A production inventory model for deteriorating items with growth of demand and shortages

In all inventory models, a general assumption is that products generated have indefinitely long lives. In general, almost all items deteriorate over time. In EPQ model, the demand rate is constant and it does not change over the period. But in real life, the demand rate is fluctuating over the period. At the end of the particular period, the demand rate will get changed. So, the rate of growth of demand is introduced in this paper. The rate of growth in the production period is D(1 + i)ⁿ and in the consumption period is D(1 + i)ⁿ. This research considers inventory systems for production inventory models where the objective is to find the optimal cycle time, which minimise the total cost and optimal amount of shortage if it is allowed. The relevant model is built, solved and closed formulas are obtained. Necessary and sufficient conditions are derived. An illustrative example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.