Most classical mathematical inventory management models assume that the decision-maker has full knowledge about all cost groups (ordering, holding and shortage costs), demand is normally distributed and lead time is constant. However, in real situations it is not always true. The first and most often existing limitation is that shortage cost is not known (there are situations when it is very difficult, even impossible to be reliably estimated). In such case the inventory models with service level constraints are applied. The other limitation is that lead time is not always constant. There might be two situations – lead time can be a random or decision variable. In the latter case, lead time can be decreased by bearing some additional costs. Also, the demand distribution might not be normal (or even only some parameters, not the shape of the distribution may be known). The aim of the article is comparison of results obtained for the continuous review áQ, rñ inventory model for backorders case with Type I and Type II (with iterative procedure and procedure proposed by Chu et al. (2005)) service level constraints and lead time demand as a decision variable. Obtained results indicate that the lowest total inventory costs were obtained for Type II service level constraints with iterative procedure. However, simpler procedure, proposed by Chu et al. (2005) yielded results that were worse only by 2% at most.