Optimal replenishment scheduling for inventory items with Weibull distributed deterioration and time-varying demand

This paper proposes a dynamic programming model for solving replenishment scheduling problems. The model is developed based on the following assumptions: the inventory items are subject to deterioration of two-parameter Weibull distribution, the demand rate is exponentially distributed over time, shortages are allowed, 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 horizon so that the present worth of the total cost is minimized. The solution procedure is illustrated by two numerical examples. The strength of the proposed model is supported by carrying out a comparison study with an existing model. 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 fixed service levels. In addition, the Weibull deterioration used in the model is a generalized form of exponentially decaying functions, and hence it is applicable to the management of a wider range of deteriorating items in practice, like agricultural products, blood, drugs, fashion goods, high-tech and electronic components, volatile liquids, and radioactive substances.