Deterioration of items is a phenomenon which cannot be neglected as it may provide absurd result. In high-tech business market, deterioration is not always constant but it is time dependent. This paper presents inventory model for time dependent deterioration and time dependent demand under shortages. The mathematical model is provided to optimize the cycle time by minimizing the total cost. Numerical results are discussed to validate the proposed model. The variation of the optimal solution for different parameters is discussed for some instances.

Traditional economic production quantity (EPQ) model assumes that the production products are perfect. However, this assumption does not hold for many real production systems due to several weaknesses. This paper considers production inventory model with defective items for deteriorating items. In this paper, production rate is considered to be greater than demand rate. Mathematical model is developed for finding optimal order quantity, cycle time and total profit. Moreover, a numerical example is provided to illustrate the proposed model. Next, sensitivity analysis is established to demonstrate the model developed. Finally, some conclusions and future research directions are proposed.