In this paper a continuous inventory model is studied with a mixture of back orders and lost sales, in which both order quantity and reorder point, are decision variables, when demand per unit time is normally distributed and lead time follows Erlang distribution. The objectives of this study is to estimate the optimal order quantity (Q) and reorder point (r), when the annual expected cost is minimum. An algorithm is developed to estimate the optimum solutions. A real example based on primary data is cited to estimate the optimal order quantity and reorder point with a mixture of back orders and lost sales, when annual expected cost is at minimum. This study reveals that the reorder point decreases, when the fraction of demand backordered during stock out period increases to get the almost same amount of optimal order quantity for different values of the fraction of demand backordered.
