Abstract: In the study, stochastic period inventory model analyzed with the back order ratio is fully depends on the length of protection interval, which is expressed as the sum of review period and lead-time. Also, back order discount and protection interval considered as decision variables, which control to wider applications for a periodic inventory model. Two parameters perfect information and partial information about the protection interval demand distributions have been discussed. We first assume that the protection interval demand follows a normal distribution and relax this assumption by considering the first and second moments of the probability distribution of protection interval demand are known.