Continuous review inventory model with a service level constraint and defective items

This study investigates and analyzes that an arrival order lot may contain some defective items, and the defective item rate is a random variable. It also considers a continuous review inventory model with a mixture of backorders and lost sales, where the order quantity and reorder point are viewed as decision variables. Instead of having a stockout term in the objective function, a service level constraint is added to the model. The purpose of this study is to develop an algorithm to find the optimal policy when the distribution of lead time demand follows a normal distribution, then try to determine the optimal ordering policy.