The stochastic inventory model analyzed in this paper explore the problem that the lead time and ordering cost reductions are interdependent in the continuous review inventory model with backorder discount. The objective of this paper is to minimize the total related cost by simultaneously optimizing the order quantity, lead time and backorder price discount. Moreover, the lead time demand is assumed to be normally distributed. A procedure of finding the optimal solution is developed. Furthermore, the sensitivity analysis is included and two numerical examples are given to illustrate the results.
