A note on the distribution free procedure for some inventory models

We study the paper of Moon and Guillermo on the distribution free procedure for some inventory models to improve the solution procedure. The purpose of this note is threefold. First, we find the criterion to ensure the existence of the nontrivial optimal order quantity. Second, from the viewpoint of practice, we observe that the criterion will hold in the real-life situation. Third, we analytically prove the optimal order quantity is the unique root for a polynomial in some restricted domain.