An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting

This paper proposes a generalized dynamic programming model for inventory items with Weibull distributed deterioration. In this model, the demand rate is assumed to be time-proportional, shortages are allowed and completely backordered, and the effects of inflation and time-value of money are taken into consideration. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of total cost associated with the inventory system is minimized. The proposed model permits variation in both the replenishment intervals and the service levels between order cycles. As a result, it generates a better solution than other optimization models having fixed order intervals and/or fixed service levels. The solution procedure is illustrated by two numerical examples, and comparison with an existing model is carried out.