On a single item single stage mixture inventory models with independent stochastic lead times

Abstract

In this paper, the optimal (r, Q) replenishment policies are developed for stochastic mixture inventory models for both the without order crossover and the order crossover cases. The shortage costs are considered on a per stockout basis. Expressions of total cost are developed for both cases, and their convexities are proved. A normal approximation method is used to determine the distribution of the lead-time demand. The effect of the changing proportions of the mixture of backorders and lost sales (q) on various inventory performance measures, such as total inventory cost, service levels and turnover ratio, is studied. Further, a simulation study is performed to validate the order crossover model. The results obtained are compared with the factorial experiments, which are conducted for the expressions developed. Regression equations are developed for determining the optimal order quantity, inventory cost and safety stock factor. It is determined that there is a remarkable reduction in inventory cost by considering ordering crossover in inventory models. Finally, a sensitivity analysis is done to study the effect of the reorder point (r) on the total inventory cost. The results of a robustness study show that the order crossover model is robust and applicable to many real-world inventory problems.