In this article, we study a continuous-review production-inventory model that assembles lost sales and backorders with service level constraint. The study under consideration assumes that the distribution of demand during the lead-time is known partially. The objective of this paper is twofold. Firstly, the distributionfree procedure is applied to obtain a closed-form solution of optimal production quantity, re-order level and lead-time in the random framework. Secondly, considering demand as a fuzzy random variable, the procedure isextended to the fuzzy random framework in which an algorithm is proposed to find the optimal global solution. Two numerical examples are provided to illustrate the methods. Furthermore, sensitivity analysis is performed to present some managerial inferences