inventory model for deteriorating items with four level system and shortages

This paper presents an inventory model for deteriorating items in which shortages are allowed. it is assumed that the production rate is proportional to the demand rate and greater than demand rate. the inventory model is developed by considering four different circumstances. the optimal of the problem is obtained with the help of mathematica 7 software. numerical examples are given to illustrate the model for different parameters. sensitivity analysis of the model has been developed to examine the effect of changes in the values of the different parameters for optimal inventory policy. truncated taylor’s series is used for finding closed form optimal solution.