Lead time and ordering cost reductions in continuous review inventory systems with partial backorders

This paper investigates the impact of ordering cost reduction on the modified continuous review inventory systems involving variable lead time with a mixture of backorders and lost sales. The objective is to simultaneously optimise the order quantity, ordering cost, reorder point and lead time. We first assume the lead time demand follows a normal distribution, then relax this assumption to consider the distribution free case where only the mean and variance of lead time demands are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.