Control model of optimal storage for products with random replenishment intervals and time-varying deterioration rate

In inventory management, many types of products with volatility or corrosiveness, such as coal, may decay in quality as time goes. However, these characteristics often have a significant impact on inventory strategies. So this paper aimed to give an inventory optimization solution to minimize the total cyclic costs for these products. In the following mathematical model, we assume (i) deterioration rate varies linearly with time; (ii) demand is a constant; (iii) the lack of the stock is not allowed. Also the supplier takes replenishing interval as a continuous random variable in a cyclical replenishment. Results show that the optimal storage level depends on the probability distribution of the replenishment interval and the lower level needs high costs; and provides a theoretical foundation for retailers in controlling actual replenishment.