In this study, we consider a periodic review inventory model involving
variable lead time with partial backorders. The objective is simultaneously
to optimize the length of review period, the backorder rate, and the lead
time in order to minimize the total expected annual cost. We first assume
that the protection interval (i.e., review period plus lead time) demand
follows a normal distribution, and then relaxes this assumption to consider
the distribution free case where only the mean and the standard deviation of
the protection interval demand are known. Two algorithm procedures of
finding the optimal solution are developed. Also two numerical examples
are given to illustrate the results.