Uncertainties in the stock control system development is one of the main concerns of researchers, several studies has been done in this research field with different fuzzy numbers by using different defuzzification methods. In this present article, at first, we have studied the scenario of increasing demand rate with the time and shortage are fully backlogged. Due to some reasons, there is flexible(uncertain) demand rate for the production, so the demand rate has to be taken as octagonal fuzzy number and the model converted into fuzzy model. The purpose of presented model is to optimize the total inventory cost in both the crisp and the fuzzy situations. The designated model included with Signed distance method for an appropriate numerical example, sensitivity analysis and graphical illustration for better explanation of the article.