Constrained Probabilistic Continuous Review Inventory System with Mixture Shortage and Stochastic Lead Time Demand

This paper derives the probabilistic continuous review backorders and lost sales inventory system when the order cost is a function of the order quantity. Our objective is to minimize the expected annual total cost under a restriction on the expected annual holding cost when the lead time demand follows some continuous distributions by using the Lagrangian method. Some published special cases are deduced and an illustrative numerical example with some graphs is added.