Managing the inventories is very important task for companies in the manufacturing industry. In this paper, we first present a mathematical model to determine an optimal production time for a single-stage production inventory problem with rework process. Next, we consider the production inventory problem in fuzzy environment by applying two types of fuzzy numbers, which are trapezoidal and triangular. Fuzzy total inventory cost functions are derived for both production inventory models with crisp production time period and fuzzy production time period, respectively, and defuzzified by using graded mean integration representation method. To illustrate the results of developed models, numerical examples are provided, and sensitivity analysis is carried out to discuss the effects of the fuzziness in the components over the production time and the total inventory cost.