PROBABILISTIC (Q,r) INVENTORY MODEL WITH PARTIALLY BACKORDERS WHEN LEAD TIME DEMAND NORMALLY DISTRIBUTED UNDER HOLDING COST RESTRICTION

This paper derives the probabilistic continuous review inventory model that has the two types of shortage when the order cost is a function of the order quantity. The objective is to minimize the expected annual total cost under a constraint on the expected holding cost when the lead time demand follows Normal distribution by using the Lagrangian method. Some published special cases are deduced and a numerical application with illustrative graphs is added.