefixed level and continued until the inventory level reaches the level . The demand rate is assumed to be constant, and the production cycle T is taken as variable. The production is started again at a time when the shortage level reaches a prefixed quantity . For this model, the total cost per unit time as a function of , , S, and T is derived. The optimal decision rules for , , S, and T are computed. The sensitivity of the optimal solution towards changes in the values of different system parameters is also studied. Results are illustrated by numerical examples.