On the distribution free continuous-review inventory model with a service level constraint

We consider a continuous-review (Q, r) inventory model with a fill rate service constraint and relax the assumption that the distribution of lead time demand is known. We adopt a distribution free approach: We assume that only the first two moments of the lead time demand distribution are known, and then, optimize the policy parameters against the worst possible distribution. We are able to derive closed-form expressions for the optimal order quantity and reorder point.